go math 4th grade chapter 6 homework answers

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Go math grade 4 chapter 6 test

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Go Math Grade 4 Chapter 4 Answer Key Pdf Divide by 1-Digit Numbers

Go Math Grade 4 Chapter 4 Answer Key Pdf: Quick and easy learning is possible with our Go Math Answer Key. We have provided the solutions for all the questions with a brief explanation. The solutions are prepared by the Math Experts. So, we suggest the students and parents to Download Go Math Grade 4 Answer Key Chapter 4 Divide by 1-Digit Numbers pdf.

Divide by 1-Digit Numbers Go Math Grade 4 Chapter 4 Answer Key Pdf

Get the step by step explanations for all the questions. This Go Math Answer Key helps a lot while doing the homework and also while preparing for the exams. All you have to do is to click on the below link and solve the questions. In addition to the exercise and homework problems, we have also provided the answers for the mid-chapter checkpoint and review test.

Chapter 4 Divide by 1-Digit Numbers – Lesson: 1

Common Core – Page No. 201

• Common Core – Lesson Check – Page No. 202

Chapter 4 Divide by 1-Digit Numbers – Lesson: 2

Page No. 205

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Chapter 4 Divide by 1-Digit Numbers – Lesson: 3

Common Core – Page No. 207

• Common Core -Lesson Check – Page No. 208

Chapter 4 Divide by 1-Digit Numbers – Lesson: 4

Common Core – Page No. 211

Page no. 212.

Chapter 4 Divide by 1-Digit Numbers – Lesson: 5

• Interpret the Remainder – Common Core – Page No. 213
• Common Core – Lesson Check – Page No. 214

Chapter 4 Divide by 1-Digit Numbers – Lesson: 6

Page No. 216

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Chapter 4 Divide by 1-Digit Numbers – Lesson: 7

Page No. 218

• Divide Tens, Hundreds, and Thousands – Common Core – Page No. 219
• Common Core – Lesson Check – Page No. 220

Chapter 4 Divide by 1-Digit Numbers – Lesson: 8

Page No. 222

Page no. 223, page no. 224.

Chapter 4 Divide by 1-Digit Numbers – Lesson: 9

• Estimate Quotients Using Compatible Numbers – Common Core – Page No. 224
• Common Core – Lesson Check – Page No. 226

Chapter 4 Divide by 1-Digit Numbers – Lesson: 10

• Model the division on the grid – Page No. 229

Page No. 230

Chapter 4 Divide by 1-Digit Numbers – Lesson: 11

• Division and the Distributive Property – Common Core – Page No. 231
• Common Core – Lesson Check – Page No. 232

Mid Chapter Checkpoint

• Mid Chapter Checkpoint – Page No. 233
• Mid Chapter Checkpoint – Page No. 234

Chapter 4 Divide by 1-Digit Numbers – Lesson: 12

• Use repeated subtraction to divide – Page No. 237
• Use repeated subtraction to divide – Page No. 238

Chapter 4 Divide by 1-Digit Numbers – Lesson: 13

• Divide Using Repeated Subtraction – Common Core – Page No. 239
• Common Core – Lesson Check – Page No. 240

Chapter 4 Divide by 1-Digit Numbers – Lesson: 14

Page No. 243

Page no. 244.

Chapter 4 Divide by 1-Digit Numbers – Lesson: 15

• Divide Using Partial Quotients – Common Core – Page No. 245
• Common Core – Lesson Check – Page No. 246

Chapter 4 Divide by 1-Digit Numbers – Lesson: 16

Page No. 249

Page no. 250.

Chapter 4 Divide by 1-Digit Numbers – Lesson: 17

• Model Division with Regrouping – Common Core – Page No. 251
• Common Core – Lesson Check – Page No. 252

Chapter 4 Divide by 1-Digit Numbers – Lesson: 18

Page No. 255

Page no. 256.

Chapter 4 Divide by 1-Digit Numbers – Lesson: 19

• Place the First Digit – Common Core – Page No. 257
• Common Core – Lesson Check – Page No. 258

Chapter 4 Divide by 1-Digit Numbers – Lesson: 20

Page No. 261

Page no. 262.

Chapter 4 Divide by 1-Digit Numbers – Lesson: 21

• Divide by 1-Digit Numbers – Common Core – Page No. 263
• Common Core – Lesson Check – Page No. 264

Chapter 4 Divide by 1-Digit Numbers – Lesson: 22

Page No. 267

Page no. 268.

Chapter 4 Divide by 1-Digit Numbers – Lesson: 23

• Problem Solving Multistep Division Problems – Common Core – Page No. 269
• Common Core – Lesson Check – Page No. 270

Chapter 4 – Review/Test

• Review/Test – Page No. 271
• Review/Test – Page No. 272
• Review/Test – Page No. 273
• Review/Test – Page No. 274
• Review/Test – Page No. 275
• Review/Test – Page No. 276
• Review/Test – Page No. 280
• Review/Test – Page No. 281
• Review/Test – Page No. 282

Estimate Quotients Using Multiples

Find two numbers the quotient is between. Then estimate the quotient.

Question 1. 175 ÷ 6 Think: 6 × 20 = 120 and 6 × 30 = 180. So, 175 ÷ 6 is between 20 and 30. Since 175 is closer to 180 than to 120, the quotient is about 30. between 20 and 30 about 30

Answer: About 30

Explanation: 6 × 20 = 120 and 6 × 30 = 180. 175 is between 120 and 180. 175 ÷ 6 is closest to 20 and 30. So, 175 ÷ 6 is between 20 and 30. So, 175 ÷ 6 will be about 30.

Question 2. 53 ÷ 3 between ______ and about ______

Answer: About 18

Explanation: 17 × 3= 51 and 18 × 3 = 54. 53 is between 51 and 54. 53 ÷ 3 is closest to 17 and 18. So, 53 ÷ 3 is between 17 and 18. So, 53 ÷ 3 will be about 18.

Go Math Grade 4 Lesson 4 Homework Answer Key Question 3. 75 ÷ 4 between ______ and about ______

Answer: About 19

Explanation: 18 × 4= 72 and 19 × 4= 76. 75 is between 72 and 76. 75 ÷ 4 is closest to 18 and 19. So, 75÷ 4 is between 18 and 19. So, 75 ÷ 4 will be about 19.

Question 4. 215 ÷ 9 between ______ and about ______

Answer: About 24

Explanation: 23 × 9= 207 and 24 × 9 = 216. 24 is between 207 and 216. 215 ÷ 9 is closest to 23 and 24. So, 215 ÷ 9 is between 23 and 24. So, 215 ÷ 9 will be about 24.

Question 5. 284 ÷ 5 between ______ and about ______

Answer: About 57

Explanation: 56 × 5 = 280 and 57 × 5 = 285. 284 is between 280 and 285. 284 ÷ 5 is closest to 56 and 57. So, 284 ÷ 5 is between 56 and 57. So, 175 ÷ 6 will be about 57.

Question 6. 191 ÷ 3 between ______ and about ______

Answer: About 64

Explanation: 63 × 3 = 189 and 64 × 3 = 192. 191 is between 189 and 192. 191 ÷ 3 is closest to 63 and 64. So, 191 ÷ 3 is between 63 and 64. So, 175 ÷ 6 will be about 64.

Question 7. 100 ÷ 7 between ______ and about ______

Answer: About 14

Explanation: 14 × 7 = 98 and 15 × 7 = 105. 100 is between 98 and 105. 100 ÷ 7 is closest to 14 and 15. So, 100 ÷ 7 is between 14 and 15. So, 100 ÷ 7 will be about 14.

Question 8. 438 ÷ 7 between ______ and about ______

Answer: About 63

Explanation: 63 × 7 = 441 and 62 × 7 = 434. 438 is between 434 and 441. 438 ÷ 7 is closest to 62 and 63. So, 438 ÷ 7 is between 62 and 63. So, 438 ÷ 7 will be about 63.

Question 9. 103 ÷ 8 between ______ and about ______

Answer: About 13

Explanation: 13 × 8 = 104 and 12 ×8 = 96. 103 is between 96 and 104. 103 ÷ 8 is closest to 12 and 13. So, 103 ÷ 8 is between 12 and 13. So, 103 ÷ 8 will be about 13.

Question 10. 255 ÷ 9 between ______ and about ______

Answer: About 28

Explanation: 28 × 9 = 252 and 29 × 9 = 261. 255 is between 252 and 261. 255 ÷ 9 is closest to 28 and 29. So, 255 ÷ 9 is between 28 and 29. So, 255 ÷ 9 will be about 28.

Problem Solving

Question 11. Joy collected 287 aluminum cans in 6 hours. About how many cans did she collect per hour? about ______ cans

Answer: About 48 cans

Explanation: 47 × 6 = 282 and 48 × 6 = 288. 287 is between 282 and 288. 287 ÷ 6 is closest to 47 and 48. So, 287 ÷ 6 is between 47 and 48. So, 287 ÷6 will be about 48.

Go Math Grade 4 Chapter 4 Pdf Question 12. Paul sold 162 cups of lemonade in 5 hours. About how many cups of lemonade did he sell each hour? about ______ cups

Answer: He about 32 cups of lemonade he sold in each hour

Explanation: 32 × 5 = 160 and 33 × 5 = 165. 162 is between 160 and 165. 162 ÷ 5 is closest to 32 and 33. So, 162 ÷ 5 is between 32 and 33. So, 162 ÷ 5 will be about 32.

Common Core – Page No. 202

Lesson Check

Question 1. Abby did 121 sit-ups in 8 minutes. Which is the best estimate of the number of sit-ups she did in 1 minute? Options: a. about 12 b. about 15 c. about 16 d. about 20

Answer: b. About 15

Explanation: 15 × 8 = 120 and 16 × 8 = 128. 121 is between 120 and 128. 121 ÷ 8 is closest to 120 and 128. So, 121 ÷ 8 is between 15 and 16. So, 121 ÷ 8 will be about 15.

Question 2. The Garibaldi family drove 400 miles in 7 hours. Which is the best estimate of the number of miles they drove in 1 hour? Options: a. about 40 miles b. about 57 miles c. about 60 miles d. about 70 miles

Answer: b. About 57 miles

Explanation: 57 × 7 = 399 and 58 × 7 = 406. 400 is between 399 and 406. 400 ÷ 7 is closest to 57 and 58. So, 400 ÷ 7 is between 57 and 58. So, 400 ÷ 7 will be about 57.

Spiral Review

Question 3. Twelve boys collected 16 aluminium cans each. Fifteen girls collected 14 aluminium cans each. How many more cans did the girls collect than the boys? Options: a. 8 b. 12 c. 14 d. 18

Explanation: Number of aluminium cans boys had= 12× 16=192 Number of aluminium cans girls had = 15× 14=210 Girls collected more cans compared to boys, Number of more cans collected by girls= 210-192=18

Question 4. George bought 30 packs of football cards. There were 14 cards in each pack. How many cards did George buy? Options: a. 170 b. 320 c. 420 d. 520

Answer: c. 420

Explanation: Number of packs of football cards= 30 Number of cards in each pack= 14 Total number of cards George bought=30×14=420

Question 5. Sarah made a necklace using 5 times as many blue beads as white beads. She used a total of 30 beads. How many blue beads did Sarah use? Options: a. 5 b. 6 c. 24 d. 25

Answer: d. 25

Explanation: Let the number of white beads be x while the number of blue beads are 5x. Total number of beads in the necklace=30 beads According to the problem, 5x+x=30 6x=30 x=30/6=5 Therefore the number of blue beads in the necklace are 5x= 5×5=25

Question 6. This year, Ms. Webster flew 145,000 miles on business. Last year, she flew 83,125 miles on business. How many more miles did Ms. Webster fly on business this year? Options: a. 61,125 miles b. 61,875 miles c. 61,985 miles d. 62,125 miles

Answer: b. 61,875 miles

Explanation: Number of miles Ms Webster flew in this year= 145,000 miles Number of miles Ms Webster flew in the last year=83,125 miles Number of more miles travelled by Ms Webster =145,000-83,125=61,875

Use counters to find the quotient and remainder.

Question 1. 10 ÷ 3 _____ R ______

Answer: Quotient: 3 Remainder: 1

Explanation: Quotient: A. Use 10 counters to represent the 10 dominoes. Then draw 3 circles to represent the divisor. B. Share the counters equally among the 3 groups by placing them in the circles. C. Number of groups of counters formed = quotient of 10 ÷ 3 D. Number of circles equally filled are 3, therefore, the quotient is 3

Remainder: The number of counters left over is the remainder. The number of counters leftover= 1

For 10 ÷ 3, the quotient is 3 and the remainder is 1, or 3 r1.

Question 2. 28 ÷ 5 _____ R ______

Answer: Quotient: 5 Remainder: 3

Explanation:

Quotient: A. Use 28 counters to represent the 28 dominoes. Then draw 5 circles to represent the divisor. B. Share the counters equally among the 5 groups by placing them in the circles. C. Number of groups of  counters formed = quotient of  28÷ 5

Remainder: The number of counters left over is the remainder. The number of counters leftover= 3

For 28 ÷ 5, the quotient is 5 and the remainder is 3, or 5 r3.

Question 3. 15 ÷ 6 _____ R ______

Answer: Quotient:2 Remainder:3

Quotient: A. Use 15 counters to represent the 15 dominoes. Then draw 6 circles to represent the divisor. B. Share the counters equally among the 6 groups by placing them in the circles. C. Number of circles filled= quotient of 28 ÷ 6

For 28 ÷ 6, the quotient is 2 and the remainder is 3, or 2 r3.

Question 4. 11 ÷ 3 _____ R ______

Answer:Quotient:3 Remainder:2

Quotient: A. Use 11 counters to represent the 3 dominoes. Then draw 3 circles to represent the divisor. B. Share the counters equally among the 3 groups by placing them in the circles. C. Number of  circles filled = quotient of 11 ÷ 3

Remainder: The number of counters left over is the remainder. The number of counters leftover= 2

For 11 ÷ 3, the quotient is 3 and the remainder is 2, or 3 r2.

Question 5. 29 ÷ 4 _____ R ______

Answer: Quotient:7  Remainder:1

Quotient: A. Use 29 counters to represent the 29 dominoes. Then draw 4 circles to represent the divisor. B. Share the counters equally among the 4 groups by placing them in the circles. C. Number of circles filled = quotient of 29 ÷ 4

For 29 ÷ 3, the quotient is 7 and the remainder is 1, or 7 r1.

Lesson 4 Problem Set 4.2 Answer Key Question 6. 34 ÷ 5 _____ R ______

Answer:Quotient: 6 Remainder: 4

Quotient: A. Use 34 counters to represent the 34 dominoes. Then draw 5 circles to represent the divisor. B. Share the counters equally among the 5 groups by placing them in the circles. C. Number of circles filled = quotient of 34 ÷ 5

Remainder: The number of counters left over is the remainder. The number of counters leftover= 4

For 34 ÷ 5, the quotient is 6 and the remainder is 4, or 6 r4.

Question 7. 25 ÷ 3 _____ R ______

Answer:Quotient: 8 Remainder: 1

Quotient: A. Use 25  counters to represent the 25 dominoes. Then draw 3 circles to represent the divisor. B. Share the counters equally among the 3 groups by placing them in the circles. C. Number of circles filled= quotient of  25 ÷ 3

For 25 ÷ 3, the quotient is 8 and the remainder is 1, or 8 r1.

Question 8. 7)\(\overline { 20 } \) _____ R ______

Answer: Quotient:2 Remainder:6

Quotient: A. Use 20 counters to represent the 20 dominoes. Then draw 7 circles to represent the divisor. B. Share the counters equally among the 7 groups by placing them in the circles. C. Number of circles filled= quotient of 7 qw20

Divide. Draw a quick picture to help.

Question 9. 4)\(\overline { 35 } \) _____ R ______

Quotient: A. Use 35 counters to represent the 35 dominoes. Then draw 4 circles to represent the divisor. B. Share the counters equally among the 4 groups by placing them in the circles. C. Number of circles filled= quotient of \(\overline { 35 } \)=8

Question 10. 23 ÷ 8 _____ R ______

Quotient: A. Use 23 counters to represent the 23 dominoes. Then draw 8 circles to represent the divisor. B. Share the counters equally among the 8 groups by placing them in the circles. C. Number of circles filled= quotient of 23 ÷ 8 = 2

Remainder: The number of counters left over is the remainder. The number of counters leftover= 7

Question 11. Explain how you use a quick picture to find the quotient and remainder. Type below: _________

Answer: Quick pictures can be used to find the quotient and the remainder visually and accurately.

Explanation: Example: 39÷ 5. Use 39 counters. Share the counters equally among 5 groups. The number of counters left over is the remainder. For 39 ÷ 5, the quotient is 7 and the remainder is 2, or 7 r2. When a number cannot be divided evenly, the amount left over is called the remainder.

Question 12. Alyson has 46 beads to make bracelets. Each bracelet has 5 beads. How many more beads does Alyson need so that all the beads she has are used? Explain. _____ more beads

Answer: 4 beads

Question 13. For 13a–13d, choose Yes or No to tell whether the division expression has a remainder. a. 36 ÷ 9 i. yes ii. no

Answer: ii. no

Question 13. b. 23 ÷ 3 i. yes ii. no

Answer: i. yes

Question 13. c. 82 ÷ 9 i. yes ii. no

Question 13. d. 28 ÷ 7 i. yes ii. no

Quotient: A. Use 13 counters to represent the 13 dominoes. Then draw 4 circles to represent the divisor. B. Share the counters equally among the 4 groups by placing them in the circles. C. Number of circles filled= quotient of 13 ÷ 4 = 3

Remainder: The number of counters left over is the remainder. The number of counters leftover= 1 Therefore each girl will get 3 marbles.

Question 1. 13 ÷ 4 3 r1

Answer: 3 r1

Quotient: A. Use 13 counters to represent the 13 dominoes. Then draw 4 circles to represent the divisor. B. Share the counters equally among the 4 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 13 ÷ 4 D. Number of circles are equally filled with 4 counters, therefore, the quotient is 3

For 13 ÷ 4, the quotient is 3 and the remainder is 1, or 3 r1.

Go Math 4th Grade Lesson 4.3 Answer Key Question 2. 24 ÷ 7 _____ R ______

Answer: 3 r3

Quotient: A. Use 24 counters to represent the 24 dominoes. Then draw 7 circles to represent the divisor. B. Share the counters equally among the 7 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 24 ÷ 7 D. Number of circles are equally filled with 3 counters, therefore, the quotient is 3

For 24 ÷ 7, the quotient is 3 and the remainder is 3, or 3 r3.

Question 3. 39 ÷ 5 _____ R ______

Answer: 7 r4

Quotient: A. Use 39 counters to represent the 39dominoes. Then draw 5 circles to represent the divisor. B. Share the counters equally among the 5 groups by placing them in the circles. C. Number of counters formed in each group = quotient 39 ÷ 5 D. Number of circles are equally filled with 7 counters, therefore, the quotient is 7

For 39 ÷ 5, the quotient is 7 and the remainder is 4, or 7 r4.

Question 4. 36 ÷ 8 _____ R ______

Answer: 4 r4

Quotient: A. Use 36 counters to represent the 36 dominoes. Then draw 8 circles to represent the divisor. B. Share the counters equally among the 8 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 36 ÷ 8 D. Number of circles are equally filled with 4 counters, therefore, the quotient is 4

For 36 ÷ 8, the quotient is 4 and the remainder is 4, or 4 r4.

Question 5. 6)\(\overline { 27 } \) _____ R ______

Answer: 4 r3

Quotient: A. Use 27 counters to represent the 27 dominoes. Then draw 6 circles to represent the divisor. B. Share the counters equally among the 6 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 27 ÷6 D. Number of circles are equally filled with 4 counters, therefore, the quotient is 4

For 27 ÷ 6, the quotient is 4 and the remainder is 3, or 4 r3.

Question 6. 25 ÷ 9 _____ R ______

Answer: 2 r7

Quotient: A. Use 25 counters to represent the 25 dominoes. Then draw 9 circles to represent the divisor. B. Share the counters equally among the 9 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 25 ÷ 9 D. Number of circles are equally filled with 2 counters, therefore, the quotient is 2

For 25 ÷ 7, the quotient is 2 and the remainder is 7, or 2 r7.

Question 7. 3)\(\overline { 17 } \) _____ R ______

Answer: 5 r2

Quotient: A. Use 17 counters to represent the 17 dominoes. Then draw 3 circles to represent the divisor. B. Share the counters equally among the 3 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 17 ÷ 3 D. Number of circles are equally filled with 5 counters, therefore, the quotient is 5

For 17 ÷ 3, the quotient is 5 and the remainder is 2, or 5 r2.

Question 8. 26 ÷ 4 _____ R ______

Answer: 6 r2

Quotient: A. Use 26 counters to represent the 26 dominoes. Then draw 4 circles to represent the divisor. B. Share the counters equally among the 4 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 26 ÷ 4 D. Number of circles are equally filled with 6 counters, therefore, the quotient is 6

For 26 ÷ 4, the quotient is 6 and the remainder is 2, or 6 r2.

Question 9. 14 ÷ 3 _____ R ______

Quotient: A. Use 14 counters to represent the 14 dominoes. Then draw 3 circles to represent the divisor. B. Share the counters equally among the 3 groups by placing them in the circles. C. Number of circles filled= quotient of 14 ÷ 3 = 4

Question 10. 5)\(\overline { 29 } \) _____ R ______

Quotient: A. Use 29 counters to represent the 29 dominoes. Then draw 5 circles to represent the divisor. B. Share the counters equally among the 5 groups by placing them in the circles. C. Number of circles filled= quotient of 29 ÷ 5 = 5

Answer: quotient:6  remainder2

Quotient: A. Use 20 counters to represent the 20 dominoes. Then draw 3 circles to represent the divisor. B. Share the counters equally among the 3  groups by placing them in the circles. C. Number of counters formed in each group = quotient of 20 ÷ 3 D. Number of circles are equally filled with 6 counters, therefore, the quotient is 6

For 20 ÷ 3, the quotient is 6 and the remainder is 2, or 6 r2.

Answer: 4 r5

Quotient: A. Use 21 counters to represent the 21 dominoes. Then draw 4 circles to represent the divisor. B. Share the counters equally among the 4 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 21 ÷ 4 D. Number of circles are equally filled with 4 counters, therefore, the quotient is 4

Remainder: The number of counters left over is the remainder. The number of counters leftover= 5

For 21 ÷ 4, the quotient is 4 and the remainder is 5, or 4 r5.

Common Core – Page No. 208

Question 1. What is the quotient and remainder for 32 ÷ 6? Options: a. 4 r3 b. 5 r1 c. 5 r2 d. 6 r1

Answer: c. 5 r2

Quotient: A. Use 32 counters to represent the 32 dominoes. Then draw 6 circles to represent the divisor. B. Share the counters equally among the 5 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 32 ÷ 6 D. Number of circles are equally filled with 5 counters, therefore, the quotient is 5

For 32 ÷ 6, the quotient is 5 and the remainder is 2, or 5 r2.

Answer: c. 3

Explanation: When a number cannot be divided evenly, the amount left over is called the remainder. The number of counters that are left  = remainder = 3

Question 3. Each kit to build a castle contains 235 parts. How many parts are in 4 of the kits? Options: a. 1,020 b. 940 c. 920 d. 840

Answer: b. 940

Question 4. In 2010, the population of Alaska was about 710,200. What is this number written in word form? Options: a. seven hundred ten thousand, two b. seven hundred twelve thousand c. seventy-one thousand, two d. seven hundred ten thousand, two hundred

Answer: d. seven hundred ten thousand, two hundred

Explanation: The ones and tens place of the number are zeroes, so the next place which is hundreds is considered and the value is 7 so, it can be written as seven hundred and in the thousands period it can be written as seven hundred ten thousand.

Question 5. At the theater, one section of seats has 8 rows with 12 seats in each row. In the center of the first 3 rows are 4 broken seats that cannot be used. How many seats can be used in the section? Options: a. 84 b. 88 c. 92 d. 96

Answer: c. 92

Explanation: Number of rows at the theatre = 8 Number of seats each row= 12 Number of seats broken and that cannot be used to sit= 4 Total number of seats that can be used = 12 x 8-4=96-4=92

Answer: d. 300, 180, 40, 24

Question 1. Olivia baked 53 mini-loaves of banana bread to be sliced for snacks at a craft fair. She will place an equal number of loaves in 6 different locations. How many loaves will be at each location? a. Divide to find the quotient and remainder. □ r □ 6)\(\overline { 53 } \) _____ R ______

Answer: Quotient: 8 Remainder: 5

Quotient: A. Use 53 counters to represent the 53 dominoes. Then draw 6 circles to represent the divisor. B. Share the counters equally among the 6  groups by placing them in the circles. C. Number of counters formed in each group = quotient of 53 ÷ 6 D. Number of circles are equally filled with 8 counters, therefore, the quotient is 8

Question 1. b. Decide how to use the quotient and remainder to answer the question. Type below: ____________

Remainder: The number of counters left over is the remainder. The number of counters leftover= 5 Therefore, there will be 8 mini loaves at each location.

Interpret the remainder to solve.

Question 2. What if Olivia wants to put only whole loaves at each location? How many loaves will be at each location? _______ whole loaves

Answer: Since there are 8 mini loaves at each location. Then there will be 4 whole loaves.

Explanation: Olivia baked 53 mini-loaves of banana bread

Go Math Grade 4 Lesson 4.4 Answer Key Question 3. Ed carved 22 small wooden animals to sell at the craft fair. He displays them in rows with 4 animals in a row. How many animals will not be in equal rows? _______ animals

Explanation: Total number of small wooden animals=22 Number of animals in each row=4 Number of rows= 22÷4 =5 The total number of animals in the rows= 5 x 4=20 Number of animals which are not in a row= 22-20=2

Question 4. Myra has a 17-foot roll of crepe paper to make 8 streamers to decorate for a party. How long will each streamer be if she cuts the roll into equal pieces? Type below: ____________

Answer: 2 foot

Question 5. Juan has a piano recital next month. Last week he practiced for 8 hours in the morning and 7 hours in the afternoon. Each practice session is 2 hours long. How many full practice sessions did Juan complete? _______ full practice sessions

Answer: 7 full practice sessions

Explanation: Number of hours he practiced in the morning= 8 hours Each practice session is 2 hours long Number of full practice sessions attended by Juan in the morning= 8÷2=4 Number of hours he practiced in the afternoon= 7 hours Number of full practice sessions attended by Juan in the evening= 7÷2=3

Question 6. A total of 25 students sign up to be hosts on Parent’s Night. Teams of 3 students greet parents. How many students cannot be on a team? Explain. _______ student

Answer: 1 student

Explanation: Total number of students = 25 Number of students in each group = 3 The number of students who cannot be in the group= remainder obtained when 25÷3= 1

Question 7. Teresa is making sock puppets just like the one in the picture. If she has 53 buttons, how many puppets can she make? _______ sock puppets

Answer: 17 sock puppets

Explanation: Total number of buttons Teresa has=53 Number of buttons each puppet needs= 3 Number of sock puppets made= Quotient of 53÷3=17 sock puppets

Question 8. Write a question about Teresa and the sock puppets for which the answer is 3. Explain the answer. Type below: ____________

Answer: How many buttons did Teresa use for one sock puppet?

Explanation: Total number of sock puppets made= 17 Number of buttons used for making 17 sock puppets = 52 then, Number of buttons used for one sock puppet= Quotient of 52÷17= 3 buttons

Question 9. Interpret a Result How many more buttons will Teresa need if she wants to make 18 puppets? Explain. _______ buttons

Answer: 1 button

Explanation: After preparing 17 puppets there was 2 buttons leftover then on the addition of 1 button gives 3 buttons which can be used to prepare another puppet.

Question 10. A total of 56 students signed up to play in a flag football league. If each team has 10 students, how many more students will need to sign up so all of the students can be on a team? _______ students

Answer: 4 students

Explanation: Total number of students in the football league= 56 Number of students in each group= 10 then, Number of groups= Quotient of 56÷10=5 groups Remainder= 6 By the addition of 4 students, the group of 6 gets completed by 10 Therefore, 4 students should be added so that all students can be on a team.

Question 11. A teacher plans for groups of her students to eat lunch at tables. She has 34 students in her class. Each group will have 7 students. How many tables will she need? Explain how to use the quotient and remainder to answer the question. _______ tables

Answer: She needs 3 tables

Quotient: A. Use 34 counters to represent the 34 dominoes. Then draw 7 circles to represent the divisor. B. Share the counters equally among the 7 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 34 ÷ 7 D. Number of circles are equally filled with 4 counters, therefore, the quotient is 4

Remainder: The number of counters left over is the remainder. The number of counters leftover= 6 The quotient is used to indicate the number of groups Therefore, there will be 4 tables. While the remainder is used to determine the number of students in the incomplete group.

Common Core – Page No. 213

Interpret the Remainder

Question 1. Hakeem has 100 tomato plants. He wants to plant them in rows of 8. How many full rows will he have? Think: 100 ÷ 8 is 12 with a remainder of 4. The question asks “how many full rows,” so use only the quotient. 12 full rows

Answer: 12 full rows

Explanation: Quotient: A. Use 100 counters to represent the 100 dominoes. Then draw 8 circles to represent the divisor. B. Share the counters equally among the 8 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 100 ÷ 8 D. Number of circles are equally filled with 12 counters, therefore, the quotient is 12 Therefore, the tomatoes placed in full rows are 12

Go Math Grade 4 Chapter 4 Review Answer Key Question 2. A teacher has 27 students in her class. She asks the students to form as many groups of 4 as possible. How many students will not be in a group? _______ students

Answer: 3 students will not be the group

Explanation: Total number of students in the class= 27 Number of students who make a group=4 Number of groups that can be made =Quotient of 27÷ 4=6 Number of students who do not come under a group= Remainder of 27÷ 4=3

Question 3. A sporting goods company can ship 6 footballs in each carton. How many cartons are needed to ship 75 footballs? _______ cartons

Answer: 12 full cartons and 0.5 or 1/2 carton to ship all the 75 footballs

Explanation: Total number of footballs that should be shipped= 75 Number of footballs placed in each carton = 6 Number of cartons required=Quotient of 75÷ 6=12

Question 4. A carpenter has a board that is 10 feet long. He wants to make 6 table legs that are all the same length. What is the longest each leg can be? _______ foot

Answer: The length of the longest leg=4 foot-long

Explanation: According to the question, Length of the board the carpenter has= 10 foot long Number of table legs that are to be made = 6 Length of the 6 table legs are equal then, Length of each table leg= Quotient of 10÷6=1 foot Length of the longest table leg= Remainder of 10÷6= 4 foot.

Question 5. Allie wants to arrange her flower garden in 8 equal rows. She buys 60 plants. What is the greatest number of plants she can put in each row? _______ plants

Explanation: Total number of plants Allie bought= 60 Number of rows= 8 Number of plants in each row= Quotient of 60÷8=7

Question 6. Joanna has 70 beads. She uses 8 beads for each bracelet. She makes as many bracelets as possible. How many beads will Joanna have left over? _______ beads

Answer: 6 beads

Explanation: Total number of beads Joanna has= 70 beads Number beads used for each bracelet= 8 beads Number of bracelets made with these beads= Quotient of 70÷8= 7 bracelets then, The number of beads leftover= Remainder of 70÷8= 6 beads

Question 7. A teacher wants to give 3 markers to each of her 25 students. Markers come in packages of 8. How many packages of markers will the teacher need? _______ packages

Answer: 10 packages

Explanation: Total number of students= 25 Number of markers each student got= 3 Total number of markers the teacher needs to distribute= 25 x 3= 75 Number of markers in each package= 8 Number of packages the teacher required= Quotient of 75÷8=9 While the remainder= 3 Therefore the total number packages=10

Common Core – Page No. 214

Question 1. Marcus sorts his 85 baseball cards into stacks of 9 cards each. How many stacks of 9 cards can Marcus make? Options: a. 4 b. 8 c. 9 d. 10

Answer: d. 10

Explanation: Total number of baseball cards=85 Number of cards in each stack=9 Number of stacks sorted= Quotient of 85÷9=9 While the remainder=4 So the total number of stacks required= 10

Question 2. A minivan can hold up to 7 people. How many minivans are needed to take 45 people to a basketball game? Options: a. 3 b. 5 c. 6 d. 7

Answer: d. 7

Explanation: A minivan can hold up to 7 people. Total number of people who want to hire the minivan= 45 people Number of minivans required= Quotient of 45÷7= 6 vans While the remainder is 3. Total number of minivans required to take the people to the baseball game= 7 minivans

Question 3. Mrs. Wilkerson cut some oranges into 20 equal pieces to be shared by 6 friends. How many pieces did each person get and how many pieces were left over? Options: a. 2 pieces with 4 pieces leftover b. 3 pieces with 2 pieces leftover c. 3 pieces with 4 pieces leftover d. 4 pieces with 2 pieces leftover

Answer: b. 3 pieces with 2 pieces leftover

Explanation: Total number of orange pieces= 20 Number of friends= 6 Number of pieces each friend got= Quotient of 20÷6= 3 pieces Number of pieces leftover= Remainder of 20÷6= 2 pieces

Question 4. A school bought 32 new desks. Each desk cost $24. Which is the best estimate of how much the school spent on the new desks? Options: a. $500 b. $750 c. $1,000 d. $1,200

Answer: b. $750

Question 5. Kris has a box of 8 crayons. Sylvia’s box has 6 times as many crayons as Kris’s box. How many crayons are in Sylvia’s box? Options: a. 48 b. 42 c. 36 d. 4

Answer: 48 crayons

Explanation: Number of crayons in Kris box=8 Number of crayons in Sylvia’s box= 6 times as many crayons as Kris’s box= 6 x 8=48

Question 6. Yesterday, 1,743 people visited the fair. Today, there are 576 more people at the fair than yesterday. How many people are at the fair today? Options: a. 1,167 b. 2,219 c. 2,319 d. 2,367

Answer: c. 2,319

Question 1. Divide. 2,800 ÷ 7 What basic fact can you use? ___________ 2,800 = 28 ___________ 28 hundreds ÷ 7 = ___________ 2,800 ÷ 7 = ___________ Type below: ___________

Answer: 400

Explanation: STEP 1 Identify the basic fact. 28 ÷ 7 STEP 2 Use place value. 2,800 = 28 hundreds STEP 3 Divide. 28 hundreds ÷ 4 = 4 hundreds 2,800 ÷ 7 = 400

Go Math Grade 4 Chapter 4 Lesson 6 Homework Answer Key Question 2. Divide. 280 ÷ 7 What basic fact can you use? ___________ 280 = 28 ___________ 28 tens ÷ _____ = 4 ___________ 280 ÷ 7 = _____ Type below: ___________

Explanation: STEP 1 Identify the basic fact. 28 ÷ 7 STEP 2 Use place value. 280 = 28 tens STEP 3 Divide. 28 tens ÷ 4 = 4 tens 280 ÷ 7 = 40

Use basic facts and place value to find the quotient.

Lesson 4.6 Answer Key 4th Grade Question 3. 360 ÷ 6 = ______

Explanation: STEP 1 Identify the basic fact. 36 ÷ 6 STEP 2 Use place value. 360 = 36 tens STEP 3 Divide. 36 tens ÷6 = 6 tens 360 ÷ 6 = 60

Question 4. 2,000 ÷ 5 = ______

Explanation: STEP 1 Identify the basic fact. 20 ÷ 5 STEP 2 Use place value. 2,000 = 20 hundreds STEP 3 Divide. 20 hundreds ÷ 5 = 4 hundreds 2,000 ÷ 5 = 400

Question 5. 4,500 ÷ 9 = ______

Answer: 500

Explanation: STEP 1 Identify the basic fact. 45 ÷ 9 STEP 2 Use place value. 4,500 = 45 hundreds STEP 3 Divide. 45 hundreds ÷ 9 = 5 hundreds 4,500 ÷ 9 = 500

Question 6. 560 ÷ 8 = ______

Explanation: STEP 1 Identify the basic fact. 56 ÷ 8 STEP 2 Use place value. 560 = 56 tens STEP 3 Divide. 56 tens ÷ 8 = 7 tens 560 ÷ 8 = 70

Question 7. 6,400 ÷ 8 = ______

Answer: 800

Explanation: STEP 1 Identify the basic fact. 64 ÷ 8 STEP 2 Use place value. 6,400 =64 hundreds STEP 3 Divide. 64 hundreds ÷ 8 = 8 hundreds 6,400 ÷ 8 = 800

Question 8. 3,500 ÷ 7 = ______

Explanation: STEP 1 Identify the basic fact. 35 ÷ 7 STEP 2 Use place value. 3,500 = 35 hundreds STEP 3 Divide. 35 hundreds ÷ 7 = 5 hundreds 3,500 ÷ 7 = 500

Use Patterns Algebra Find the unknown number.

Question 9. 420 ÷ ______ = 60

Lesson 4.6 Division and the Distributive Property Question 10. ______ ÷ 4 = 30

Answer: 120

Explanation: To find the dividend (the missing number) we must multiply the divisor and the quotient. Therefore the dividend is 30 x 4=120.

Question 11. 810 ÷ ______ = 90

Question 12. Divide 400 ÷ 40. Explain how patterns and place value can help. ______

Explanation: STEP 1 Identify the basic fact. 40 ÷ 4 STEP 2 Use place value. 400 = 40 tens STEP 3 Divide. 40 tens ÷ 4 = 1 tens 400 ÷ 40 = 10

Question 13. Eileen collected 98 empty cans to recycle, and Carl collected 82 cans. They packed an equal number of cans into each of three boxes to take to the recycling center. How many cans were in each box? ______ cans

Answer: 60 cans

Explanation: Total number of cans = 98+82=180 cans Number of boxes= 3 Number of cans in each box= 180 ÷3=60 cans

Question 14. It costs a baker $18 to make a small cake. He sells 8 small cakes for $240. How much more is the selling price of each cake than the cost? $ ______

Answer: $96

Explanation: Cost of each cake= $18 Number of cakes baked= 8 The actual cost of the cakes = $18 x $8=$144 The selling price of the cakes=$240 Amount gained on the cakes= $240-$144=$96

Answer: 100 pennies

Explanation: Total number of pennies= 600 Number of rolls= 6 The number of pennies= Quotient of 600 ÷ 6=100

Question 16. Sela has 6 times as many coins now as she had 4 months ago. If Sela has 240 coins now, how many coins did she have 4 months ago? ______ coins

Answer: 60 coins

Explanation: Let the number of coins four months ago be x coins. According to the question, Number of coins Sela has at present = 4x 4x=240 x= 240 ÷ 4=60 Therefore the number of coins Sela has=60

Question 17. Chip collected 2,090 dimes. Sue collected 1,910 dimes. They divided all their dimes into 8 equal stacks. How many dimes are in each stack? ______ dimes

Explanation: Number of dimes Chip collected= 2,090 Number of dimes Sue collected= 1,910 Total number of dimes= 2,090+1,910= 4100 Number of stacks= 8 Number of dimes in each stack = Quotient of 4100 ÷8=512

Question 18. Communicate Mr. Roberts sees a rare 1937 penny. The cost of the penny is $210. If he saves $3 each week, will Mr. Roberts have enough money to buy the penny in one year? Explain. ______

Answer: No Mr. Roberts cannot buy the penny in one year.

Explanation: Amount saved in each week= $3 Number of weeks in a year= 52 The total amount saved= 52 x 3=$156 Cost of the penny=$210 Therefore Mr. Roberts cannot buy the penny in one year.

Question 19. Mrs. Fletcher bought 5 coins for $32 each. Later, she sold all the coins for $300. How much more did Mrs. Fletcher receive for each coin than she paid? Explain. $ ______

Explanation: Number of coins=5 Cost of each coin = $32 Total cost of the coins= $32 x 5=$160 She sold the coins for $300 Cost of each coin= $300 ÷ 5= $60

Question 20. Which quotients are equal to 20? Mark all that apply. Options: a. 600 ÷ 2 b. 1,200 ÷ 6 c. 180 ÷ 9 d. 140 ÷ 7 e. 500 ÷ 5

Answer: c. 180 ÷ 9 d. 140 ÷ 7

Explanation: Quotient: A. Use 180 counters to represent the 180 dominoes. Then draw 9 circles to represent the divisor. B. Share the counters equally among the 9 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 180 ÷ 9 D. Number of circles are equally filled with 20 counters, therefore, the quotient is 20

Quotient: A. Use 140 counters to represent the 140 dominoes. Then draw 7 circles to represent the divisor. B. Share the counters equally among the 7 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 140 ÷ 7 D. Number of circles are equally filled with 20 counters, therefore, the quotient is 20

Insect Flight

Question 21. About how many times does a damselfly’s wings beat in 1 minute? ______ times

Answer: 900

Explanation: Total number of wingbeats of Damselfly in 3 minutes= 2,700 Number of wingbeats of Damselfly in 1 minute= 2,700 ÷3=900

Question 22. About how many times do a scorpion fly’s wings beat in 6 minutes? ______ times

Answer: 10,000

Explanation: Total number of wingbeats of scorpionfly in 3 minutes=5,000 Number of parts of time-intervals in 6 minutes = 6÷3=2 Number of wingbeats of scorpionfly in 6 minutes= 5,000 x 2 = 10,000

Question 23. In one minute, about how many more times do a damselfly’s wings beat than a large white butterfly’s wings? ______ more times

Answer: 200

Total number of wingbeats of large white butterfly in 3 minutes= 2,100 Number of wingbeats of large white butterfly in 1 minute= 2,100 ÷3=700

Number of more times the damselfly’s wings beat than a large white butterfly=900-700=200

Lesson 4.7 Divide Using Repeated Subtraction Question 24. What’s the Question? The answer is about 2,300 times. Type below: ___________

Answer: About how many times do an Aeschind dragonfly’s wings beat in 1 minute?

Explanation: Total number of wingbeats of Aeschind dragonfly’s in 3 minutes= 6,900 Number of wingbeats of Aeschind dragonfly’s in 1 minute= 6,900 ÷3=2,300

Common Core – Page No. 219

Divide Tens, Hundreds, and Thousands

Question 1. 3,600 ÷ 4 = 900 Think: 3,600 is 36 hundreds. Use the basic fact 36 ÷ 4 = 9. So, 36 hundreds ÷ 4 = 9 hundreds, or 900.

Explanation: STEP 1 Identify the basic fact. 36 ÷ 4 STEP 2 Use place value. 3,600 = 36 hundreds STEP 3 Divide. 36 hundered ÷ 4 = 9 hundreds 3,600 ÷ 4 = 900

Question 2. 240 ÷ 6 = ______

Explanation: STEP 1 Identify the basic fact. 24 ÷ 6 STEP 2 Use place value. 240 = 24 tens STEP 3 Divide. 24 tens ÷ 6 = 4 tens 240 ÷ 6 = 40

Go Math Chapter 4 Grade 4 Lesson 4.7 Answer Key Question 3. 5,400 ÷ 9 = ______

Answer: 600

Explanation: STEP 1 Identify the basic fact. 54 ÷ 9 STEP 2 Use place value. 5,400 = 54 hundreds STEP 3 Divide. 54 hundreds ÷ 9 = 6 hundreds 5,400 ÷ 9 = 600

Question 4. 300 ÷ 5 = ______

Explanation: STEP 1 Identify the basic fact. 30 ÷ 5 STEP 2 Use place value. 300 = 30 tens STEP 3 Divide. 30 tens ÷ 5 = 60 tens 300 ÷ 5 = 60

Question 5. 4,800 ÷ 6 = ______

Explanation: STEP 1 Identify the basic fact. 48 ÷ 6 STEP 2 Use place value. 4,800 = 48 hundreds STEP 3 Divide. 48 hundreds ÷ 6 = 80 hundreds 4,800 ÷ 6 = 800

Question 6. 420 ÷ 7 = ______

Explanation: STEP 1 Identify the basic fact. 42 ÷ 7 STEP 2 Use place value. 420 = 42 tens STEP 3 Divide. 42 tens ÷ 7 = 60 tens 420 ÷ 7 = 60

Question 7. 150 ÷ 3 = ______

Explanation: STEP 1 Identify the basic fact. 15 ÷ 3 STEP 2 Use place value. 150 = 15 tens STEP 3 Divide. 15 tens ÷ 3 = 5 tens 150 ÷ 3 = 50

Question 8. 6,300 ÷ 7 = ______

Explanation: STEP 1 Identify the basic fact. 63 ÷ 7 STEP 2 Use place value. 6,300 = 63 hundreds STEP 3 Divide. 63 hundreds ÷ 7 = 9 hundreds 6,300 ÷ 7 = 900

Question 9. 1,200 ÷ 4 = ______

Answer: 300

Explanation: STEP 1 Identify the basic fact. 12 ÷ 4 STEP 2 Use place value. 1,200 = 12 hundreds STEP 3 Divide. 12 hundreds ÷ 4 = 3 hundreds 1,200 ÷ 4 = 300

Question 10. 360 ÷ 6 = ______

Explanation: STEP 1 Identify the basic fact. 36 ÷ 6 STEP 2 Use place value. 360 = 36 tens STEP 3 Divide. 36 tens ÷ 6 = 6 tens 360 ÷ 6 = 60

Find the quotient.

Question 11. 28 ÷ 4 = ______ 280 ÷ 4 = ______ 2,800 ÷ 4 = ______

Answer: 7, 70, 700

Explanation: Quotient: A. Use 28 counters to represent the 28 dominoes. Then draw 4 circles to represent the divisor. B. Share the counters equally among the 4 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 28 ÷ 4 D. Number of circles are equally filled with 7 counters, therefore, the quotient is 7

STEP 1 Identify the basic fact. 28 ÷ 4 STEP 2 Use place value. 280 = 28 tens STEP 3 Divide. 28 tens ÷ 4 = 7 tens 280 ÷ 4 = 70

STEP 1 Identify the basic fact. 28 ÷ 4 STEP 2 Use place value. 2,800 = 28 hundreds STEP 3 Divide. 28 hundreds ÷ 4 = 7 hundreds 2,800 ÷ 4 = 700

Go Math Grade 4 Lesson 4.7 Answer Key Question 12. 18 ÷ 3 = ______ 180 ÷ 3 = ______ 1,800 ÷ 3 = ______

Answer: 6, 60, 600

Explanation: Quotient: A. Use 18 counters to represent the 18 dominoes. Then draw 3 circles to represent the divisor. B. Share the counters equally among the 3 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 18 ÷ 3 D. Number of circles are equally filled with 6 counters, therefore, the quotient is 6

STEP 1 Identify the basic fact. 18 ÷ 3 STEP 2 Use place value. 180 = 18 tens STEP 3 Divide. 18 tens ÷ 3 = 6 tens 180 ÷ 6 = 60

STEP 1 Identify the basic fact. 18 ÷ 3 STEP 2 Use place value. 1,800 = 18 hundreds STEP 3 Divide. 18 hundreds ÷ 3 = 6 hundreds 1,800 ÷ 3 = 600

Question 13. 45 ÷ 9 = ______ 450 ÷ 9 = ______ 4,500 ÷ 9 = ______

Answer: 5, 50, 500

Explanation: Quotient: A. Use 45 counters to represent the 45 dominoes. Then draw 9 circles to represent the divisor. B. Share the counters equally among the 9 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 45 ÷ 9 D. Number of circles are equally filled with 5 counters, therefore, the quotient is 5

STEP 1 Identify the basic fact. 45 ÷ 9 STEP 2 Use place value. 450 = 45 tens STEP 3 Divide. 45 tens ÷ 9 = 5 tens 450 ÷ 9 = 50

STEP 1 Identify the basic fact. 45 ÷ 9 STEP 2 Use place value. 4,500 = 45 hundreds STEP 3 Divide. 45 hundreds ÷ 9 = 5 hundreds 4,500 ÷ 9 = 500

Question 14. At an assembly, 180 students sit in 9 equal rows. How many students sit in each row? ______ students

Explanation: Total number of students= 180 Number of rows= 9 Number of students in each row= 180 ÷9=20

Question 15. Hilary can read 560 words in 7 minutes. How many words can Hilary read in 1 minute? ______ words

Explanation: Total number of words Hilary can read in 7 minutes = 560 Number of words Hilary can read in 1 minute= 560 ÷ 7= 80

Question 16. A company produces 7,200 gallons of bottled water each day. The company puts 8 one-gallon bottles in each carton. How many cartons are needed to hold all the one-gallon bottles produced in one day? ______ cartons

Explanation: Total number of gallons bottled in each day= 7,200 Number of gallons bottled in each carton= 8 Number of cartons used= 7,200 ÷ 8= 900

Question 17. An airplane flew 2,400 miles in 4 hours. If the plane flew the same number of miles each hour, how many miles did it fly in 1 hour? ______ miles

Explanation: Total number of miles flew in 4 hours= 2,400 Number of miles flew in 1 hour= 2,400÷4=600

Common Core – Page No. 220

Question 1. A baseball player hits a ball 360 feet to the outfield. It takes the ball 4 seconds to travel this distance. How many feet does the ball travel in 1 second? Options: a. 9 feet b. 40 feet c. 90 feet d. 900 feet

Answer: c. 90 feet

Explanation: The height to which the player hits a ball=360 feet Height to which the ball travels in 1 second= 360÷4= 90 feet

Question 2. Sebastian rides his bike 2,000 meters in 5 minutes. How many meters does he bike in 1 minute? Options: a. 4 meters b. 40 meters c. 50 meters d. 400 meters

Answer: d. 400 meters

Explanation: Total number of meters travelled in 5 minutes= 2,000 Number of meters travelled in 1 minute= 2,000÷5= 400

Question 3. A full container of juice holds 63 ounces. How many 7-ounce servings of juice are in a full container? Options: a. 1 b. 8 c. 9 d. 10

Answer: c. 9

Explanation: A full container of juice holds= 63 ounces Quantity of servings of juice in one glass=7 ounce The number of servings of the juice are = 63÷7=9

Go Math Lesson 4.7 4th Grade Answer Key Question 4. Paolo pays $244 for 5 identical calculators. Which is the best estimate of how much Paolo pays for one calculator? Options: a. $40 b. $50 c. $60 d. $245

Answer: b. $50

Explanation: Amount Paolo pays for the identical calculators = $244 Number of identical calculators=5 The best estimated value of each identical calculator=$244 ÷ 5is approximately $50

Question 5. A football team paid $28 per jersey. They bought 16 jerseys. How much money did the team spend on jerseys? Options: a. $44 b. $196 c. $408 d. $448

Answer: d. $448

Explanation: Cost of each jersey=$28 Number of jerseys= 16 Total cost of the jerseys= $28 x 16= $448

Question 6. Suzanne bought 50 apples at the apple orchard. She bought 4 times as many red apples as green apples. How many more red apples than green apples did Suzanne buy? Options: a. 10 b. 25 c. 30 d. 40

Answer: d. 40

Explanation: Let the number of green apples be x and the number of red apples be 4x 4x + x = 50 x = 50  ÷ 5= 10 Number of red balls = 4x = 4 x 10 = 40

Question 1. Estimate. 1,718 ÷ 4 Think: What number close to 1,718 is easy to divide by 4? ______ is close to 1,718. What basic fact can you use? ______ ÷ 4 ______ is close to 1,718. What basic fact can you use? ______ ÷ 4 Choose 1,600 because __________________________________. 16 ÷ 4 = ______ 1,600 ÷ ______ = ______ 1,718 ÷ 4 is about ______ Type below: _________

Explanation: What number close to 1,718 is easy to divide by 4? 1,600 is close to 1,718. What basic fact can you use? 1,600 ÷ 4 Choose 1,600 because it is close to 1,718 and can easily be divided by 4. 16 ÷ 4 = 4 1,600 ÷ 4 = 400 1,600 ÷ 4 is about 400

Use compatible numbers to estimate the quotient.

Question 2. 455 ÷ 9 ______

Explanation: What number close to 455 is easy to divide by 9? 450 is close to 455. What basic fact can you use? 450 ÷ 9 Choose 450 because it is close to 455 and can easily be divided by 9. 45 ÷ 9 = 5 450 ÷ 9 = 50 455 ÷ 9 is about 50

Question 3. 1,509 ÷ 3 ______

Explanation: What number close to 1,509 is easy to divide by 3? 1,500 is close to 1,509. What basic fact can you use? 1,500 ÷ 3 Choose 1,500 because it is close to 1,509 and can easily be divided by 3. 15 ÷ 3 = 5 1,500 ÷ 3 = 500 1,509 ÷ 3 is about 500

Question 4. 176 ÷ 8 ______

Explanation: What number close to 176 is easy to divide by 8? 160 is close to 176. What basic fact can you use? 160 ÷ 8 Choose 160 because it is close to 176 and can easily be divided by 8. 16 ÷ 8 = 2 160 ÷ 8 = 20 176 ÷ 8 is about 20

Go Math Grade 4 Chapter 4 Answer Key Lesson 4.8 Question 5. 2,795 ÷ 7 ______

Answer:  400

Explanation: What number close to 2,795 is easy to divide by 7? 2,800 is close to 2,795. What basic fact can you use? 2,800 ÷ 7 Choose 2,800 because it is close to 2,795 and can easily be divided by 7. 28 ÷ 7 = 4 2,800 ÷ 7 = 400 2,795 ÷ 7 is about 400

Use compatible numbers to find two estimates that the quotient is between.

Question 6. 5,321 ÷ 6 ______ and ______

Explanation: What number close to 5,321 is easy to divide by 6? 5,400 is close to 5,321. What basic fact can you use? 5,400 ÷ 6 Choose 5,400 because it is close to 5,321 and can easily be divided by 6. 54 ÷ 6 = 9 5,400 ÷ 6 = 900 5,321 ÷ 6 is about 900

Question 7. 1,765 ÷ 6 ______ and ______

Explanation: What number close to 1,765 is easy to divide by 6? 1,800 is close to 1,765. What basic fact can you use? 1,800 ÷ 6 Choose 1,800 because it is close to 1,765 and can easily be divided by 6. 18 ÷ 6 = 3 1,800 ÷ 6 = 300 1,765 ÷ 6 is about 300

Question 8. 1,189 ÷ 3 ______ and ______

Explanation: What number close to 1,189 is easy to divide by 3? 1,200 is close to 1,189. What basic fact can you use? 1,200 ÷ 3 Choose 1,200 because it is close to 1,189 and can easily be divided by 3. 12 ÷ 3 = 4 1,200 ÷ 3 = 400 1,189 ÷ 3 is about 400

Question 9. 2,110 ÷ 4 ______ and ______

Explanation: What number close to 2,110 is easy to divide by 4? 2,000 is close to 2,110. What basic fact can you use? 2,000 ÷ 4 Choose 2,000 because it is close to 2,110 and can easily be divided by 4. 20 ÷ 4 = 5 2,000 ÷ 4 = 500 2,110 ÷ 4 is about 500

Reason Abstractly Algebra Estimate to compare. Write <, >, or =.

Question 10. 613 ÷ 3 ______ 581 ÷ 2

Answer: 613 ÷ 3 <  581 ÷ 2

Explanation: What number close to 613 is easy to divide by 3? 600 is close to 613. What basic fact can you use? 600 ÷ 3 Choose 600 because it is close to 613 and can easily be divided by 3. 6 ÷ 3 = 2 600 ÷ 3 = 200 613 ÷ 3 is about 200

What number close to 581 is easy to divide by 2? 580 is close to 581. What basic fact can you use? 580 ÷ 2 Choose 580 because it is close to 581 and can easily be divided by 2. 58 ÷ 2 = 29 580 ÷ 2 = 290 581 ÷ 2 is about 290

Question 11. 364 ÷ 4 ______ 117 ÷ 6

Answer: 364 ÷ 4 >  117 ÷ 6

Explanation: What number close to 364 is easy to divide by 4? 360 is close to 364. What basic fact can you use? 360 ÷ 4 Choose 360 because it is close to 364 and can easily be divided by 4. 36 ÷ 4 = 9 360 ÷ 4 = 90 364 ÷ 4 is about 90

What number close to 117 is easy to divide by 6? 120 is close to 117. What basic fact can you use? 120 ÷ 6 Choose 120 because it is close to 117 and can easily be divided by 6. 12 ÷ 6 = 2 120 ÷ 6 = 20 117 ÷ 6 is about 20

Question 12. 2,718 ÷ 8 ______ 963 ÷ 2

Answer: 2,718 ÷ 8 < 963 ÷ 2

Explanation: What number close to 2,718 is easy to divide by 8? 2,400 is close to 2,718. What basic fact can you use? 2,400 ÷ 8 Choose 2,400 because it is close to 2,718 and can easily be divided by 8. 24 ÷ 8 = 3 2,400 ÷ 8 = 300 2,718 ÷ 8 is about 300

What number close to 963 is easy to divide by 2? 960 is close to 963. What basic fact can you use? 960 ÷ 2 Choose 960 because it is close to 963 and can easily be divided by 2. 96 ÷ 2 = 48 960 ÷ 2 = 480 963 ÷ 2 is about 480

Question 13. If Cade shoots 275 free throw baskets in 2 hours, about how many can he shoot in 5 hours? about ______ free throw baskets

Answer: 688 free throw baskets

Explanation: Number of free-throw baskets in 2 hours= 275 Number of free-throw baskets in 1 hour = 275÷2=137.5 Number of free-throw baskets in 5 hours= 137.5 x 5= 687.5 =rounding to nearest whole number 688 free throw baskets ( approx)

Question 14. A carpenter has 166 doorknobs in his workshop. Of those doorknobs, 98 are round and the rest are square. If he wants to place 7 square doorknobs in each bin, about how many bins would he need? about ______ bins

Explanation: The total number of doorknobs in a workshop= 166 Number of round doorknobs in a workshop= 98 Number of square doorknobs in a workshop=166-98=68 Number of square doorknobs in each bin= 7 Number of bins= 68÷7= 9.7= rounding to nearest whole number 10 bins (approx)

Question 15. About how many times does a chicken’s heart beat in 1 minute? about ______ times

Answer: 275

Explanation: Number of times the chicken’s heartbeats in 5 minutes= 1,375 Number of times the chicken’s heartbeats in 1 minute= 1,375÷ 5= 275

Question 16. About how many times does a cow’s heart beat in 2 minutes? about ______ times

Answer: 130

Explanation: Number of times the cow’s heartbeats in 5 minutes= 325 Number of times the cow’s heartbeats in 1 minute= 325÷5=65 Number of times the cow’s heartbeats in 2 minutes= 65 x 2=130

Question 17. Use Reasoning About how many times faster does a cow’s heartbeat than a whale’s? about ______ times

Answer: nearly 11 times

Explanation: Number of times the cow’s heartbeats in 5 minutes= 325 Number of times the cow’s heartbeats in 1 minute= 325÷5=65

Number of times the whale’s heartbeats in 5 minutes= 31 Number of times the whale’s heartbeats in 1 minute= 31÷5=6.2= rounding to nearest whole number 6 (approx)

Number of more times the cow’s heartbeats compared to whale’s=65÷6=10.8 times=rounding to a nearest whole number 11(approx)

Question 18. Martha had 154 stamps and her sister had 248 stamps. They combined their collections and put the stamps in an album. If they want to put 8 stamps on each page, about how many pages would they need? about ______ times

Answer: 50.25 pages

Explanation: Number of stamps Martha has= 154 Number of stamps Martha’s sister has= 248 The total number of stamps they have= 154+248=402 Number of stamps on each page= 8 Number of pages= 402÷8= 50.25 pages= 51 (approx)

Question 19. Jamie and his two brothers divided a package of 125 toy cars equally. About how many cars did each of them receive? about ______ times

Answer: 41.67

Explanation: Number of toys Jamie has= 125 toy cars Number of toys Jamie and his two brothers divide= 125÷3= 41.67

Go Math Grade 4 Chapter 4 Test Pdf Question 20. Harold and his brother collected 2,019 cans over a 1-year period. Each boy collected the same number of cans. About how many cans did each boy collect? Explain how you found your answer. about ______ times

Answer: 1,010

Explanation: Number of cans Harold and his brother collected = 2,019 cans Number of cans each boy collected = 2,019÷2= 1,009.5 cans = 1,010 cans(approx)

Answer: Chet can afford the 3-months layaway plan.

Explanation: What number close to $276  is easy to divide by 3? $270 is close to $276. What basic fact can you use? $270 ÷ 3 Choose 270 because it is close to 276 and can easily be divided by 3. 27 ÷ 3 = 9 270 ÷ 3 = 90 $276 ÷ 3 is about 90

Use estimation to solve.

Question 21. Sofia wants to buy a new bike that costs $214. Sofia helps her grandmother with chores each week for $18. Estimate to find which layaway plan Sofia should choose and why. Type below: ___________

Answer: 3 months

Explanation: What number close to $214  is easy to divide by 3? $215 is close to $214. What basic fact can you use? $215 ÷ 3 Choose 215 because it is close to 214 and can easily be divided by 3. 215 ÷ 3 = 71.6=72 (approx) $214 ÷ 3 is about 72

Question 22. Describe a situation when you have used cause and effect to help you solve a math problem. Type below: ___________

Answer: To buy a bike

Explanation: 3-month layaway: $276 ÷ 3 Estimate. $270 ÷ 3 ______ 6-month layaway: $276 ÷ 6 Estimate. $300 ÷ 6 _____ Chet earns $15 each week. Since there are usually 4 weeks in a month, multiply to see which payment he can afford. $15 × 4 = _______ So, Chet can afford the ______ layaway plan.

The above is a profit gaining plan to buy a bike.

Common Core – Page No. 224

Estimate Quotients Using Compatible Numbers

Question 1. 389 ÷ 4 400 ÷ 4 = 100

Answer: 100

Explanation: What number close to 389 is easy to divide by 4? 400 is close to 389. What basic fact can you use? 400 ÷ 4 Choose 400 because it is close to 389 and can easily be divided by 4. 40 ÷ 4 = 10 400 ÷ 4 = 100 389 ÷ 4 is about 100

Question 2. 358 ÷ 3 _____ ÷ 3 = _____

Explanation: What number close to 358 is easy to divide by 3? 360 is close to 358. What basic fact can you use? 360 ÷ 3 Choose 360 because it is close to 358 and can easily be divided by 3. 36 ÷3 = 12 360 ÷ 3 =120 358 ÷ 3 is about 120

Question 3. 784 ÷ 8 _____ ÷ 8 = _____

Explanation: What number close to 784 is easy to divide by 8? 800 is close to 784. What basic fact can you use? 800 ÷ 8 Choose 800 because it is close to 784 and can easily be divided by 8. 80 ÷ 8 = 10 800 ÷ 8 = 100 784 ÷ 8 is about 100

Question 4. 179 ÷ 9 _____ ÷ 9 = _____

Explanation: What number close to 179 is easy to divide by 9? 180 is close to 179. What basic fact can you use? 180 ÷ 9 Choose 180 because it is close to 179 and can easily be divided by 9. 18 ÷ 9 = 2 180 ÷ 9 = 20 179 ÷ 9 is about 20

Question 5. 315 ÷ 8 _____ ÷ 8 = _____

Explanation: What number close to 315 is easy to divide by 8? 320 is close to 315. What basic fact can you use? 320 ÷ 8 Choose 320 because it is close to 315 and can easily be divided by 8. 32 ÷ 8 = 4 320 ÷ 8 =40 315 ÷ 8 is about 40

Question 6. 2,116 ÷ 7 _____ ÷ 7 = _____

Explanation: What number close to 2,116 is easy to divide by 7? 2,100 is close to 2,116. What basic fact can you use? 2,100 ÷ 7 Choose 2,100 because it is close to 2,116 and can easily be divided by 7. 21 ÷ 7= 3 2,100 ÷ 7 = 300 2,116 ÷ 7 is about 300

Grade 4 Chapter 4 Divide By A One Digit Number Question 7. 4,156 ÷ 7 _____ ÷ 7 = _____

Explanation: What number close to 4,156 is easy to divide by 7? 4,200 is close to 4,156. What basic fact can you use? 4,200 ÷7 Choose 4,200 because it is close to 4,156 and can easily be divided by 7. 42 ÷ 7 = 6 4,200 ÷ 7 = 600 4,156 ÷ 7 is about 600

Question 8. 474 ÷ 9 _____ ÷ 9 = _____

Explanation: What number close to 474 is easy to divide by 9? 450 is close to 474. What basic fact can you use? 450 ÷ 9 Choose 450 because it is close to 474 and can easily be divided by 9. 45 ÷ 9 = 5 450 ÷ 9 = 50 474 ÷ 9 is about 50

Question 9. 1,624 ÷ 3 _____ ÷ 3 = _____ _____ ÷ 3 = _____

Answer: The quotient is between 500 and 600

Explanation: What number close to 1,624 is easy to divide by 3? 1,500 is close to 1,624. What basic fact can you use? 1,500 ÷ 3 Choose 1,500 because it is close to 1,624 and can easily be divided by 3. 15 ÷ 3 = 5 1,500 ÷ 3 = 500 1,624 ÷ 3 is about 500

What number close to 1,624 is easy to divide by 3? 1,800 is close to 1,624. What basic fact can you use? 1,800 ÷ 3 Choose 1,800 because it is close to 1,624 and can easily be divided by 3. 18 ÷ 3 = 6 1,800 ÷ 3 = 600 1,624 ÷ 3 is about 600

Question 10. 2,593 ÷ 6 _____ ÷ 6 = _____ _____ ÷ 6 = _____

Answer: The quotient is between 400 and 500

Explanation: What number close to 2,593 is easy to divide by 6? 2,400 is close to 2,593. What basic fact can you use? 2,400 ÷ 6 Choose 2,400 because it is close to 2,593 and can easily be divided by 6. 24 ÷ 6 = 4 2,400 ÷ 6 = 400 2,593 ÷ 6 is about 400

What number close to 2,593 is easy to divide by 6? 3,000 is close to 2,593. What basic fact can you use? 3000 ÷ 6 Choose 3,000 because it is close to 2,593 and can easily be divided by 6. 30 ÷ 6 = 5 3,000 ÷ 6 = 500 2,593 ÷ 6 is about 500

Question 11. 1,045 ÷ 2 _____ ÷ 2 = _____ _____ ÷ 2 = _____

Answer: The quotient is between 520 and 525

Explanation: What number close to 1,045 is easy to divide by 2? 1,040 is close to 1,045. What basic fact can you use? 1,040 ÷ 2 Choose 1,040 because it is close to 1,045 and can easily be divided by 2. 1,04 ÷ 2 = 52 1,040 ÷ 2 = 520 1,045 ÷ 2 is about 520

What number close to 1,045 is easy to divide by 2? 1,050 is close to 1,045. What basic fact can you use? 1,050 ÷ 2 Choose 1,050 because it is close to 1,045 and can easily be divided by 2. 1,050 ÷ 2 = 525 1,045 ÷ 2 is about 525

Go Math Grade 4 Chapter 4 Answer Key Pdf Question 12. 1,754 ÷ 9 _____ ÷ 9 = _____ _____ ÷ 9 = _____

Answer: The quotient is between 195 and 200

Explanation: What number close to 1,754 is easy to divide by 9? 1,755 is close to 1,754. What basic fact can you use? 1,755 ÷ 9 Choose 1,755 because it is close to 1,754 and can easily be divided by 9. 1,755 ÷ 9 = 195 1,754 ÷ 9 is about 195

What number close to 1,754 is easy to divide by 9? 1,800 is close to 1,754. What basic fact can you use? 1,800 ÷ 9 Choose 1,800 because it is close to 1,754 and can easily be divided by 9. 18 ÷ 9 = 2 1,800 ÷ 9 = 200 1,754 ÷ 9 is about 200

Question 13. 2,363 ÷ 8 _____ ÷ 8 = _____ _____ ÷ 8 = _____

Answer: The quotient is between 295 and 300

Explanation: What number close to 2,363 is easy to divide by 8? 2,360 is close to 2,363. What basic fact can you use? 2,360 ÷ 8 Choose 2,360 because it is close to 2,363 and can easily be divided by 8. 2,360 ÷ 8 = 295 2,363 ÷ 8 is about 295

What number close to 2,363 is easy to divide by 8? 2,400 is close to 2,363. What basic fact can you use? 2,400 ÷ 8 Choose 2,400 because it is close to 2,363 and can easily be divided by 8. 24 ÷ 8 = 3 2,400 ÷ 8= 300 2,363 ÷ 8 is about 300

Question 14. 1,649 ÷ 5 _____ ÷ 5 = _____ _____ ÷ 5 = _____

Answer: The quotient is between 329 and 330

Explanation: What number close to 1,649 is easy to divide by 5? 1,645 is close to 1,649. What basic fact can you use? 1,645 ÷ 5 Choose 1,645 because it is close to 1,649 and can easily be divided by 5. 1,645 ÷ 5 = 329 1,649 ÷ 5 is about 329

What number close to 1,650 is easy to divide by 5? 1,650 is close to 1,649. What basic fact can you use? 1,650 ÷ 5 Choose 1,650 because it is close to 1,649 and can easily be divided by 5. 1,650 ÷ 5 = 330 1,649 ÷ 5 is about 330

Question 15. 5,535 ÷ 7 _____ ÷ 7 = _____ _____ ÷ 7 = _____

Answer: The quotient is between 790 and 791

Explanation: What number close to 5,535 is easy to divide by 7? 5,530 is close to 5,535. What basic fact can you use? 5,530 ÷ 7 Choose 5,530 because it is close to 5,535 and can easily be divided by 7. 553 ÷ 7 = 79 5,530 ÷ 7 = 790 5,535 ÷ 7 is about 790

What number close to 5,535 is easy to divide by 7? 5,537 is close to 5,535. What basic fact can you use? 5,537 ÷ 7 Choose 5,537 because it is close to 5,535 and can easily be divided by 7. 553 ÷ 7 = 79 5,537 ÷ 7 = 791 5,535 ÷ 7 is about 791

Question 16. 3,640 ÷ 6 _____ ÷ 6 = _____ _____ ÷ 6 = _____

Answer: The quotient is between 606 and 607

Explanation: What number close to 3,640 is easy to divide by 6? 3,636 is close to 3,640. What basic fact can you use? 3,636 ÷ 6 Choose 3,636 because it is close to 3,640 and can easily be divided by 6. 36 ÷ 6 = 6 3,636 ÷ 6 = 606 3,640 ÷ 6 is about 606

What number close to 3,640 is easy to divide by 6? 3,642 is close to 3,640. What basic fact can you use? 3,642 ÷ 6 Choose 3,642 because it is close to 3,640 and can easily be divided by 6. 3,642 ÷ 6 = 607 3,640 ÷ 6 is about 607

Question 17. A CD store sold 3,467 CDs in 7 days. About the same number of CDs were sold each day. About how many CDs did the store sell each day? about _____ CDs

Answer: 495(approx)

Explanation: Total number of CDs in the store= 3,467 Number of days= 7 Number of CDs sold on one day= 3,467 ÷ 7=495(approx)

Question 18. Marcus has 731 books. He puts about the same number of books on each of 9 shelves in his a bookcase. About how many books are on each shelf? about _____ books

Answer: 81 books(approx)

Explanation: Total number of books Marcus has= 731 Number of shelves= 9 Number of books on each shelf= 731÷9= 81 (approx)

Common Core – Page No. 226

Question 1. Jamal is planting seeds for a garden nursery. He plants 9 seeds in each container. If Jamal has 296 seeds to plant, about how many containers will he use? Options: a. about 20 b. about 30 c. about 200 d. about 300

Answer: b. about 30

Explanation: Total number of seeds Jamal has= 296 Number of seeds placed in each container= 9 Number of containers Jamal used= 296÷9= 32.8=33 (approx) Therefore, the number of containers used is about 30

Question 2. Winona purchased a set of vintage beads. There are 2,140 beads in the set. If she uses the beads to make bracelets that have 7 beads each, about how many bracelets can she make? Options: a. about 30 b. about 140 c. about 300 d. about 14,000

Answer: c. about 300

Explanation: Total number of beads Winona has= 2,140 Number of beads in each bracelet= 7 Number of bracelets made= 2,140÷7=305.7=306(approx) Therefore, the number of bracelets made are about 30

Question 3. A train traveled 360 miles in 6 hours. How many miles per hour did the train travel? Options: a. 60 miles per hour b. 66 miles per hour c. 70 miles per hour d. 600 miles per hour

Answer: a. 60 miles per hour

Explanation: Total number of miles travelled by the train= 360 Time taken by the train to cover 360 miles= 6 hours Number of miles travelled in each hour= 360÷6=60 miles

Go Math Workbook Grade 4 Chapter 4 Multiply With One Digit Numbers Question 4. An orchard has 12 rows of pear trees. Each row has 15 pear trees. How many pear trees are there in the orchard? Options: a. 170 b. 180 c. 185 d. 190

Answer: b. 180

Explanation: Number of rows of pear trees in an orchard= 12 Number of pear trees in each row=15 Total number of pear trees in the orchard= 12 x 15=180

Question 5. Megan rounded 366,458 to 370,000. To which place did Megan round the number? Options: a. hundred thousand b. ten thousand c. thousands d. hundreds

Answer: b. ten thousand

Explanation: The given number is 366,458, the ten thousand place digit has 6 which while rounding off should be changed to the next consecutive number and the digits in the other places should be written as zeroes.

Question 6. Mr. Jessup, an airline pilot, flies 1,350 miles a day. How many miles will he fly in 8 days? Options: a. 1,358 miles b. 8,400 miles c. 10,800 miles d. 13,508 miles

Answer: c. 10,800 miles

Explanation: Number of miles flew by Mr.Jessup in one day= 1,350 miles Number of days=8 Total number of miles flew by Mr.Jessup in 8 days= 1,350 x 8= 10,800 miles

Page No. 229

Model the division on the grid.

Answer: 26 ÷ 2 = (20 ÷ 2) + (6 ÷ 2) = 10 + 3 = 13

Explanation: A. Outline a rectangle on a grid to model 26 ÷ 2. Shade columns of 2 until you have 26 squares. How many groups of 2 can you make? B. Think of 26 as 20 + 6. Break apart the model into two rectangles to show (20 + 6 ) ÷ 2. Label and shade the smaller rectangles. Use two different colours. C. Each rectangle models a division. 26 ÷ 2 = (20÷ 2 ) + (6÷ 2) = 10+ 3 = 13

Answer: 45 ÷ 3 = (15 ÷ 3) + (30 ÷ 3) = 5 + 10 = 15

Explanation: A. Outline a rectangle on a grid to model 45 ÷ 3. Shade columns of 3 until you have 45 squares. How many groups of 3 can you make? _ B. Think of 45 as 15 + 30. Break apart the model into two rectangles to show (15 + 30 ) ÷ 3. Label and shade the smaller rectangles. Use two different colours. C. Each rectangle models a division. 45 ÷ 3 = (15÷ 3 ) + (30÷ 3 ) = 5 + 10 = 15

Question 3. 82 ÷ 2 = (□ ÷ 2) + (□ ÷ 2) = □ + □ = □ ______

Answer: 82 ÷ 2 = (80 ÷ 2) + ( 2÷ 2) = 40 + 1 = 41

Explanation: A. Outline a rectangle on a grid to model 82 ÷ 2. Shade columns of 2 until you have 80 squares. How many groups of 2 can you make? B. Think of 82 as 80 + 2. Break apart the model into two rectangles to show (80 + 2 ) ÷ 2. Label and shade the smaller rectangles. Use two different colors. C. Each rectangle models a division. 82 ÷ 2 = (80 ÷ 2 ) + (2÷ 2) = 40 + 1 = 41

Question 4. 208 ÷ 4 = (□ ÷ 4) + (□ ÷ 4) = □ + □ = □ ______

Answer: 208 ÷ 4 = (200 ÷ 4) + (8 ÷ 4) = 50 + 4 = 54

Explanation: A. Outline another model to show 208 ÷ 4. How many groups of 4 can you make? B. Think of 208 as 200 + 8. Break apart the model, label, and shade to show two divisions. 208 ÷ 4 = (200 ÷ 4 ) + (8 ÷ 4 ) = 50 + 4 = 54

Use base-ten blocks to model the quotient. Then record the quotient.

Question 5. 88 ÷ 4 = ______

Question 6. 36 ÷ 3 = ______

Question 7. 186 ÷ 6 = ______

Question 8. Explain how you can model finding quotients using the Distributive Property. Type below: _________

Answer: We can use the Distributive Property to break apart numbers to make them easier to divide.

Explanation: 50 The Distributive Property of division says that dividing a sum by a number is the same as dividing each addend by the number and then adding the quotients.

Question 9. Justin earned $50 mowing lawns and $34 washing cars. He wants to divide his money into 3 equal accounts. How much will he put in each account? Explain. $ ______

Answer: $28

Explanation: The amount earned by Justin on mowing lawns=$50 The amount earned by Justin on washing cars=$34 Total amount earned=$50 + $34= $84 Number of parts into which he wanted to divide the amount he earned= 3 The amount put in each account= $84 ÷ 3 = $28

Answer: Question: How many candles are there in the gift shop?

Explanation: Count the number of candles in the rows and columns and then multiply them, by this we can find out the total number of candles in the gift shop.

Describe how you could change the problem by changing the number of rows of candles. Then solve the problem. Type below: _________

Answer: There will be no change in the solution by changing the number of rows of candles.

Explanation: By changing the number of rows of candles the number of columns increase but there will be no change in the total number of candles.

Question 11. For 11a–11d, choose Yes or No to indicate if the expression shows a way to break apart the dividend to find the quotient 147 ÷ 7. a. (135 ÷ 7) + (10 ÷ 7) i. yes ii. no

Explanation: Because 137+10 is not equal to 147

Question 11. b. (147 ÷ 3) + (147 ÷ 4) i. yes ii. no

Explanation: Because according to the distributive property we need to divide the dividend into two parts, but not the divisor.

Question 11. c. (140 ÷ 7) + (7 ÷ 7) i. yes ii. no

Explanation: 147 ÷ 7 STEP1 Find the nearest estimates of the number 147 STEP2 We can break the number 147 into 140 + 7 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (140 ÷ 7) + (7 ÷ 7) STEP5 Add quotients of the above 20 +1= 21

Question 11. d. (70 ÷ 7) + (77 ÷ 7) i. yes ii. no

Explanation: 147 ÷ 7 STEP1 Find the nearest estimates of the number 147 STEP2 We can break the number 147 into 70 + 77 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (70 ÷ 7) + (77 ÷ 7) STEP5 Add quotients of the above 10 +11= 21

Common Core – Page No. 231

Division and the Distributive Property

Explanation: 54 ÷ 3 STEP1 Find the nearest estimates of the number 54 STEP2 We can break the number 54 into 30 + 24 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (30 ÷ 3) + (24÷ 3) STEP5 Add quotients of the above 10 +8= 18

Question 2. 81 ÷ 3 = ______

Explanation: 81 ÷ 3 STEP1 Find the nearest estimates of the number 81 STEP2 We can break the number 81 into 21 + 60 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (60 ÷ 3) + (21 ÷ 3) STEP5 Add quotients of the above 20 +7= 27

Question 3. 232 ÷ 4 = ______

Explanation: 232 ÷ 4 STEP1 Find the nearest estimates of the number 232 STEP2 We can break the number 232 into 200 + 32 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (200 ÷ 4) + (32 ÷ 4) STEP5 Add quotients of the above 50 +8= 58

Question 4. 305 ÷ 5 = ______

Explanation: 305 ÷ 5 STEP1 Find the nearest estimates of the number 305 STEP2 We can break the number 305 into 300 + 5 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (300 ÷ 5) + (5 ÷ 5) STEP5 Add quotients of the above 60 +1= 61

Place The First Digit Lesson 4.10 Answer Key Question 5. 246 ÷ 6 = ______

Explanation: 246 ÷ 6 STEP1 Find the nearest estimates of the number 246 STEP2 We can break the number 246 into 240 + 6 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (240 ÷ 6) + (6 ÷ 6) STEP5 Add quotients of the above 40 +1= 41

Question 6. 69 ÷ 3 = ______

Explanation: 69 ÷ 3 STEP1 Find the nearest estimates of the number 69 STEP2 We can break the number 69 into 60 + 9 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (60 ÷ 3) + (9 ÷ 3) STEP5 Add quotients of the above 20 +3= 23

Question 7. 477 ÷ 9 = ______

Explanation: 477 ÷ 9 STEP1 Find the nearest estimates of the number 477 STEP2 We can break the number 477 into 450 + 27 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (450 ÷ 9) + (27 ÷ 9) STEP5 Add quotients of the above 50 +3= 53

Question 8. 224 ÷ 7 = ______

Explanation: 224 ÷ 7 STEP1 Find the nearest estimates of the number 224 STEP2 We can break the number 224 into 210 + 14 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (210 ÷ 7) + (14 ÷ 7) STEP5 Add quotients of the above 30 +2= 32

Question 9. 72 ÷ 4 = ______

Explanation: 72 ÷ 4 STEP1 Find the nearest estimates of the number 72 STEP2 We can break the number 72 into 40 + 32 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (40 ÷ 4) + (32 ÷ 4) STEP5 Add quotients of the above 10 +8= 18

Question 10. 315 ÷ 3 = ______

Answer: 105

Explanation: 315 ÷ 3 STEP1 Find the nearest estimates of the number 315 STEP2 We can break the number 315 into 300 + 15 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (300 ÷ 3) + (15 ÷3) STEP5 Add quotients of the above 100 +5= 105

Question 11. Cecily picked 219 apples. She divided the apples equally into 3 baskets. How many apples are in each basket? ______ apples

Answer: 73 apples

Explanation: The total number of apples Cecily picked= 219 apples Number of parts into which she wanted to divide the apples= 3 Number of apples in each part = Quotient of 147 ÷ 7 STEP1 Find the nearest estimates of the number 219 STEP2 We can break the number 219 into 210 + 9 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (210 ÷ 3) + (9 ÷ 3) STEP5 Add quotients of the above 70 +3= 73

Question 12. Jordan has 260 basketball cards. He divides them into 4 equal groups. How many cards are in each group? ______ cards

Answer: 65 cards

Explanation: The total number of basketball cards Jordan has= 260 basketball cards Number of parts into which he wanted to divide the cards= 4 Number of apples in each part = Quotient of 260 ÷ 4 STEP1 Find the nearest estimates of the number 260 STEP2 We can break the number 260 into 240 + 20 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (240 ÷ 4) + (20 ÷ 4) STEP5 Add quotients of the above 60 +5= 65

Question 13. The Wilsons drove 324 miles in 6 hours. If they drove the same number of miles each hour, how many miles did they drive in 1 hour? ______ miles

Answer: 54 miles

Explanation: The total number of miles drove by Wilson= 324 miles Number of hours he drove = 6 Number of miles drove in each hour = Quotient of 324 ÷ 6 STEP1 Find the nearest estimates of the number 324 STEP2 We can break the number 324 into 300 + 24 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (300 ÷ 6) + (24 ÷ 6) STEP5 Add quotients of the above 50 +4= 54

Question 14. Phil has 189 stamps to put into his stamp album. He puts the same number of stamps on each of 9 pages. How many stamps does Phil put on each page? ______ stamps

Answer: 21 stamps

Explanation: The total number of stamps Phil has= 189 stamps Number of pages= 9 Number of stamps put on each page  = Quotient of 189 ÷ 9 STEP1 Find the nearest estimates of the number 189 STEP2 We can break the number 189 into 180 + 9 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (180 ÷ 9) + (9 ÷ 9) STEP5 Add quotients of the above 20 +1= 21

Common Core – Page No. 232

Question 1. A landscaping company planted 176 trees in 8 equal rows in the new park. How many trees did the company plant in each row? Options: a. 18 b. 20 c. 22 d. 24

Answer: c. 22

Explanation: The total number of trees in the landscaping= 176 trees Number of rows= 8 Number of trees in each row = Quotient of 176 ÷ 8 STEP1 Find the nearest estimates of the number 176 STEP2 We can break the number 176 into 160 + 16 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (160 ÷ 8) + (16 ÷ 8) STEP5 Add quotients of the above 20 +2= 22

Question 2. Arnold can do 65 pushups in 5 minutes. How many pushups can he do in 1 minute? Options: a. 11 b. 13 c. 15 d. 17

Answer: b. 13

Explanation: The total number of pushups done by Arnold = 65 Number of minutes spent on pushups= 5 Number of pushups done in each minute = Quotient of 65 ÷ 5 STEP1 Find the nearest estimates of the number 65 STEP2 We can break the number 65 into 60 + 5 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (60 ÷ 5) + (5 ÷ 5) STEP5 Add quotients of the above 12 +1= 13

Question 3. Last Saturday, there were 1,486 people at the Cineplex. There were about the same number of people in each of the 6 theaters. Which is the best estimate of the number of people in each theater? Options: a. between 20 and 30 b. between 80 and 90 c. between 100 and 200 d. between 200 and 300

Answer: d. between 200 and 300

Explanation: Total number of people at the Cineplex= 1,486 people Number of theatres =  6 Number of people at each theatre= estimate of the number of people 1,486 ÷ 6

What number close to 1,486 is easy to divide by 6? 1,488 is close to 1,486. What basic fact can you use? 1,488 ÷ 6 Choose 1,488 because it is close to 1,486 and can easily be divided by 6. 1,488 ÷ 6 = 248 1,486 ÷ 6 is about 248

What number close to 1,486 is easy to divide by 6? 1,482 is close to 1,486. What basic fact can you use? 1,482 ÷ 6 Choose 1,482 because it is close to 1,486 and can easily be divided by 6. 1,482 ÷ 6 = 247 1,486 ÷ 6 is about 247

Question 4. Nancy walked 50 minutes each day for 4 days last week. Gillian walked 35 minutes each day for 6 days last week. Which statement is true? Options: a. Gillian walked 10 minutes more than Nancy. b. Gillian walked 20 minutes more than Nancy. c. Nancy walked 10 minutes more than Gillian. d. Nancy walked 15 minutes more than Gillian.

Answer: d. Nancy walked 15 minutes more than Gillian.

Explanation: Time walked by Nancy= 50 minutes Time walked by Gillian= 35 minutes Nancy walked more time compared to Gillian 50-35=15 minutes Therefore,  Nancy walked 15 minutes more than Gillian.

Question 5. Three boys share 28 toy cars equally. Which best describes how the cars are shared? Options: a. Each gets 3 cars with 1 left over. b. Each gets 8 cars with 2 left over. c. Each gets 9 cars with 1 left over. d. Each gets 10 cars with 2 left over.

Answer: c. Each gets 9 cars with 1 left over.

Explanation: Total number of toys three boys have= 28 Number of toys each boy got= 28 ÷3=9.33 Therefore we can say that each gets 9 cars with 1 leftover.

Question 6. An airplane flies at a speed of 474 miles per hour. How many miles does the plane fly in 5 hours? Options: a. 2,070 miles b. 2,140 miles c. 2,370 miles d. 2,730 miles

Answer: c. 2,370 miles

Explanation: Number of miles flew by aeroplane in one hour= 474 Number of hours the aeroplane flew= 5 hours Total number of miles flew in 5 hours= 474 x 5=  2,370 miles

Page No. 233

Question 1. A number that is the product of a number and a counting number is called a _____________. ___________

Answer: Multiple

Explanation: 3 x 4 = 12 In which 4 is a multiple and also 4 is a counting number

Question 2. Numbers that are easy to compute mentally are called _____________. ___________

Answer: Compatible numbers

Explanation: Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally. When using estimation to approximate a calculation, replace actual numbers with compatible numbers.

Question 3. When a number cannot be divided evenly, the amount left over is called the _____________. ___________

Answer: Remainder

Explanation: When we divide 10 with 3 there will be 1 remaining, which is called remainder.

Question 4. 26 ÷ 3 _____ R _____

Answer: Quotient: 8 Remainder: 2

Quotient: A. Use 26 counters to represent the 26 dominoes. Then draw 3 circles to represent the divisor. B. Share the counters equally among the 8 groups by placing them in the circles. C. Number of circles filled= quotient of 26 ÷ 3 = 8

Question 5. 19 ÷ 4 _____ R _____

Answer: Quotient: 4 Remainder: 3

Quotient: A. Use 19 counters to represent the 19 dominoes. Then draw 4 circles to represent the divisor. B. Share the counters equally among the 4 groups by placing them in the circles. C. Number of circles filled= quotient of 19 ÷ 4 = 4

Question 6. 810 ÷ 9 = _____

Explanation: STEP 1 Identify the basic fact. 81 ÷ 9 STEP 2 Use place value. 810 = 81 tens STEP 3 Divide. 81 tens ÷ 9 = 9 tens 810 ÷ 9 = 90

Question 7. 210 ÷ 7 = _____

Explanation: STEP 1 Identify the basic fact. 21 ÷ 7 STEP 2 Use place value. 210 = 21 tens STEP 3 Divide. 21 tens ÷ 7 = 3 tens 210 ÷ 7 = 30

Question 8. 3,000 ÷ 6 = _____

Explanation: STEP 1 Identify the basic fact. 30 ÷ 6 STEP 2 Use place value. 3,000 = 30 hundreds STEP 3 Divide. 30 hundreds ÷ 6 = 5 hundreds 3,000 ÷ 6 = 500

Question 9. 635 ÷ 9 about _____

Explanation: What number close to 635 is easy to divide by 9? 630 is close to 635. What basic fact can you use? 630 ÷ 9 Choose 630 because it is close to 635 and can easily be divided by 9. 63 ÷ 9 = 7 630 ÷ 9 = 70 635 ÷ 9 is about 70

Question 10. 412 ÷ 5 about _____

Explanation: What number close to 412 is easy to divide by 5? 410 is close to 412. What basic fact can you use? 410 ÷ 5 Choose 410 because it is close to 412 and can easily be divided by 5. 410 ÷ 5 = 82 412 ÷ 5 is about 82

Question 11. 490 ÷ 8 about _____

Explanation: What number close to 490 is easy to divide by 8? 480 is close to 490. What basic fact can you use? 480 ÷ 8 Choose 480 because it is close to 490 and can easily be divided by 8. 48 ÷ 8 = 6 480 ÷ 8 = 60 490 ÷ 8 is about 60

Use grid paper or base-ten blocks to model the quotient. Then record the quotient.

Question 12. 63 ÷ 3 = _____

Question 13. 85 ÷ 5 = _____

Question 14. 168 ÷ 8 = _____

Page No. 234

Question 15. Ana has 296 coins in her coin collection. She put the same number of coins in each of 7 jars. About how many coins are in each jar? about _____ coins

Explanation: The total number of coins Ana has= 296 coins Number of Jars= 7 Number of coins in each Jar= 296 ÷ 7 = 42 coins

Question 16. Which two estimates is the quotient 345 ÷ 8 between? _____ and _____

Answer: The quotient is between 42 and 43

What number close to 345 is easy to divide by 8? 336 is close to 1,624. What basic fact can you use? 336 ÷ 8 Choose 336  because it is close to 345 and can easily be divided by 8. 336 ÷ 8 = 42 345 ÷ 8 is about 42

What number close to 345 is easy to divide by 8? 344 is close to 345. What basic fact can you use? 344 ÷ 8 Choose 344 because it is close to 345 and can easily be divided by 8. 344 ÷ 8 = 43 345 ÷ 8 is about 43

Go Math Grade 4 Chapter 4 Mid Chapter Checkpoint Answer Key Question 17. A total of 8,644 people went to the football game. Of those people, 5,100 sat on the home side and the rest sat on the visitor’s side. If the people sitting on the visitor’s side filled 8 equal-sized sections, how many people sat in each of the sections? about _____ people

Answer: 443

Explanation: Total number of people in the football game= 8,644 Number of people who sat on the homeside= 5,100 Number of people who sat on the visitor’s side= 3,544 Number of equal-sized sections= 8 Number of people who sat in each of the sections= 3,544 ÷ 8= 443

Question 18. There are 4 students on a team for a relay race. How many teams can be made from 27 students? _____ teams

Explanation: The total number of students= 27 Number of students in each team= 4 Number of teams = 27 ÷ 4= 6.75 = 7 (approx)

Question 19. Eight teams of high school students helped clean up trash in the community. Afterwards, they shared 23 pizzas equally. How many pizzas did each team get? _____ \(\frac{ □ }{ □ }\)

Explanation: Total number of pizzas= 23 Number of teams= 8 Number of pizzas each team got= 23 ÷ 8=2.8=3(approx)

Page No. 237

Use repeated subtraction to divide.

Question 1. 84 ÷ 7 _____

Explanation: A. Begin with 84 counters. Subtract 7 counters. B. Subtract 7 counters from 84 and repeat the processes until the remainder cannot be subtracted from the divisor. C. Record the number of counters left and the number of times you subtracted. D. The number of times you subtracted is the quotient is 12.

Question 2. 60 ÷ 4 _____

Explanation: A. Begin with 60 counters. Subtract 4 counters. B. Subtract 4 counters from 60 and repeat the processes until the remainder cannot be subtracted from the divisor. C. Record the number of counters left and the number of times you subtracted. D. The number of times you subtracted is the quotient is 15.

Question 3. 91 ÷ 8 _____ R _____

Answer: 11.3=11(approx)

Explanation: A. Begin with 91 counters. Subtract 8 counters. B. Subtract 8 counters from 91 and repeat the processes until the remainder cannot be subtracted from the divisor. C. Record the number of counters left and the number of times you subtracted. D. The number of times you subtracted is the quotient is 11

Draw a number line to divide.

Question 4. 65 ÷ 5 = _____

Explanation: A. Begin with 65 counters. Subtract 5 counters. B. Subtract 5 counters from 65 and repeat the processes until the remainder cannot be subtracted from the divisor. C. Record the number of counters left and the number of times you subtracted. D. The number of times you subtracted is the quotient is 13

Answer: 11 (approx)

Explanation: How many equal groups of 3 did you subtract? So, 32 ÷ 3 = 10.8=11(approx).

Question 6. John has $40 to spend at the yard sale. He buys 6 books for $2 each. He would like to spend the rest of his money on model cars for his collection. If the cars cost $7 each, how many can he buy? Explain. _____ cars

Answer: 4 cars

Explanation: Total amount John spent at the yard sale= $40 Number of books= 6 Cost of each book= $2 Cost of 6 books= 6 x $2 = $12 Amount left after John bought 6 books= $40 – $12 = $28 Cost of each car= $7 Number of cars bought = $28 ÷ $7 = $4

Page No. 238

Explanation: A. Begin with 108 counters. Subtract 9 counters. B. Subtract 9 counters from 108 and repeat the processes until the remainder cannot be subtracted from the divisor. C. Record the number of counters left and the number of times you subtracted. D. The number of times you subtracted is the quotient is 12.

Question 7. b. How can you use repeated subtraction to solve the problem? Type below: __________

Answer: Repeated subtraction is a method to solve and find the quotient.

Explanation: Example: A. Begin with 65 counters. Subtract 5 counters. B. Subtract 5 counters from 65 and repeat the processes until the remainder cannot be subtracted from the divisor. C. Record the number of counters left and the number of times you subtracted. D. The number of times you subtracted is the quotient is 13

Question 7. c. Tell why you might use multiples of the divisor to solve the problem. Type below: __________

Answer: The multiple which divides 108 is 12

Explanation: The number 108 has multiples which divide 108 evenly, 1 x 108 =108 2 x 54   =108 3 x 36   =108 4 x 27   =108 6 x 18   =108 9 x  12  =108 12 x 9   =108 18 x 6   =108 27 x 4   =108 36 x 3   =108 54 x 2   =108 108 x 1   =108 Multiples which divide 108 are 1,2,3,4,5,6,9,12,18,27,36,54,108.

Question 7. d. Show steps to solve the problem. Type below: __________

Answer: 108 ÷ 9 =12

Explanation: A. Begin with 108 counters. Subtract 9 counters. B. Subtract 9 counters from 108 and repeat the processes until the remainder cannot be subtracted from the divisor. C. Record the number of counters left and the number of times you subtracted. D. The number of times you subtracted is the quotient is 12

Question 7. e. Complete the sentences. There are _______ equal parts of the playground, each _______ feet long. So, _______ climbers can fit along the length of the playground. Type below: __________

Answer: There are ___108____ equal parts of the playground, each __09_____ feet long. So, __12_____ climbers can fit along the length of the playground.

Explanation: A new playground will be 108 feet long. Builders need to allow 9 feet of space for each piece of climbing equipment. Number of climbers that can fit along the length of the playground= 108 ÷ 9 =12

Answer: 240 ÷ 80 expression resembles the second model while 240 ÷ 60 expression resembles the first model.

Explanation: 240 ÷ 80 A. Draw a number line with 80 as each interval. B. Draw up to 240 and count the intervals, it gives the quotient. C. The quotient is 3 240 ÷ 60 A. Draw a number line with 60 as each interval. B. Draw up to 240 and count the intervals, it gives the quotient. C. The quotient is 4

Common Core – Page No. 239

Divide Using Repeated Subtraction Use repeated subtraction to divide.

Question 1. 42 ÷ 3 = 14 3)\(\overline { 42 } \) -30 ← 10 × 3 | 10 ——- 12 -12 ← 4 × 3 | +4 ——-    ———– 0             14

Explanation: A. Begin with 42 counters. Subtract 3 counters. B. Subtract 3 counters from 42 and repeat the processes until the remainder cannot be subtracted from the divisor. C. Record the number of counters left and the number of times you subtracted. D. The number of times you subtracted is the quotient is 14

Question 2. 72 ÷ 4 = _____

Explanation: A. Begin with 72 counters. Subtract 4 counters. B. Subtract 4 counters from 72 and repeat the processes until the remainder cannot be subtracted from the divisor. C. Record the number of counters left and the number of times you subtracted. D. The number of times you subtracted is the quotient is 18

Question 3. 93 ÷ 3 = _____

Explanation: A. Begin with 93 counters. Subtract 3 counters. B. Subtract 3 counters from 93 and repeat the processes until the remainder cannot be subtracted from the divisor. C. Record the number of counters left and the number of times you subtracted. D. The number of times you subtracted is the quotient is 31

Question 4. 35 ÷ 4 = _____ r _____

Answer: 8r3

Quotient: A. Use 35 counters to represent the 35 dominoes. Then draw 4 circles to represent the divisor. B. Share the counters equally among the 4 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 35 ÷ 4 D. Number of circles are equally filled with 4 counters, therefore, the quotient is 8

For 35 ÷ 4, the quotient is 8 and the remainder is 3, or 8 r3.

Question 5. 93 ÷ 10 = _____ r _____

Answer: 9r3

Quotient: A. Use 93 counters to represent the 93 dominoes. Then draw 10 circles to represent the divisor. B. Share the counters equally among the 10 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 93 ÷ 10 D. Number of circles are equally filled with 10 counters, therefore, the quotient is 9

For 93 ÷ 10, the quotient is 9 and the remainder is 3, or 9 r3.

Question 6. 86 ÷ 9 = _____ r _____

Answer: 9r5

Quotient: A. Use 86 counters to represent the 86 dominoes. Then draw 9 circles to represent the divisor. B. Share the counters equally among the 9 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 86 ÷ 9 D. Number of circles are equally filled with 9 counters, therefore, the quotient is 9

For 86 ÷ 9, the quotient is 9 and the remainder is 5, or 9 r5.

Question 7. 70 ÷ 5 = _____

Explanation: A. Draw a number line with 5 as each interval. B. Draw up to 70 and count the intervals, it gives the quotient. C. The quotient is 14

Question 8. Gretchen has 48 small shells. She uses 2 shells to make one pair of earrings. How many pairs of earrings can she make? _____ pairs

Answer: 24 pairs

Explanation: Total number of small shells= 48 Number of shells used to make one pair of earrings = 2 Number of pair of earrings made = 48 ÷ 2 =24

Question 9. James wants to purchase a telescope for $54. If he saves $3 per week, in how many weeks will he have saved enough to purchase the telescope? _____ weeks

Answer: $18

Explanation: Cost of the telescope=$54 Amount saved each week = $3 Number of weeks he has to save the money to purchase the telescope = $54 ÷ $3 = $18

Common Core – Page No. 240

Question 1. Randall collects postcards that his friends send him when they travel. He can put 6 cards on one scrapbook page. How many pages does Randall need to fit 42 postcards? Options: a. 3 b. 4 c. 6 d. 7

Explanation: Total number of postcards Randall has = 42 postcards Number of postcards on one scrapbook page = 6 cards Number of pages needed to fit the postcards = 42 ÷ 6=7

Question 2. Ari stocks shelves at a grocery store. He puts 35 cans of juice on each shelf. The shelf has 4 equal rows and another row with only 3 cans. How many cans are in each of the equal rows? Options: a. 6 b. 7 c. 8 d. 9

Answer: c. 8

Explanation: Total number of cans of juice on each shelf = 35 Number of rows = 4 Number of cans on the other shelf = 3 Number of cans placed on the first shelf = 35 – 3 = 32 Number of juice cans in the first row = 32 ÷ 4 = 8 cans

Question 3. Fiona sorted her CDs into separate bins. She placed 4 CDs in each bin. If she has 160 CDs, how many bins did she fill? Options: a. 4 b. 16 c. 40 d. 156

Answer: c. 40

Explanation: Total number of CD’s in Fiona has = 160 CD’s Number of CD’s placed in each bin = 4 Number of bins required to place the CD’s = 160 ÷ 4 = 40

Question 4. Eamon is arranging 39 books on 3 shelves. If he puts the same number of books on each shelf, how many books will there be on each shelf? Options: a. 11 b. 12 c. 13 d. 14

Answer: c. 13

Explanation: Total number of books Eamon has = 39 books Number of shelves = 3 Number of books in each shelf = 39 ÷ 3 = 13

Question 5. A newborn boa constrictor measures 18 inches long. An adult boa constrictor measures 9 times the length of the newborn plus 2 inches. How long is the adult? Options: a. 142 inches b. 162 inches c. 164 inches d. 172 inches

Answer: c. 164 inches

Explanation: Length of newborn boa constrictor = 18 inches Length of an adult boa constrictor = 9 x Length of newborn boa constrictor = 9 x 18 = 162 Total length of an adult boa constrictor = 162 + 2 = 164 inches

Question 6. Madison has 6 rolls of coins. Each roll has 20 coins. How many coins does Madison have in all? Options: a. 110 b. 120 c. 125 d. 130

Answer: b. 120

Explanation: Number of rolls of coins = 6 Number of coins in each roll = 20 Total number of coins Madison has = 20 x 6 = 120

Answer: 37 yards (approx)

Explanation: STEP 1 Start by subtracting a greater multiple, such as 100 times the divisor. For example, you know that you can make at least 100 ft which is long 33 yards. Continue subtracting until the remaining number is less than the multiple, 3. STEP 2 Subtract smaller multiples, such as 3 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 110 ft =  110 ÷ 3 = 36.6 yards = 37 yards (approx).

Divide. Use partial quotients.

Question 2. 3)\(\overline { 225 } \) ____

Explanation: STEP 1 Start by subtracting a greater multiple, such as 50 times the divisor. Continue subtracting until the remaining number is less than the multiple, 3. STEP 2 Subtract smaller multiples, such as 3 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 50 x 3 = 150 : 225 – 150 = 75 3 x 25 = 75 : 75 – 75 = 0 Therefore the quotient is 75 ( 50 + 25)

Divide. Use rectangular models to record the partial quotients.

Question 3. 428 ÷ 4 = ____

Answer: 107

Question 4. 7)\(\overline { 224 } \) ____

Explanation: STEP 1 Start by subtracting a greater multiple, such as 30 times the divisor. Continue subtracting until the remaining number is less than the multiple, 7. STEP 2 Subtract smaller multiples, such as 7 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 30 x 7 = 210 : 224 – 210 = 14 7 x 2 = 14 : 14 – 14 = 0 Therefore the quotient is 32 ( 30 + 2)

Question 5. 7)\(\overline { 259 } \) ____

Explanation: STEP 1 Start by subtracting a greater multiple, such as 30 times the divisor. Continue subtracting until the remaining number is less than the multiple, 7. STEP 2 Subtract smaller multiples, such as 7 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 30 x 7 = 210 : 225 – 210 = 49 7 x 7 = 49 : 49 – 49 = 0 Therefore the quotient is 37 ( 30 + 7)

Question 6. 8)\(\overline { 864 } \) ____

Answer: 108

Explanation: STEP 1 Start by subtracting a greater multiple, such as 100 times the divisor. Continue subtracting until the remaining number is less than the multiple, 8. STEP 2 Subtract smaller multiples, such as 8 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 100 x 8 = 800 : 864 – 800 = 64 8 x 8 = 64 : 64 – 64 = 0 Therefore the quotient is 108 ( 100 + 8)

Question 7. 6)\(\overline { 738 } \) ____

Answer: 123

Explanation: STEP 1 Start by subtracting a greater multiple, such as 100 times the divisor. Continue subtracting until the remaining number is less than the multiple, 6. STEP 2 Subtract smaller multiples, such as 6 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 100 x 6 = 600 : 738 – 600 = 138 6 x 23 = 138 : 138 – 138 = 0 Therefore the quotient is 123 ( 100 + 23)

Question 8. 328 ÷ 2 = ____

Answer: 164

Question 9. 475 ÷ 5 = ____

Question 10. 219 ÷ 3 = ____

Question 11. 488 ÷ 4 = ____

Answer: 122

Question 12. Use Reasoning What is the least number you can divide by 5 to get a three-digit quotient? Explain how you found your answer. ____

Answer: The quotient can be a three-digit number or a two-digit number.

Explanation: Example:

475 ÷ 5 = ____

Explanation: STEP 1 Start by subtracting a greater multiple, such as 90 times the divisor. Continue subtracting until the remaining number is less than the multiple, 5. STEP 2 Subtract smaller multiples, such as 5 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 90 x 5 = 450 : 475 – 450 = 25 5 x 5 = 25 : 25 – 25 = 0 Therefore the quotient is 95 (90 + 5)

Question 13. Rob wants to put 8 baseball cards on each page in an album. How many pages will he fill? ____ pages

Answer: 31 pages

Explanation: Total number of baseball cards = 248 Number of cards in each page = 8 Number of pages required = 248 ÷ 8 = 31 pages

Question 14. Rob filled 5 plastic boxes with hockey cards. There were the same number of cards in each box. How many cards did he put in each box? How many cards were left over? Type below: ___________

Answer: There where 12 hockey cards in each box, number of cards leftover = 4

Explanation: Total number of hockey cards = 64 Number of boxes = 5 Number of cards in each box = 64 ÷ 5 = 12.8 that is exactly 60 cards can be fit in 5 boxes and 12 in each box Number of cards leftover = 64 – 60 = 4

Question 15. Rob filled 3 fewer plastic boxes with football cards than basketball cards. He filled 9 boxes with basketball cards. How many boxes did he fill with football cards? How many football cards were in each box? ____ boxes ____ cards

Answer: 6 boxes and 16 cards in each box

Explanation: Number of basketball cards= 189 Number of boxes in which the basketball cards were kept= 9 boxes Number of football cards= 96 Number of boxes in which the football cards were kept =  number of boxes in which the basketball cards were kept – 3 = 9-3=6boxes Number of football cards in each box = 96 ÷ 6 =16 cards

Question 16. Marshall can buy 5 T-shirts for $60. If each shirt costs the same amount, what is the cost of 4 T-shirts? $ ____

Answer: $48

Explanation: Number of T-shirts = 5 Cost of 5 T-shirts = $60 Cost of each T- shirt = $60 ÷ 5 = $12 Cost of 4 T-shirts = 12 x 4 = $48

Explanation: STEP 1 Start by subtracting a greater multiple, such as 80 times the divisor. Continue subtracting until the remaining number is less than the multiple, 5. STEP 2 Subtract smaller multiples, such as 5 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 80 x 5 = 400 : 485 – 400 = 85 5 x 17 = 85 : 85 – 85 = 0 Therefore the quotient is 97 ( 80 + 17)

Common Core – Page No. 245

Divide Using Partial Quotients Divide. Use partial quotients.

Question 1. 8)\(\overline { 184 } \) -80 ← 10 × 8 10 ——- 104 -80 ← 10 × 8 + 10 ——- -24 -24 ← 3 × 8 + 3 ——– ——– 0 23

Explanation: STEP 1 Start by subtracting a greater multiple, such as 10 times the divisor. Continue subtracting until the remaining number is less than the multiple, 8. STEP 2 Subtract smaller multiples, such as 10 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 10 x 8 = 80 : 184 – 80 = 104 10 x 8 = 80 : 104 – 80 = 24 : 3 x 8 = 24 : 24 – 24 = 0 Therefore the quotient is 23 ( 10 + 10 + 3)

Question 2. 6)\(\overline { 258 } \) _____

Explanation: STEP 1 Start by subtracting a greater multiple, such as 40 times the divisor. Continue subtracting until the remaining number is less than the multiple, 6. STEP 2 Subtract smaller multiples, such as 3 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 40 x 6 = 240 : 258 – 240 = 18 3 x 6 = 18 : 18 – 18 = 0 Therefore the quotient is 43 ( 40 + 3)

Question 3. 5)\(\overline { 630 } \) _____

Answer: 126

Explanation: STEP 1 Start by subtracting a greater multiple, such as 100 times the divisor. Continue subtracting until the remaining number is less than the multiple, 5. STEP 2 Subtract smaller multiples, such as 20 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 100 x 5 = 500 : 630 – 500 = 130 5 x 20 = 100 : 130 – 100 = 30 : 5 x 6 = 30 : 30 – 30 = 0 Therefore the quotient is 126 ( 100 + 20 + 6)

Question 4. 246 ÷ 3 = _____

Question 5. 126 ÷ 2 = _____

Question 6. 605 ÷ 5 = _____

Answer: 121

Divide. Use either way to record the partial quotients.

Question 7. 492 ÷ 3 = _____

Explanation: STEP 1 Start by subtracting a greater multiple, such as 100 times the divisor. Continue subtracting until the remaining number is less than the multiple, 3. STEP 2 Subtract smaller multiples, such as 50 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 100 x 3 = 300 : 492 – 300 = 192 50 x 3 = 150 : 192 – 150 = 42 : 3 x 14 = 42 : 42 – 42 = 0 Therefore the quotient is 164  ( 100 + 50 + 14)

Question 8. 224 ÷ 7 = _____

Explanation: STEP 1 Start by subtracting a greater multiple, such as 30 times the divisor. Continue subtracting until the remaining number is less than the multiple, 7. STEP 2 Subtract smaller multiples, such as 30 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 30 x 7 = 210 : 224 – 210 = 14 7 x 2 = 14 : 14 – 14 = 0 Therefore the quotient is 32 ( 30 + 2)

Question 9. 692 ÷ 4 = _____

Answer: 173

Explanation: STEP 1 Start by subtracting a greater multiple, such as 100 times the divisor. Continue subtracting until the remaining number is less than the multiple, 4. STEP 2 Subtract smaller multiples, such as 100 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 100 x 4 = 400 : 692 – 400 = 392 4 x 50 = 200 : 392 – 200 = 192 : 4 x 48 = 192 : 192 – 192 = 0 Therefore the quotient is 198 ( 100 + 50 + 48)

Question 10. Allison took 112 photos on vacation. She wants to put them in a photo album that holds 4 photos on each page. How many pages can she fill? _____ pages

Explanation: STEP 1 Start by subtracting a greater multiple, such as 20 times the divisor. Continue subtracting until the remaining number is less than the multiple, 4. STEP 2 Subtract smaller multiples, such as 20 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 20 x 4 = 80 : 112 – 80 = 32 4 x 8 = 32 : 32 – 32 = 0 Therefore the quotient is 28 ( 20 + 8)

Question 11. Hector saved $726 in 6 months. He saved the same amount each month. How much did Hector save each month? $ _____

Answer: $121

Explanation: STEP 1 Start by subtracting a greater multiple, such as 100 times the divisor. Continue subtracting until the remaining number is less than the multiple, 6. STEP 2 Subtract smaller multiples, such as 100 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 100 x 6 = 600 : 726 – 600 = 126 6 x 20 = 120 : 126 – 120 = 6 : 6 x 1 = 6 : 6 – 6 = 0 Therefore the quotient is 121 ( 100 + 20 +1)

Common Core – Page No. 246

Question 1. Annaka used partial quotients to divide 145 ÷ 5. Which shows a possible sum of partial quotients? Options: a. 50 + 50 + 45 b. 100 + 40 + 5 c. 10 + 10 + 9 d. 10 + 4 + 5

Answer: c. 10 + 10 + 9

Explanation: STEP 1 Start by subtracting a greater multiple, such as 100 times the divisor. Continue subtracting until the remaining number is less than the multiple, 4. STEP 2 Subtract smaller multiples, such as 10 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 10 x 5 = 50 : 145 – 50 = 95 5 x 10 = 50 : 95 – 50 = 45 : 5 x 9 = 45 : 45 – 45 = 0 Therefore the quotient is 29 ( 10 + 10 +9)

Question 2. Mel used partial quotients to find the quotient 378 ÷ 3. Which might show the partial quotients that Mel found? Options: a. 100, 10, 10, 9 b. 100, 10, 10, 6 c. 100, 30, 30, 6 d. 300, 70, 8

Answer: b. 100, 10, 10, 6

Explanation: STEP 1 Start by subtracting a greater multiple, such as 100 times the divisor. Continue subtracting until the remaining number is less than the multiple, 3. STEP 2 Subtract smaller multiples, such as 10 times the divisor until the remaining number is less than the divisor. In other words, keep going until you no longer a remainder is left in the place of the remainder. Then add the partial quotients to find the quotient. So, there are 100 x 3 = 300 : 378 – 300 = 78 10 x 3 =30 : 78 – 30 = 48 : 3 x 16 = 48 : 48 – 48 = 0 Therefore the quotient is 126 ( 100 + 10 +10 + 6)

Question 3. What are the partial products of 42 × 5? Options: a. 9 and 7 b. 20 and 10 c. 200 and 7 d. 200 and 10

Answer: d. 200 and 10

Explanation: STEP1 42 x 5 Start by multiplying the digit five with the units digit 2 = 5 x 2 =10 Multiply the digit 5 with 4 in the tens place = 4 x 5 = 20 Since 4 is in the tens place when we multiply 4 and 5 we must place it in the hundreds place by assuming units digit to be zero. Therefore, the partial product of 42 x 5 = 200

Question 4. Mr. Watson buys 4 gallons of paint that cost $34 per gallon. How much does Mr. Watson spend on paint? Options: a. $38 b. $126 c. $136 d. $1,216

Answer: c. $136

Explanation: Cost of each gallon of paint = $34 Number of gallons = 4 The total cost of the gallons = $ 34 x 4 = $136

Answer: d. 896

Question 6. An adult male lion eats about 108 pounds of meat per week. About how much meat does an adult male lion eat in one day? Options: a. about 14 pounds b. about 15 pounds c. about 16 pounds d. about 17 pounds

Answer: b. about 15 pounds

Explanation: Mass of meat an adult lion eats in one week = 108 Number of days in a week = 7 Mass of meat ate by the lion in one day = 108 ÷ 7 = 15.4 pounds = about 15 pounds

Divide. Use base-ten blocks.

Question 1. 48 ÷ 3 _____

Explanation: A. Draw 3 circles to represent the divisor. Then use base-ten blocks to model 48. Show 48 as 4 tens and 8 ones. B. Share the tens equally among the 3 groups. C. If there are any tens left, regroup them as ones. Share the ones equally among the 3 groups. D. There are 1 ten(s) and 6 one(s) in each group. So, the quotient is 16.

Question 2. 84 ÷ 4 _____

Explanation: A. Draw 4 circles to represent the divisor. Then use base-ten blocks to model 84. Show 84 as 8 tens and 4 ones. B. Share the tens equally among the 4 groups. C. If there are any tens left, regroup them as ones. Share the ones equally among the 4 groups. D. There are 2 ten(s) and 1 one(s) in each group. So, the quotient is 21.

Question 3. 72 ÷ 5 _____ R _____

Answer: 14 (approx) with 2 as remainder.

Explanation: A. Draw 5 circles to represent the divisor. Then use base-ten blocks to model 72. Show 72 as 7 tens and 2 ones. B. Share the tens equally among the 5 groups. C. If there are any tens left, regroup them as ones. Share the ones equally among the 5 groups. D. There are 1 ten(s) and 4 one(s) in each group. So, the quotient is 14.

Question 5. Explain why you did not need to regroup in Exercise 2. Type below: ___________

Answer: We did not regroup in exercise two because we used the method of counters in which we placed the counters one after the other in the circles and concluded with number of counters in each group and the number of counters left over.

Explanation: Example: 28 ÷ 3(in the form of exercise 2) A. Use 28 counters to represent the 28 dominoes. Then draw 3 circles to represent the 3 players. B. Share the counters equally among the 3 groups by placing them in the circles. C. Find the number of counters in each group and the number of counters left over. Record your answer. 9 counters in each group and 3 counters are leftover.

Example: 84 ÷ 3

A. Draw 3 circles to represent the divisor. Then use base-ten blocks to model 84. Show 84 as 8 tens and 4 ones. B. Share the tens equally among the 3 groups. C. If there are any tens left, regroup them as ones. Share the ones equally among the 3 groups. D. There are 2 ten(s) and 8 one(s) in each group. So, the quotient is 28.

Question 6. Mindy is preparing fruit boxes for gifts. She divides 36 apples evenly into 6 boxes. Then she divided 54 bananas evenly into the same 6 boxes. How many pieces of fruit are in each of Mindy’s boxes? _____ pieces of fruit

Answer: 6+9=15 pieces of fruits are in each box of Mindy’s

Explanation: Total number of apples = 36 Number of boxes in which the apples were kept = 6 Number of apple pieces in each box = 36 ÷ 6 = 6 Total number of bananas = 54 Number of boxes in which the bananas were kept = 6 Number of banana pieces in each box = 54 ÷ 6 = 9 Total number of fruit pieces in each box = 9 + 6 = 15

Explanation: A. Draw 4 circles to represent the divisor. Then use base-ten blocks to model 56. Show 56 as 5 tens and 6 ones. B. Share the tens equally among the 4 groups. C. If there are any tens left, regroup them as ones. Share the ones equally among the 4 groups. D. There are 1 ten(s) and 4 one(s) in each group. So, the quotient is 14.

Sense or Nonsense?

Answer: Zach’s quick picture is correct while Angela’s is not correct.

Explanation: A. Draw 4 circles to represent the divisor. Then use base-ten blocks to model 68. Show 68 as 6 tens and 8 ones. B. Share the tens equally among the 4 groups. C. If there are any tens left, regroup them as ones. Share the ones equally among the 4 groups. D. There are 1 ten(s) and 7 one(s) in each group. So, the quotient is 17. Hence Zach’s statement and the quick picture are correct.

Question 9. Analyze What did Angela forget to do after she shared the tens equally among the 4 groups? Type below: ___________

Answer: Angela forgot to regroup the leftover tens into ones. Share the ones equally among the 4 groups.

Explanation: Since there are 6 tens and 4 circles only 4 tens can be placed in them while the other 2 tens are leftover which must be converted into 20 ones.

Common Core – Page No. 251

Model Division with Regrouping

Answer: 15 r 3

Explanation: A. Draw 4 circles to represent the divisor. Then use base-ten blocks to model 63. Show 63 as 6 tens and 3 ones. B. Share the tens equally among the 4 groups. C. If there are any tens left, regroup them as ones. Share the ones equally among the 4 groups. D. There are 1 ten(s) and 5 one(s) in each group. So, the quotient is 15. E. After grouping, there are 3 blocks which weren’t grouped. So, the remainder is 3

Question 2. 83 ÷ 3 _____ R _____

Answer: 27 r 2

Divide. Draw quick pictures. Record the steps.

Question 3. 85 ÷ 5 _____

Question 4. 97 ÷ 4 _____ R _____

Answer: 24 r 1

Question 5. Tamara sold 92 cold drinks during her 2-hour shift at a festival food stand. If she sold the same number of drinks each hour, how many cold drinks did she sell each hour? _____ cold drinks

Answer: 46 cold drinks

Explanation: Total number of cold drinks Tamara sold = 92 The time in which she sold the drinks = 2 hours Number of drinks she sold in each hour = 92 ÷ 2 = 46

Question 6. In 3 days Donald earned $42 running errands. He earned the same amount each day. How much did Donald earn from running errands each day? $ _____

Answer: $14

Explanation: Total amount earned by Donald = $42 Number of days = 3 Amount earned on each day = $42 ÷ 3 = $14

Common Core – Page No. 252

Question 1. Gail bought 80 buttons to put on the shirts she makes. She uses 5 buttons for each shirt. How many shirts can Gail make with the buttons she bought? Options: a. 14 b. 16 c. 17 d. 18

Answer: b. 16

Explanation: Total number of buttons = 80 Number of buttons used for each shirt = 5 Number of shirts she can make = 80 ÷ 5 =16

Question 2. Marty counted how many breaths he took in 3 minutes. In that time, he took 51 breaths. He took the same number of breaths each minute. How many breaths did Marty take in one minute? Options: a. 15 b. 16 c. 17 d. 19

Answer: c. 17

Explanation: Total number of breaths Marty counted = 51 Time in which the breath was counted = 3 minutes Number of breaths in one minute = 51 ÷ 3 = 17

Question 3. Kate is solving brain teasers. She solved 6 brain teasers in 72 minutes. How long did she spend on each brain teaser? Options: a. 12 minutes b. 14 minutes c. 18 minutes d. 22 minutes

Answer: a. 12 minutes

Explanation: Number of brain teasers solved = 6 Number of minutes spent on brain teasers = 72 minutes Number of minutes spent on each problem = 72 ÷ 6 =12 minutes

Question 4. Jenny works at a package delivery store. She puts mailing stickers on packages. Each package needs 5 stickers. How many stickers will Jenny use if she is mailing 105 packages? Options: a. 725 b. 625 c. 525 d. 21

Answer: c. 525

Explanation: Number of packages = 105 Number of stickers on each package = 5 Total number of stickers on the packages = 105 x 5 = 525

Question 5. The Puzzle Company packs standardsized puzzles into boxes that hold 8 puzzles. How many boxes would it take to pack up 192 standard-sized puzzles? Options: a. 12 b. 16 c. 22 d. 24

Answer: d. 24

Explanation: Total number of puzzles = 192 Number of puzzles in each box = 8 Number of boxes used = 192 ÷ 8 = 24 boxes

Question 6. Mt. Whitney in California is 14,494 feet tall. Mt. McKinley in Alaska is 5,826 feet taller than Mt. Whitney. How tall is Mt. McKinley? Options: a. 21,310 feet b. 20,320 feet c. 20,230 feet d. 19,310 feet

Answer: b. 20,320 feet

Explanation: Height of Mt. Whitney in California = 14,494 feet Height of Mt. McKinley in Alaska is 5,826 feet taller than Mt. Whitney. Therefore the height of Mt. McKinley in Alaska = 14,494 feet + 5,826 feet  =  20,320 feet

Answer: 113

Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 452. 400 hundred can be shared among 4 groups without regrouping. Now there is 1 ten to share among 4 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 45 ÷ 4 Multiply. 4 × 11 = 44 Subtract. 45  − 44 = 1 tens STEP 3 Divide the ones. Regroup 1 ten as 10 ones. Now there are 12 ones to share among 4 groups. Divide. 12 ones ÷ 4 Multiply. 4×3 ones Subtract. 12 ones − 12 ones = 0

So, the quotient is 113

Question 2. 4)\(\overline { 166 } \) ______ R ______

Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 166. 1 hundred cannot be shared among 4 groups without regrouping. Now there is 1 ten to share among 4 groups. The first digit of the quotient will be in the tens place. STEP 2 Divide the tens. Divide. 166 ÷ 4 Multiply. 4 × 40 = 160 Subtract. 166 − 160 = 6 STEP 3 Divide the ones. Now there are 6 ones to share among 4 groups. Divide. 6 ones ÷ 4 Multiply. 4×1 ones Subtract. 6 ones − 4 ones = 2

So, the quotient is 41 and remainder is 2

Question 3. 5)\(\overline { 775 } \) ______

Answer: 155

Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 775. 700 hundred can be shared among 5 groups without regrouping. Now there is 70 ten to share among 5 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 700 ÷ 5 Multiply. 5 × 140 = 700 Subtract. 700  − 700 = 0 STEP 3 Divide the ones. Now there are 70 tens to share among 5 groups. Divide. 70 tens  ÷ 5 Multiply. 5×14 Subtract. 75 − 70 tens = 5 ones Multiply 5 x 1 = 5 Subtract 5 ÷ 5 = 0

So, the quotient is 155 (140 + 14 + 1)

Question 4. 4)\(\overline { 284 } \) ______

Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 284. 200 hundred can be shared among 4 groups without regrouping. Now there are 20 tens to share among 4 groups. The first digit of the quotient will be in the tens place. STEP 2 Divide the tens. Divide. 200 ÷ 4 Multiply. 4 × 50 = 200 Subtract. 20  − 20 = 0 tens STEP 3 Divide the ones. Now there are 80 tens to share among 4 groups. Divide. 80 tens ÷ 4 Multiply. 4×20 = 80 Subtract. 80 tens − 80 tens = 0 ones There are 4 ones Multiply 4 x 1 = 4 Subtract 4-4 =0

So, the quotient is 71 (50+20+1)

Question 5. 5)\(\overline { 394 } \) ______ R ______

Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 394. 300 hundred can be shared among 5 groups without regrouping. Now there is 30 ten to share among 5 groups. The first digit of the quotient will be in the tens place. STEP 2 Divide the tens. Divide. 300 ÷ 5 Multiply. 5 × 60 = 300 Subtract. 300  − 300 = 0 tens STEP 3 Divide the tens. Now there are 9 tens to share among 5 groups. Divide. 9 tens ÷ 5 Multiply. 5×18 tens Subtract. 90 tens − 90 tens = 0 ones There are 4 ones 4 is the remainder. So, the quotient is 78(60+18)

Question 6. 3)\(\overline { 465 } \) ______

Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 465. 400 hundred can be shared among 3 groups without regrouping. Now there are 40 tens to share among 3 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 400 ÷ 3 Multiply. 3 × 130  = 390 Subtract. 400  − 390 = 1 tens STEP 3 Divide the tens. Now there are 7 tens and 5 ones to share among 3 groups. Divide. 75  ÷ 3 Multiply. 3 × 25 = 75 Subtract. 75 tens − 75 tens = 0

So, the quotient is 155 ( 130+ 25)

Question 7. 8)\(\overline { 272 } \) ______

Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 272. 200 hundred can be shared among 8 groups without regrouping. Now there is 27 tens and 2 ones to share among 8 groups. The first digit of the quotient will be in the tens place. STEP 2 Divide the tens. Divide. 270 ÷ 8 Multiply. 8 × 30 = 240 Subtract. 270  − 240 = 3 tens STEP 3 Divide the ones. Regroup 3 tens as 30 ones. Now there are 30 + 2 = 32 ones to share among 8 groups. Divide. 32 ones ÷ 8 Multiply. 8×4 ones Subtract. 32 ones − 32 ones = 0

So, the quotient is 34 (30 + 4)

Practice: Copy and Solve Divide.

Question 8. 516 ÷ 2 = ______

Answer: 258

Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 516. 500 hundred can be shared among 2 groups without regrouping. Now there is 50 tens and 16 ones to share among 2 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 500 ÷ 2 Multiply. 2 × 250 = 500 Subtract. 516  − 500 = 16 ones STEP 3 Divide the ones. Now there are 16 ones to share among 2 groups. Divide. 16 ones ÷ 2 Multiply. 2×8 ones Subtract. 16 ones − 16 ones = 0

So, the quotient is 258 (250 + 8)

Question 9. 516 ÷ 3 = ______

Answer: 172

Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 516. 500 hundred can be shared among 3 groups without regrouping. Now there is 50 tens and 16 ones to share among 3 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 500 ÷ 3 Multiply. 3 × 160 = 480 Subtract. 516  − 480 = 36 ones STEP 3 Divide the ones. Now there are 36 ones to share among 3 groups. Divide. 36 ones ÷ 3 Multiply. 3×12 ones Subtract. 36 ones − 36 ones = 0

So, the quotient is 172 (160 + 12)

Question 10. 516 ÷ 4 = ______

Answer: 129

Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 516. 500 hundred can be shared among 4 groups without regrouping. Now there is 50 tens and 16 ones to share among 4 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 500 ÷ 4 Multiply. 4 × 125 = 500 Subtract. 516  − 500 = 16 ones STEP 3 Divide the ones. Now there are 16 ones to share among 4 groups. Divide. 16 ones ÷ 4 Multiply. 4×4 ones Subtract. 16 ones − 16 ones = 0

So, the quotient is 129 (125 + 4)

Question 11. 516 ÷ 5 = ______ R ______

Answer: 103 R 1

Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 516. 500 hundred can be shared among 5 groups without regrouping. Now there is 50 tens and 16 ones to share among 5 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 500 ÷ 5 Multiply. 5 × 100 = 500 Subtract. 516  − 500 = 16 ones STEP 3 Divide the ones. Now there are 16 ones to share among 5 groups. Divide. 16 ones ÷ 5 Multiply. 5×3 ones Subtract. 16 ones − 15 ones = 1 one

So, the quotient is 103 (100 + 3) and the remainder is 1

Question 12. Look back at your answers to Exercises 8–11. What happens to the quotient when the divisor increases? Explain. The quotient ______

Answer: The quotient gets decreased when we increase the divisor.

516 ÷ 4 = ______

516 ÷ 5 = ______ R ______

Question 13. Reggie has 192 pictures of animals. He wants to keep half and then divide the rest equally among three friends. How many pictures will each friend get? ______ pictures

Explanation: Total number of animal pictures = 192 Number of animal pictures he kept with him = 192 ÷ 2 = 96 Number of pictures each of his friends got = 96 ÷ 3 = 32 pictures

Question 14. There are 146 students, 5 teachers, and 8 chaperones going to the theater. To reserve their seats, they need to reserve entire rows. Each row has 8 seats. How many rows must they reserve? ______ rows

Answer: 20 rows

Explanation: Total people who went to the theatre = 146 + 5 + 8 = 159 Number of seats in each row = 8 Number of rows which must be reserved for the students = 159 ÷ 8 =19.8 = 20 (approx)

Answer: How many full pages will she have in her album? We can find number of pictures in blue pages? We can find number of pictures in green pages? We can find number of pictures in red pages?

Question 15. b. How will you use division to find the number of full pages? Type below: _________

Answer: Since the total number of pictures and the number of colour pages are given we can divide the total number of pictures are the number of pages to find the number of full pages.

Explanation: Total number of pictures =234 Number of pictures per page = 4 + 6+ 8 = 18 Number of full pages  = 234 ÷ 18 =13

Question 15. c. Show the steps you will use to solve the problem. Type below: _________

Question 15. d. Complete the following sentences. Nan has _______ pictures. She wants to put the pictures in an album with pages that each hold _______ pictures. She will have an album with _______ full pages and _______ pictures on another page. Type below: _________

Answer: 234 pictures, 18 pictures, 13 full pages, 0 pictures on another page

Explanation: Total number of pictures =234 Number of pictures per page = 4 + 6+ 8 = 18 Number of full pages  = 234 ÷ 18 =13 full pages

Since the remainder is 0 the number of pictures on another page = 0

Question 16. Mr. Parsons bought 293 apples to make pies for his shop. Six apples are needed for each pie. If Mr. Parsons makes the greatest number of apple pies possible, how many apples will be left? _____ pies _____ apples left over.

Answer: 48 pies and 5 apples are leftover

Explanation: Total number of apples= 293 Number of apples that make a pie = 6 Number of pies = Quotient of 293 ÷ 6 = 48 Number of apples leftover = 5

Answer: tens

Explanation: Total number of stickers = 320 Number of classes = 4 Number of stickers in each class = Quotient of 320 ÷ 4 = 80 The first digit of quotient is in the tens place.

Common Core – Page No. 257

Place the First Digit

Question 1. 62 ——- 3)\(\overline { 186 } \) -18 ——- 06 -6 ——- 0

Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 186. 180 hundred can be shared among 3 groups without regrouping. Now there is 18 tens and 6 ones to share among 3 groups. The first digit of the quotient will be in the tens place. STEP 2 Divide the tens. Divide. 180 ÷ 3 Multiply. 3 × 60 = 180 Subtract. 186  − 180 = 6 ones STEP 3 Divide the ones. Now there are 6 ones to share among 3 groups. Divide. 6 ones ÷ 3 Multiply. 2×3 ones Subtract. 6 ones − 2 ones =0 one

So, the quotient is 62 (60 + 2) and the remainder is 0

Question 2. 4)\(\overline { 298 } \) _____ R _____

Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 298. 280 hundred can be shared among 4 groups without regrouping. Now there is 28 tens and 18 ones to share among 4 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 280 ÷ 4 Multiply. 4 × 70 = 280 Subtract. 280  − 280 = 0 ones STEP 3 Divide the ones. Now there are 18 ones to share among 4 groups. Divide. 18 ones ÷ 4 Multiply. 4×4 ones Subtract. 18 ones − 16 ones = 2 ones

So, the quotient is 74 (70 + 4) and the remainder is 2

Question 3. 3)\(\overline { 461 } \) _____ R _____

Answer: 153

Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 461. 450 hundred can be shared among 3 groups without regrouping. Now there is 45 tens and 11 ones to share among 3 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 450 ÷ 3 Multiply. 3 × 150 = 450 Subtract. 450  − 450 = 0 ones STEP 3 Divide the ones. Now there are 11 ones to share among 3 groups. Divide. 11 ones ÷ 3 Multiply. 3×3 ones Subtract. 11 ones − 9 ones = 2 ones

So, the quotient is 153 (150 + 3) and the remainder is 2

Question 4. 9)\(\overline { 315 } \) _____ R _____

Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 315. 310 hundred can be shared among 9 groups without regrouping. Now there is 31 tens and 5 ones to share among 9 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide.310 ÷ 9 Multiply. 9 × 30 = 270 Subtract. 310  − 270 = 40 ones STEP 3 Divide the ones. Now there are 40 + 5 = 45 ones to share among 9 groups. Divide. 45 ones ÷ 9 Multiply. 5×9 ones Subtract. 45 ones − 45 ones = 0 ones

So, the quotient is 35 (30 + 5) and the remainder is 0

Question 5. 2)\(\overline { 766 } \) _____ R _____

Answer: 383

Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 766. 760 hundred can be shared among 2 groups without regrouping. Now there is 76 tens and 6 ones to share among 2 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 760 ÷ 2 Multiply. 2 × 380 = 760 Subtract. 760  − 760 = 0 ones STEP 3 Divide the ones. Now there are 6 ones to share among 2 groups. Divide. 6 ones ÷ 2 Multiply. 2×3 ones Subtract. 6 ones − 6 ones = 0 ones

So, the quotient is 383 (380 + 3) and the remainder is 0

Question 6. 4)\(\overline { 604 } \) _____ R _____

Answer: 151

Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 604. 600 hundred can be shared among 4 groups without regrouping. Now there is 60 tens and 4 ones to share among 4 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 600 ÷ 4 Multiply. 4 × 150 = 600 Subtract. 600  − 600 = 0 ones STEP 3 Divide the ones. Now there are 4 ones to share among 4 groups. Divide. 4 ones ÷ 4 Multiply. 4×1 ones Subtract. 4 ones − 4 ones = 0 ones

So, the quotient is 151 (150 + 1) and the remainder is 0

Question 7. 6)\(\overline { 796 } \) _____ R _____

Answer: 132

Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 796. 790 hundred can be shared among 6 groups without regrouping. Now there is 79 tens and 6 ones to share among 6 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 790 ÷ 6 Multiply. 6 × 131 = 786 Subtract. 790  − 786 = 4 ones STEP 3 Divide the ones. Now there are 4 + 6 = 10 ones to share among 6 groups. Divide. 10 ones ÷ 6 Multiply. 6×1 ones Subtract. 10 ones − 6 ones = 4 ones

So, the quotient is 132 (131 + 1) and the remainder is 4

Question 8. 5)\(\overline { 449 } \) _____ R _____

Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 449. 440 hundred can be shared among 5 groups without regrouping. Now there is 44 tens and 9 ones to share among 5 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 440 ÷ 5 Multiply. 5 × 88 = 440 Subtract. 440  − 440 = 0 ones STEP 3 Divide the ones. Now there are 9 ones to share among 5 groups. Divide. 9 ones ÷ 5 Multiply. 5×1 ones Subtract. 9 ones − 5 ones = 4 ones

So, the quotient is 89 (88 + 1) and the remainder is 4

Question 9. 6)\(\overline { 756 } \) _____ R _____

Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 756. 750 hundred can be shared among 6 groups without regrouping. Now there is 75 tens and 6 ones to share among 6 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 750 ÷ 6 Multiply. 6 × 125 = 750 Subtract. 750  − 750 = 0 ones STEP 3 Divide the ones. Now there are 6 ones to share among 6 groups. Divide. 6 ones ÷ 6 Multiply. 6×1 ones Subtract. 6 ones − 6 ones =  0 ones

So, the quotient is 126 (125 + 1) and the remainder is 0

Question 10. 7)\(\overline { 521 } \) _____ R _____

Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 521. 520 hundred can be shared among 7 groups without regrouping. Now there is 52 tens and 1 one to share among 7 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 520 ÷ 7 Multiply. 7 × 74 = 518 Subtract. 520  − 518 = 2 ones STEP 3 Divide the ones. Now there are 2 + 1 = 3 ones to share among 7 groups. Divide. 3 ones ÷ 7 (not possible)

So, the quotient is 74  and the remainder is 3

Question 11. 5)\(\overline { 675 } \) _____ R _____

Answer: 135

Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 675. 670 hundred can be shared among 5 groups without regrouping. Now there is 67 tens and 5 ones to share among 5 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 670 ÷ 5 Multiply. 5 × 134 = 670 Subtract. 670  − 670 = 0 ones STEP 3 Divide the ones. Now there are 5 ones to share among 5 groups. Divide. 5 ones ÷ 5 Multiply. 5×1 ones Subtract. 5 ones − 5 ones = 0 ones

So, the quotient is 135 (134 + 1) and the remainder is 0

Question 12. 8)\(\overline { 933 } \) _____ R _____

Answer: 116

Explanation: STEP 1 Use place value to place the first digit. Look at the hundreds in 933. 930 hundred can be shared among 8 groups without regrouping. Now there is 93 tens and 3 ones to share among 8 groups. The first digit of the quotient will be in the hundreds place. STEP 2 Divide the tens. Divide. 930 ÷ 8 Multiply. 8 × 116 = 928 Subtract. 930  − 928 = 2 ones STEP 3 Divide the ones. Now there are 2 + 3 = 5 ones to share among 8 groups. Divide. 5 ones ÷ 8 (not possible)

So, the quotient is 116 (100 + 3) and the remainder is 5

Question 13. There are 132 projects in the science fair. If 8 projects can fit in a row, how many full rows of projects can be made? How many projects are in the row that is not full? _____ full rows _____ projects in the non-full row

Answer: 16 full rows and 4 projects in the non-full row

Explanation: Total number of projects = 132 Number of projects placed in full row = 8 Number of rows having full projects =Quotient of  132 ÷ 8 = 16 Number of projects in the non-full row = Remainder of 132 ÷ 8 = 4

Question 14. There are 798 calories in six 10-ounce bottles of apple juice. How many calories are there in one 10-ounce bottle of apple juice? _____ R _____ calories in one 10-ounce bottles of juice

Answer: 133 calories

Explanation: Number of calories in 6 bottles of apple juice = 798 Number of calories in each bottle = 798 ÷6 = 133 calories

Common Core – Page No. 258

Question 1. To divide 572 ÷ 4, Stanley estimated to place the first digit of the quotient. In which place is the first digit of the quotient? Options: a. ones b. tens c. hundreds d. thousands

Answer: c. hundreds

Explanation: The quotient of  572÷ 4 is 143 STEP 1 Use place value to place the first digit. Look at the hundreds in 572. 560 hundred can be shared among 4 groups without regrouping. Now there is 1 ten to share among 4 groups. The first digit of the quotient will be in the hundreds place.

Question 2. Onetta biked 325 miles in 5 days. If she biked the same number of miles each day, how far did she bike each day? Options: a. 1,625 miles b. 320 miles c. 65 miles d. 61 miles

Answer: c. 65 miles

Explanation: Total number of miles biked = 325 miles Number of days biked = 5 Number of miles biked on each day = Quotient of 325 ÷ 5 = 65

Question 3. Mort makes beaded necklaces that he sells for $32 each. About how much will Mort make if he sells 36 necklaces at the local art fair? Options: a. $120 b. $900 c. $1,200 d. $1,600

Answer: c. $1,200

Explanation: Cost of each beaded necklace = $32 Number of necklaces = 36 The total cost of the necklaces = $32 x 36 = $1,200 (approx)

Question 4. Which is the best estimate of 54 × 68? Options: a. 4,200 b. 3,500 c. 3,000 d. 350

Answer: b. 3,500

Question 5. Ms. Eisner pays $888 for 6 nights in a hotel. How much does Ms. Eisner pay per night? Options: a. $5,328 b. $882 c. $148 d. $114

Answer: c. $148

Explanation: Total pays of Ms Eisner in a hotel = $888 Number of nights = 6 Amount Ms Eisner pay per night = $888 ÷ 6 = $148

Answer: d. 54 ÷ 3

Explanation: Number of counters in each model = 18 Number of models = 3 Total number of counters = 18 x 3 = 54 Therefore the model displays = 54 ÷ 3

Answer: 213

Divide and check.

Question 2. 2)\(\overline { 394 } \) _____

Answer: 197

Question 3. 2)\(\overline { 803 } \) _____ R _____

Answer: 401 R 1

Question 4. 3)\(\overline { 3,448 } \) _____ R _____

Answer: 1149 R 1

Question 5. 2)\(\overline { 816 } \) _____

Answer: 408

Question 6. 4)\(\overline { 709 } \) _____ R _____

Answer: 177 R 1

Question 7. 3)\(\overline { 267 } \) _____

Question 8. The flower shop received a shipment of 248 pink roses and 256 red roses. The shop owner uses 6 roses to make one arrangement. How many arrangements can the shop owner make if he uses all the roses? _____ arrangement

Answer: 84 arrangements

Explanation: Number of pink roses = 248 Number of red roses = 256 Total number of roses = 504 Number of roses in each arrangement = 6 Number of arrangements = 504 ÷ 6 = 84

Question 9. Four teachers bought 10 origami books and 100 packs of origami paper for their classrooms. They will share the cost of the items equally. How much should each teacher pay? _____ $

Answer: $210

Explanation: Number of origami books = 10 Cost of each origami book = $24 Total cost of origami books = $24 x 10 = $240 Number of origami papers = 100 Cost of each origami book = $6 Total cost of origami books = $6 x 100 = $600 Total cost of items = $240 + $600 = $840 Number of teachers = 4 Cost earned by each teacher = $840 ÷ 4 = $210

Question 10. Communicate Six students shared equally the cost of 18 of one of the items in the chart. Each student paid $24. What item did they buy? Explain how you found your answer. __________

Answer: The students bought origami kit.

Explanation: Number of students = 6 Number of items they bought = 18 Amount each student paid = $24 The total amount paid = $24 x 6 =$144 The item they bought can be found by knowing the cost of the item: Cost of the item= The total amount paid ÷ Number of items =  144 ÷ 18 = $8 Therefore the item is origami kit.

Question 11. Ms Alvarez has $1,482 to spend on origami paper. How many packs can she buy? _____ packs

Answer: 247

Explanation: Cost of origami paper = $6 Amount Ms Alvarez was supposed to spend on origami paper = $1,482 Number of packs bought = $1,482 ÷ $6 = 247

Question 12. Evan made origami cranes with red, blue, and yellow paper. The number of cranes in each color is the same. If there are 342 cranes, how many of them are blue or yellow? _____ blue, or yellow

Answer: 114

Explanation: Evan made origami cranes with red, blue, and yellow paper. The number of cranes in each colour is the same. Total number of cranes = 342 Number of cranes of each colour = 342 ÷ 3 = 114 Therefore there are 114 cranes of blue and yellow.

Question 13. On Monday 336 fourth graders went on a field trip to a local park. The teachers divided the students into 8 groups. Use a basic fact. Estimate the number of students in each group. Show your work. _____ about

Explanation: Total number who went to the field trip = 336 Number of groups into which they were divided = 8 groups Number of students in each group = 336 ÷ 8 = 42 students

Common Core – Page No. 263

Divide by 1-Digit Numbers

Question 1. 318 2)\(\overline { 636 } \) 318 -6       × 2 ——   ——- 03    636 -2 —— 16 -16 ——- 0

Answer: 318

Question 2. 4)\(\overline { 631 } \) _____ R _____

Question 3. 8)\(\overline { 906 } \) _____ R _____

Question 4. 6)\(\overline { 6,739 } \) _____ R _____

Question 5. 4)\(\overline { 2,328 } \) _____ R _____

Question 6. 5)\(\overline { 7,549 } \) _____ R _____

Question 7. The Briggs rented a car for 5 weeks. What was the cost of their rental car per week? $ _____

Answer: $197

Explanation: Cost of the car of Briggs = $985 Number of weeks = 5 Cost of rent per week = $985 ÷ 5 =$ 197

Question 8. The Lees rented a car for 4 weeks. The Santos rented a car for 2 weeks. Whose weekly rental cost was lower? Explain. The rental cost of _____

Answer: Weekly rental cost was lower for Lees compared to Santos

Explanation: Cost of the car of Lees = $632 Number of weeks = 4 Cost of rent per week = $632 ÷ 4 =$ 158

Cost of the car of Santos = $328 Number of weeks = 2 Cost of rent per week = $328 ÷ 2 =$ 164 Therefore weekly rental cost was lower for Lees compared to Santos.

Common Core – Page No. 264

Question 1. Which expression can be used to check the quotient 646 ÷ 3? Options: a. (251 × 3) + 1 b. (215 × 3) + 2 c. (215 × 3) + 1 d. 646 × 3

Answer: c. (215 × 3) + 1

Explanation: Multiply 215 x 3 = 645 Then add 1 to 645 Then the dividend is 645 + 1 = 646

Question 2. There are 8 volunteers at the telethon. The goal for the evening is to raise $952. If each volunteer raises the same amount, what is the minimum amount each needs to raise to meet the goal? Options: a. $7,616 b. $944 c. $119 d. $106

Answer: a. $7,616

Answer: d. 5 × 17 = 85

Explanation: By counting the number of counters we can give the expression. Number of counters in one row = 17 Number of rows = 5 Therefore the expression = 5 × 17 = 85

Question 4. The computer lab at a high school ordered 26 packages of CDs. There were 50 CDs in each package. How many CDs did the computer lab order? Options: a. 1,330 b. 1,300 c. 1,030 d. 130

Answer: b. 1,300

Explanation: Number of packages = 26 Number of CDs in each pack = 50 Total number of CDs the computer lab ordered = 26 x 50 = 1,300

Question 5. Which of the following division problems has a quotient with the first digit in the hundreds place? Options: a. 892 ÷ 9 b. 644 ÷ 8 c. 429 ÷ 5 d. 306 ÷ 2

Answer: d. 306 ÷ 2

Explanation: Use place value to place the first digit. Look at the hundreds in 306. 300 hundred can be shared among 2 groups without regrouping. Now there is 30 tens and 6 ones to share among 2 groups. The first digit of the quotient will be in the hundreds place.

Question 6. Sharon has 64 ounces of juice. She is going to use the juice to fill as many 6-ounce glasses as possible. She will drink the leftover juice. How much juice will Sharon drink? Options: a. 4 ounces b. 6 ounces c. 10 ounces d. 12 ounces

Answer: a. 4 ounces

Question 1. A firehouse pantry has 52 cans of vegetables and 74 cans of soup. Each shelf holds 9 cans. What is the least number of shelves needed for all the cans? First, draw a bar model for the total number of cans. Next, add to find the total number of cans. Then, draw a bar model to show the number of shelves needed. Finally, divide to find the number of shelves needed. So, _______ shelves are needed to hold all of the cans. _______ shelves

Question 2. What if 18 cans fit on a shelf? What is the least number of shelves needed? Describe how your answer would be different. _______ shelves

Answer: 7 shelves

Explanation: Total number of cans = 126 Number of cans which can fit in one shelf = 18 Number of shelves required to place all the cans = 126 ÷ 18 = 7 shelves

Question 3. Julio’s dad bought 10 dozen potatoes. The potatoes were equally divided into 6 bags. How many potatoes are in each bag? _______ potatoes

Answer: 20 potatoes

Explanation: Total number of potatoes = 10 dozens x 12 = 120 Number of bags = 6 Number of potatoes in each bag = 120 ÷ 6 = 20

Question 4. At the garden shop, each small tree costs $125 and each large tree costs $225. How much will 3 small trees and 1 large tree cost? $ _______

Answer: $600

Explanation: Number of small trees = 3 Cost of each small tree = $125 Total cost of the small trees = $125 x 3 = $375 Number of large trees = 1 Cost of each large tree = $225 Total cost of the plants = $375 + $225 = $600

Question 5. Ms Johnson bought 6 bags of balloons. Each bag has 25 balloons. She fills all the balloons and puts 5 balloons in each bunch. How many bunches can she make? _______ bunches

Explanation: Number of bags = 6 Number of ballons in each bag = 25 Total number of ballons = 25 x 6 = 150 Number of ballons in each bunch = 5 Number of bunches = Total number of ballons ÷ Number of ballons in each bunch = 150 ÷ 5 = 30

Question 6. An adult’s dinner costs $8. A family of 2 adults and 2 children pays $26 for their dinners. How much does a child’s dinner cost? Explain. $ _______

Answer: $10

Explanation: Number of adults = 2 Number of children = 2 Cost of dinner of an adult = $8 The total cost of dinner of the adults = $8 x 2 = $16 Total amount paid = $26 Amount spent on children dinner = $26 – $16 = $10 Cost of dinner for the diner = $10 ÷ 2 = $5

Question 7. Communicate Use the table at the right. Maria bought 80 ounces of apples. She needs 10 apples to make a pie. How many apples will be left over? Explain. _______ apples

Explanation: Given the average weight of the apples = 5 ounces Mass of apples Maria bought = 80 ounces Number of apples =  Mass of apples Maria bought ÷ average weight of the apples = 80 ÷ 5 = 16 Number of apples which make a pie = 10 Number of apples leftover = 16 – 10 = 6

Question 8. Taylor has 16 tacks. She buys 2 packages of 36 tacks each. How many garage sale posters can she put up if she uses 4 tacks for each poster? _______ posters

Explanation: Number of packages = 2 Number of posters in each package = 36 Total number of tacks = 36 x 2 = 72 Number of tacks for each poster = 4 Number of garage sale posters = 72 ÷ 4 = 18

Question 9. Ryan bought 8 dozen bandages for the track team first-aid kit. The bandages were divided equally into 4 boxes. How many bandages are in each box? _______ bandages

Explanation: Number of bandages bought for the track team first-aid kit = 8 dozens x 12 = 96 Number of boxes = 4 Number of bandages in each box = 96 ÷ 4 = 24

Common Core – Page No. 269

Problem Solving Multistep Division Problems

Solve. Draw a diagram to help you.

Answer: 45 people can be served.

Question 2. There are 8 pencils in a package. How many packages will be needed for 28 children if each child gets 4 pencils? ________ packages

Answer: 14 packages

Question 3. There are 3 boxes of tangerines. Each box has 93 tangerines. The tangerines will be divided equally among 9 classrooms. How many tangerines will each classroom get? ________ tangerines

Question 4. Misty has 84 photos from her vacation and 48 photos from a class outing. She wants to put all the photos in an album with 4 photos on each page. How many pages does she need? ______ pages

Common Core – Page No. 270

Question 1. Gavin buys 89 blue pansies and 86 yellow pansies. He will plant the flowers in 5 rows with an equal number of plants in each row. How many plants will be in each row? Options: a. 875 b. 175 c. 35 d. 3

Answer: c. 35

Explanation: Number of blue pansies = 89 Number of yellow pansies = 86 Total number of pansies = 89 + 86 = 175 Number of rows = 5 Number of plants in each row = 175 ÷ 5 = 35

Question 2. A pet store receives 7 boxes of cat food. Each box has 48 cans. The store wants to store the cans in equal stacks of 8 cans. How many stacks can be formed? Options: a. 8 b. 42 c. 56 d. 336

Answer: b. 42

Explanation: Number of boxes of cat food = 7 Number of cans in a box = 48 Total number of cans = 48 x 7 = 336 Number of cans in each stack = 8 Number of stacks = 336 ÷ 8 = 42

Answer: d. 364

Explanation: Length = 20 +6 = 26 Breadth = 10 + 4 = 14 Area of the rectangle = 26 x 14 = 364

Question 4. Mr. Hatch bought 4 round-trip airplane tickets for $417 each. He also paid $50 in baggage fees. How much did Mr. Hatch spend? Options: a. $467 b. $1,698 c. $1,718 d. $16,478

Answer: c. $1,718

Explanation: Cost of each ticket of the airplane = $417 Cost baggage fees = $50 Number of trips of the airplane = 5 Cost of the trips = $417 x 5 = $1,668 The total cost of the trip = $1,668 + $50 = $1,718

Question 5. Mae read 976 pages in 8 weeks. She read the same number of pages each week. How many pages did she read each week? Options: a. 109 b. 120 c. 122 d. 984

Answer: c. 122

Explanation: Total number of pages = 976 Number of weeks = 8 Number of pages Mae read in each week = 976 ÷ 8 = 122

Question 6. Yolanda and her 3 brothers shared a box of 156 toy dinosaurs. About how many dinosaurs did each child get? Options: a. 40 b. 50 c. 60 d. 80

Answer: b. 50

Explanation: Total number of  toy dinosaurs = 156 Number of brothers = 3 Number of toy dinosaurs each brother got = 156 ÷ 3 = 50

Page No. 271

Answer: B. 50 C. 60 The quotient is between 50 and 60

Answer: The quotient is between 15 and 20.

Answer: 19 ÷ 3 = 6 r 1

Explanation: Count the total number of counters =Dividend = 19 Number of circles = Divisor = 3 After the distribution of the counters, The quotient is 6 because in each circle there are 6 counters The leftover counter is the remainder = 1

For 4a–4d, choose Yes or No to tell whether the division sentence has a remainder.

Question 4. a. 28 ÷ 4 i. yes ii. no

Question 4. b. 35 ÷ 2 i. yes ii. no

Question 4. c. 40 ÷ 9 i. yes ii. no

Question 4. d. 45 ÷ 5 i. yes ii. no

Page No. 272

Question 5. A park guide plans the swan boat rides for 40 people. Each boat can carry 6 people at a time. What is the best way to interpret the remainder in this situation so that everyone gets a ride? Type below: ____________

Answer: 4 people are leftover after the boat takes 6 people at a time for a ride, therefore, these four people go on the ride in the next round.

Explanation: Quotient: A. Use 40 counters to represent the 40 people. Then draw 6 circles to represent the divisor. B. Share the counters equally among the 6 groups by placing them in the circles. C. Number of counters formed in each group = quotient of 40 ÷ 6 D. Number of circles are equally filled with 6 counters, therefore, the quotient is 6 Therefore, the quotient is 6 and the remainder is 4 It means that the boat takes 7 rounds in which 6 are filled with 6 people while 4 people are leftover they take the last ride.

Question 6. Nolan divides his 88 toy cars into boxes. Each box holds 9 cars. How many boxes does Nolan need to store all of his cars? ______ boxes

Explanation: Total number of toys Nolan has = 88 Number of cars placed in each box  = 9 Number of boxes = 88 ÷ 9 = 9.7 = 10 (approx) We take approximate value because all the toys must be fit in the box.

A group of 140 tourists are going on a tour. The tour guide rents 15 vans. Each van holds 9 tourists.

Question 7. Part A Write a division problem that can be used to find the number of vans needed to carry the tourists. Then solve. Type below: ____________

Answer: 140 divided by 9 gives the number of vans  needed to carry the tourists

Question 7. Part B What does the remainder mean in the context of the problem? Type below: ____________

Answer: The leftover of tourists = Remainder =5

Explanation: The leftover of tourists= Remainder =5 Can be placed in a different van or can be adjusted in the 15 vans.

Question 7. Part C How can you use your answer to determine if the tour guide rented enough vans? Explain. Type below: ____________

Answer: The number of vans would be correct if they were 16 instead of 15

Explanation: Then the answer can be determined as all the 140  tourists have enjoyed their trip to the fullest and traveled comfortably without any hassle and bustle.

Question 8. Solve. 3,200 ÷ 8 = ______

Page No. 273

Question 9. Which quotients are equal to 300? Mark all that apply. Options: a. 1,200 ÷ 4 b. 180 ÷ 9 c. 2,400 ÷ 8 d. 2,100 ÷ 7 e. 90 ÷ 3 f. 3,000 ÷ 3

Answer: a. 1,200 ÷ 4, c. 2,400 ÷ 8, d. 2,100 ÷ 7

Question 10. Margo estimated 188 ÷ 5 to be between 30 and 40. Which basic facts did she use to help her estimate? Mark all that apply. Options: a. 10 ÷ 5 b. 15 ÷ 5 c. 20 ÷ 5 d. 25 ÷ 5

Answer: b. 15 ÷ 5 c. 20 ÷ 5

Explanation: 188 ÷ 5 STEP 1 Identify the basic fact. 15 ÷ 5 STEP 2 Use place value. 150 = 15 tens STEP 3 Divide. 15 tens ÷ 5 = 3 tens 150 ÷ 3 = 30

STEP 1 Identify the basic fact. 20 ÷ 5 STEP 2 Use place value. 200 = 20 tens STEP 3 Divide. 20 tens ÷ 5 = 4 tens 200 ÷ 5 = 40

Therefore we can say that the quotient is between 30 to 40

Question 11. Mathias and his brother divided 2,029 marbles equally. About how many marbles did each of them receive? About _________

Answer: about 1,014 marbles each one recieved

Explanation: Total number of marbles = 2,029 Number of people = 2 Number of marbles each one received = 2,029 ÷ 2 = 1,014

For 12a–12d, choose Yes or No to show how to use the Distributive Property to break apart the dividend to find the quotient 132 ÷ 6.

Question 12. a. (115 ÷ 6) + (17 ÷ 6) i. yes ii. no

Explanation: According to the question, the nearest estimates are 115 and 17 but these are not divisible by 6.

Question 12. b. (100 ÷ 6) + (32 ÷ 6) i. yes ii. no

Explanation: According to the question, the nearest estimates are 100 and 32 but these are not divisible by 6.

Question 12. c. (90 ÷ 6) + (42 ÷ 6) i. yes ii. no

Explanation: STEP1 Find the nearest estimates of the number 132 STEP2 We can break the number 132 into 90 + 42 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (90 ÷ 6) + (42 ÷ 6) STEP5 Add quotients of the above 15 +7= 22

Question 12 d. (72 ÷ 6) + (60 ÷ 6) i. yes ii. no

Explanation: STEP1 Find the nearest estimates of the number 132 STEP2 We can break the number 132 into 72 + 60 STEP3 We must divide the two parts of the number (dividend) with the divisor. STEP4 (72 ÷ 6) + (60 ÷ 6) STEP5 Add quotients of the above 12 +10= 22

Explanation: Total number of people = 60 Number of people each river raft can hold = 15 Number of rafts needed to give a ride to all the people = 60 ÷ 15 = 4

Page No. 274

A travelling circus brings along everything it needs for a show in big trucks.

Question 14. Part A The circus sets up chairs in rows with 9 seats in each row. How many rows will need to be set up if 513 people are expected to attend the show? ______ rows

Explanation: The total number of people = 513 Number of seats in each row = 9 Number of rows = 513 ÷ 9 = 57

Question 14. Part B Can the rows be divided into a number of equal sections? Explain how you found your answer. Type below: _________

Answer: Yes, the rows can be divided into equal sections. 57 ÷ 3 = 19

Explanation: We can divide 57 using the divisor as 3, then the quotient is 19 and the remainder is 0.

Question 14. Part C Circus horses eat about 250 pounds of horse food per week. About how many pounds of food does a circus horse eat each day? Explain. About ______ pounds

Answer: About 35 pounds

Question 15. Hilda wants to save 825 digital photographs in an online album. Each folder of the album can save 6 photographs. She uses division to find out how may full folders she will have. In what place is the first digit of the quotient? _________

Answer: Hundreds place

Explanation: Use place value to place the first digit. Look at the hundreds in 825. 800 hundred can be shared among 6 groups without regrouping. Now there is 80 tens and 25 ones to share among 6 groups. The first digit of the quotient will be in the hundreds place.

Page No. 275

Answer: 1st picture – 150 ÷ 30 2nd picture – 160 ÷ 40 3rd picture – 150 ÷ 50 4th picture – 160 ÷ 80

Question 17. Popcorn was donated for the school fair by 3 different popcorn vendors. They donated a total of 636 bags of popcorn. Each vendor donated the same number of bags. How many bags of popcorn did each vendor donate? ______ bags

Answer: 212

Page No. 276

Answer: tens place

Explanation: Use place value to place the first digit. Look at the hundreds in 750. 720 hundred can be shared among 9 groups without regrouping. Now there is 72 tens and 30 ones to share among 9 groups. The first digit of the quotient will be in the tens place.

Question 21. Ursula bought 9 dozen rolls of first aid tape for the health office. The rolls were divided equally into 4 boxes. How many rolls are in each box? _____ rolls

Answer: 27 rolls

Explanation: Number of rolls = 9 dozen x 12 = 108 Number of boxes = 4 Number of rolls in each box = Quotient of 108 ÷ 4 = 27 rolls

Question 22. There are 112 seats in the school auditorium. There are 7 seats in each row. There are 70 people seated, filling up full rows of seats. How many rows are empty? _____ empty rows

Answer: 6 rows are empty

Explanation: Total number of seats = 112 Number of seats in each row = 7 Number of rows = 112÷7 = 16

Number of people seated = 70 Number of rows fully occupied by the people = 70 ÷ 7 = 10 Number of empty rows = 16 – 10 = 6

Page No. 280

Answer: 6 x 2 = 12

Explanation: There are a total of 12 counters in the given figure. So, we can see that 6 + 6 = 12 from the above figure. Hence we can write as 6 x 2 = 12

Question 1.

Answer: 4 x 3 = 12

Explanation: The number of columns and rows are 4 and 3 respectively. So we can calculate the multiplication by 4 x 3 = 12

Explanation: The number of columns and rows are 4 and 3 respectively. So we can calculate the multiplication by 4 x 3 = 12.

Use tiles to find all the factors of the product. Record the arrays and write the factors shown.

Question 2. 5: __________ Type below: ________

Question 3. 20: __________ Type below: ________

Question 4. 25: __________ Type below: ________

Page No. 281

Practice: Copy and Solve Use tiles to find all the factors of the product. Record the arrays on grid paper and write the factors shown.

Question 5. 9: ______________ Type below: ________

Question 6. 21: ______________ Type below: ________

Question 7. 17: ______________ Type below: ________

Question 8. 18: ______________ Type below: ________

Question 9. Pablo is using 36 tiles to make a patio. Can he arrange the tiles in another way and show the same factors? Draw a quick picture and explain. Type below: ________

Question 10. How many different rectangular arrays can Pablo make with all 36 tiles, so none of the arrays show the same factors? ________ rectangular arrays

Question 11. If 6 is a factor of a number, what other numbers must be factors of the number? Type below: ________

Question 12. Jean spent $16 on new T-shirts. If each shirt cost the same whole-dollar amount, how many could she have bought? Type below: ________

Page No. 282

Question 13. b. How is finding the number of ways to model a rectangular house related to finding factor pairs? Type below: ________

Question 13. c. Why is finding the factor pairs only the first step in solving the problem? Type below: ________

Question 13. d. Show the steps you used to solve the problem. Type below: ________

Question 13. Complete the sentences. Factor pairs for 18 are ___________________ . There are ______ different ways Carmen can arrange the cubes to model the house. Type below: ________

Question 14. Sarah was organizing vocabulary words using index cards. She arranged 40 index cards in the shape of a rectangle on a poster. For 14a–14e, choose Yes or No to tell whether a possible arrangement of cards is shown. a. 4 rows of 10 cards i. yes ii. no

Question 14. b. 6 rows of 8 cards i. yes ii. no

Question 14. c. 20 rows of 2 cards i. yes ii. no

Question 14. d. 40 rows of 1 card i. yes ii. no

Question 14. e. 35 rows of 5 cards i. yes ii. no

Conclusion:

I think the answers provided in the Go Math Grade 4 Answer Key Chapter 4 Divide by 1-Digit Numbers are beneficial for all the students of 4th grade. Our aim is to help the students to become masters in maths. So, Refer to our HMH Go Math 4th Grade Answer Key Chapter 4 Divide by 1-Digit Numbers and secure good marks in the exams.

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Add and Subtract Fractions with Unlike Denominators

Lesson(s): 6.1–6.3, 6.9

Use equivalent fractions as a strategy to add and subtract fractions. MAFS.5.NF.1.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

Lesson(s): 6.4–6.8, 6.10

Use equivalent fractions as a strategy to add and subtract fractions. MAFS.5.NF.1.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

Student Workbook Chapter 6

Enrich chapter 6, reteach chapter 6, student textbook chapter 6.

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Go Math! 6 Common Core Edition, Grade: 6 Publisher: Houghton Mifflin Harcourt

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Go Math Grade 4 Answer Key Chapter 7 Add and Subtract Fractions

One of the best study guides for grade 4 students is Go Math Grade 4 Answer Key Chapter 7 Add and Subtract Fractions . Make use of these pdf formatted chapter 7 Go Math HMH 4th Grade Answer Key for free and learn the topics efficiently. Download the Go Math Grade 4 Answer Key Chapter 7 Add and Subtract Fractions pdf from here and get the step-wise answers to all the questions. From this page, you’ll find the different possible models & techniques that students use to find the correct way to solve the fractions.

Approaching the best ways will make you understand the concepts of adding and subtracting fractions. Master in the Go Math Grade 4 Chapter 7 Add and Subtract Fractions by using the clear cut explanation for all the questions with images. Obtain the knowledge to write the fractions as sum and subtractions from Go Math Grade 4 Solution Key of Chapter 7 Add and Subtract Fractions.

Lesson: 1 – Add and Subtract Parts of a Whole

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Lesson: 2 – Add and Subtract Parts of a Whole

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Lesson: 3 – Add and Subtract Parts of a Whole

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Lesson: 4 – Add and Subtract Parts of a Whole

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Lesson: 5 – Add Fractions Using Models

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Lesson: 6 – Subtract Fractions Using Models

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Lesson: 7 – Subtract Fractions Using Models

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Lesson: 8 – Add and Subtract Fractions

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Lesson: 9 – Add and Subtract Fractions

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Lesson: 10 – Add and Subtract Fractions

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Lesson: 11 – Rename Fractions and Mixed Numbers

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Lesson: 12 – Rename Fractions and Mixed Numbers

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Lesson: 13 – Add and Subtract Mixed Numbers

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Lesson: 14 – Add and Subtract Mixed Numbers

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Lesson: 15 – Record Subtraction with Renaming

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Lesson: 16 – Record Subtraction with Renaming

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Lesson: 17 – Fractions and Properties of Addition

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Lesson: 18 – Fractions and Properties of Addition

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Lesson: 19 – Fractions and Properties of Addition

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Lesson: 20 – Fractions and Properties of Addition

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Lesson: 21 – Fractions and Properties of Addition

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Lesson: 22 – Fractions and Properties of Addition

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Use the model to write an equation.

Answer: 3/8 + 2/8 = 5/8

Explanation: By seeing the above 3 figures we can say that the fraction of the shaded part of the first circle is 3/8, the fraction of the second figure is 2/8 By adding the 2 fractions we get the fraction of the third circle. 3/8 + 2/8 = 5/8

Answer: 4/5 – 3/5 = 1/5

Explanation: The fraction of the shaded part for the above rectangle is 4/5 The fraction of the box is 3/5 The equation for the above figure is 4/5 – 3/5 = 1/5

Answer: 1/4 + 2/4 = 3/4

Explanation: The name of the fraction for the shaded part of first figure is 1/4 The name of the fraction for the shaded part of second figure is 1/4 The name of the fraction for the shaded part of third figure is 3/4 So, The equation for the above figure is 1/4 + 2/4 = 3/4

Answer: \(\frac { 2 }{ 6 } +\frac { 3 }{ 6 } =\frac { 5 }{ 6 } \)

Explanation: The name of the fraction for the shaded part of first figure is 2/6 The name of the fraction for the shaded part of second figure is 3/6 The name of the fraction for the shaded part of third figure is 5/6 So, The equation for the above figure is \(\frac { 2 }{ 6 } +\frac { 3 }{ 6 } =\frac { 5 }{ 6 } \)

Answer: \(\frac { 3 }{ 5 } -\frac { 2 }{ 5 } =\frac { 1 }{ 5 } \)

Explanation: The name of the fraction for the shaded part of figure is 3/5 The name of the fraction for the shaded part of closed box is 2/5 So, The equation for the above figure is \(\frac { 3 }{ 5 } -\frac { 2 }{ 5 } =\frac { 1 }{ 5 } \)

Question 6: Jake ate \(\frac { 4 }{ 8 } \) of a pizza. Millie ate \(\frac { 3}{ 8 } \) of the same pizza. How much of the pizza was eaten by Jake and Millie?

Answer: 7/8 of pizza

Explanation: Given that, Jake ate \(\frac { 4 }{ 8 } \) of a pizza. Millie ate \(\frac { 3}{ 8 } \) of the same pizza. To find how much of the pizza was eaten by Jake and Millie We have to add both the fractions \(\frac { 4 }{ 8 } \) + \(\frac { 3 }{ 8 } \) = \(\frac { 7 }{ 8 } \) Thus the fraction of the pizza eaten by Jake and Millie is \(\frac { 7 }{ 8 } \)

Question 7: Kate ate \(\frac { 1 }{ 4 } \) of her orange. Ben ate \(\frac { 2 }{ 4 } \) of his banana. Did Kate and Ben eat \(\frac { 1 }{ 4 } +\frac { 2}{ 4 } =\frac { 3}{ 4 } \) of their fruit?

Answer: No, one whole refers to orange and the other whole to a banana.

Question 1: A whole pie is cut into 8 equal slices. Three of the slices are served. How much of the pie is left? (a) \(\frac { 1 }{ 8 } \) (b) \(\frac { 3 }{ 8 } \) (c) \(\frac { 5 }{ 8} \) (d)\(\frac { 7 }{ 8 } \)

Answer: \(\frac { 5 }{ 8} \)

Explanation: Given, A whole pie is cut into 8 equal slices. Three of the slices are served. The fraction of 8 slices is 8/8. Out of which 3/8 are served. 8/8 – 3/8 = 5/8 Therefore \(\frac { 5 }{ 8} \) of the pie is left. Thus the correct answer is option c.

Question 2: An orange is divided into 6 equal wedges. Jody eats 1 wedge. Then she eats 3 more wedges. How much of the orange did Jody eat? (a) \(\frac { 1 }{ 6} \) (b) \(\frac { 4}{ 6 } \) (c) \(\frac { 5}{ 6 } \) (d) \(\frac { 6}{ 6} \)

Answer: \(\frac { 4}{ 6 } \)

Explanation: Given, An orange is divided into 6 equal wedges. Jody eats 1 wedge. Then she eats 3 more wedges. The fraction of orange that Jody eat is \(\frac { 4}{ 6 } \). Thus the correct answer is option b.

Question 3: Which list of distances is in order from least to greatest? (a) \(\frac { 1 }{ 8 } \) Mile, \(\frac { 3 }{ 16 } \) Mile, \(\frac { 3 }{ 4 } \) Mile (b) \(\frac { 3 }{ 4 } \) Mile, \(\frac { 1 }{ 8 } \) Mile, \(\frac { 3 }{ 16 } \) Mile (c) \(\frac { 1 }{ 8} \) Mile, \(\frac { 3 }{ 4 } \) Mile, \(\frac { 3 }{ 16 } \) Mile (d)\(\frac { 3 }{ 16 } \) Mile, \(\frac { 1 }{ 8 } \) Mile, \(\frac { 3 }{ 4 } \) Mile

Answer: \(\frac { 1 }{ 8 } \) Mile, \(\frac { 3 }{ 16 } \) Mile, \(\frac { 3 }{ 4 } \) Mile

Explantion: Compare the three fractions 1/8, 3/4 and 3/16 Make the common denominators. 1/8 × 2/2 = 2/16 3/4 × 4/4 = 12/16 The fractions are 2/16, 12/16 and 3/16 The numerator with the highest number will be the greatest. The fractions from least to greatest is \(\frac { 1 }{ 8 } \) Mile, \(\frac { 3 }{ 16 } \) Mile, \(\frac { 3 }{ 4 } \) Mile. Thus the correct answer is option d.

Question 4: Jeremy walked 6/8 of the way to school and ran the rest of the way. What fraction, in simplest form, shows the part of the way that Jeremy walked? (a) \(\frac { 1 }{ 4 } \) (b) \(\frac { 3 }{ 8 } \) (c) \(\frac { 1 }{ 2} \) (d)\(\frac { 3 }{ 4 } \)

Answer: \(\frac { 3 }{ 4 } \)

Explanation: Given, Jeremy walked 6/8 of the way to school and ran the rest of the way. The simplest form of 6/8 is 3/8. The simplest form of part of the way that Jeremy walked is 3/8. Thus the correct answer is option b.

Question 5: An elevator starts on the 100th floor of a building. It descends 4 floors every 10 seconds. At what floor will the elevator be 60 seconds after it starts? (a) 60th floor (b) 66th floor (c) 72nd floor (d) 76th floor

Answer: 76th floor

Explanation: Given, An elevator starts on the 100th floor of a building. It descends 4 floors every 10 seconds. 4 floors – 10 seconds ? – 60 seconds 60 × 4/10 = 240/10 = 24 floors 100 – 24 = 76th floor Thus the correct answer is option d.

Question 6: For a school play, the teacher asked the class to set up chairs in 20 rows with 25 chairs in each row. After setting up all the chairs, they were 5 chairs short. How many chairs did the class set up? (a) 400 (b) 450 (c) 495 (d) 500

Answer: 495

Explanation: Given, For a school play, the teacher asked the class to set up chairs in 20 rows with 25 chairs in each row. After setting up all the chairs, they were 5 chairs short. 20 × 25 = 500 500 – 5 = 495 Therefore the class set up 495 chairs. Thus the correct answer is c.

Answer: The sum of the unit fraction for 3/4 is 1/4 + 1/4 + 1/4

Explanation: A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. The sum of the unit fraction for 3/4 is 1/4 + 1/4 + 1/4.

Answer: The sum of the unit fraction for 5/6 is 1/6 + 1/6 + 1/6 + 1/6 + 1/6

Explanation: A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. The sum of the unit fraction for 5/6 is 1/6 + 1/6 + 1/6 + 1/6 + 1/6

Answer: The sum of the unit fraction for 2/3 is 1/3 + 1/3.

Explanation: A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. The sum of the unit fraction for 2/3 is 1/3 + 1/3.

Question 4: \(\frac { 4 }{ 12 } = \)

Answer: The sum of the unit fraction for 4/12 is 1/12 + 1/12 + 1/12 + 1/12

Explanation: A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. The sum of the unit fraction for 4/12 is 1/12 + 1/12 + 1/12 + 1/12

Question 5: \(\frac { 6 }{ 8 } = \)

Answer: The sum of the unit fraction for 6/8 is 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8

Explanation: A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. The sum of the unit fraction for 6/8 is 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8

Question 6: \(\frac { 8 }{ 10 } = \)

Answer: The sum of the unit fraction for 8/10 is 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10

Explanation: A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. The sum of the unit fraction for 8/10 is 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10

Question 7: \(\frac { 6 }{ 6 } = \)

Answer: The sum of the unit fraction for 6/6 is 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6

Explanation: A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. The sum of the unit fraction for 6/6 is 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6

Question 8: Compare Representations How many different ways can you write a fraction that has a numerator of 2 as a sum of fractions? Explain.

Answer: Let’s say we have the fraction 2/9. We can split this one fraction into two by modifying the numerator, like so: 2/9 = 1/9 + 1/9 This works because since both fractions have a numerator of 9, you can easily add the numerators to give 2, and that will give 2/9 in return. However, you can’t separate the denominators. 2/9 is not equal to 2/6 + 2/3 2/9 = 1/9 + 1/9 2/9 = 0.5/9 + 1.5/9 (which simplifies to 1/18 + 3/18, also giving 2/9) 2/9 = 0.5/9 + 0.5/9 + 0.5/9 + 0.5/9 = 1/18 + 1/18 + 1/18 + 1/18 I basically split it up into more and more fractions that add up to give 2/9. So, in short, there are infinitely many ways to do it.

Answer: We need the information about the equal sections and fence the garden into 3 areas by grouping some equal sections together.

b. How can writing an equation help you solve the problem?

Answer: The equation helps to find what part of the garden could each fenced area be.

Explanation: If you write an equation with 3 addends whose sum is 5/5, you could find the possible sizes of each fenced area. The size of each section is 1/5. Each addend represents the size of a fenced area.

c. How can drawing a model help you write an equation?

Answer: If you draw a model that shows 5 fifth-size parts representing the sections, you can see how to group the parts into 3 areas in different ways.

d. Show how you can solve the problem.

Question 9: Complete the sentence. The garden can be fenced into ______, ______, and ______ parts or ______, ______, and ______ parts.

Answer: 3/5, 1/5 and 1/5 parts or 2/5, 2/5 and 1/5 parts

Explanation: The sum of the unit fractions for 4/5 is 1/5 + 1/5 + 1/5 + 1/5.

Question 2: \(\frac { 3 }{ 8 }= \)

Answer: 1/8 + 1/8 + 1/8

Explanation: The sum of the unit fractions for 3/8 is 1/8 + 1/8 + 1/8

Question 3: \(\frac { 6 }{ 12 }= \)

Answer: 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12

Explanation: The sum of the unit fractions for 6/12 is 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12

Question 4: \(\frac { 4 }{ 4 }= \)

Answer: 1/4 + 1/4 + 1/4 + 1/4

Explanation: The sum of the unit fractions for 4/4 is 1/4 + 1/4 + 1/4 + 1/4

Question 5: \(\frac { 7 }{ 10 }= \)

Answer: 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10

Explanation: The sum of the unit fractions for 7/10 is 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10

Question 6: \(\frac { 6 }{ 6 } =\)

Answer: 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6

Explanation: The sum of the unit fractions for 6/6 is 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6

Question 7: Miguel’s teacher asks him to color \(\frac { 4 }{ 8 }\) of his grid. He must use 3 colors: red, blue, and green. There must be more green sections than red sections. How can Miguel color the sections of his grid to follow all the rules?

Answer: 1/8 red, 1/8 blue, and 2/8 green

Explanation: If there are 8 tiles, coloring \(\frac { 4 }{ 8 }\) means coloring 4 tiles. Using those three colors, we could use each 1 time with 1 leftover. Since we must have more green, we would use it twice; this would give us 2 green, 1 red and 1 blue. Since the grid is not necessarily 8 squares, we must account for this by saying 2/8 green, 1/8 red, and 1/8 blue.

Question 8: Petra is asked to color \(\frac { 6 }{ 6 }\) of her grid. She must use 3 colors: blue, red, and pink. There must be more blue sections than red sections or pink sections. What are the different ways Petra can color the sections of her grid and follow all the rules?

Answer: 3/6 blue, 2/6 red, 1/6 pink

Explanation: 1. 3 blues, 2 red, 1 pink. 2. 3 blues, 2 pink, 1 red. 3. 4 blues, 1 red, 1 pink The different ways in which Petra can color the sections of her grid and follow the rules are; 1. 3 blues, 2 red, 1 pink. 2. 3 blues, 2 pink, 1 red. 3. 4 blues, 1 red, 1 pink All these three ways follows the rules that; there must be three colors an also Blue sections are more than red sections or pink sections.

Question 1: Jorge wants to write \(\frac { 4 }{ 5 } \) as a sum of unit fractions. Which of the following should he write? (a) \(\frac { 3 }{ 5 } +\frac { 1 }{ 5 } \) (b) \(\frac { 2 }{ 5 } +\frac { 2 }{ 5 } \) (c) \(\frac { 1 }{ 5 } +\frac { 1 }{ 5 }+\frac { 2 }{ 5 } \) (d) \(\frac { 1 }{ 5 } +\frac { 1 }{ 5 } +\frac { 1 }{ 5 } +\frac { 1 }{ 5 } \)

Answer: \(\frac { 1 }{ 5 } +\frac { 1 }{ 5 } +\frac { 1 }{ 5 } +\frac { 1 }{ 5 } \)

Explanation: Given, Jorge wants to write \(\frac { 4 }{ 5 } \) as a sum of unit fractions. The sum of the unit fraction for \(\frac { 4 }{ 5 } \) is \(\frac { 1 }{ 5 } +\frac { 1 }{ 5 } +\frac { 1 }{ 5 } +\frac { 1 }{ 5 } \) Thus the correct answer is option d.

Question 2: Which expression is equivalent to \(\frac { 7 }{ 8 } \) ? (a) \(\frac { 5 }{ 8 } +\frac { 2 }{ 8}+\frac { 1 }{ 8 } \) (b) \(\frac { 3 }{ 8 } +\frac {3 }{ 8 } +\frac { 1 }{ 8 } +\frac { 1 }{ 8 } \) (c) \(\frac { 4 }{ 8 } +\frac { 2 }{ 8 }+\frac { 1 }{ 8 } \) (d) \(\frac { 4 }{ 8 } +\frac { 2 }{ 8 }+\frac { 2 }{ 8 } \)

Answer: \(\frac { 4 }{ 8 } +\frac { 2 }{ 8 }+\frac { 1 }{ 8 } \)

Explanation: The fraction equivalent to \(\frac { 7 }{ 8 } \) is \(\frac { 4 }{ 8 } +\frac { 2 }{ 8 }+\frac { 1 }{ 8 } \). Thus the correct answer is option c.

Question 3: An apple is cut into 6 equal slices. Nancy eats 2 of the slices. What fraction of the apple is left? (a) \(\frac { 1 }{ 6 } \) (b) \(\frac { 2 }{ 6 } \) (c) \(\frac { 3 }{ 6 } \) (d) \(\frac { 4 }{ 6 } \)

Answer: \(\frac { 4 }{ 6 } \)

Explanation: Given, An apple is cut into 6 equal slices. Nancy eats 2 of the slices. 6 – 2 = 4 \(\frac { 6 }{ 6 } \) – \(\frac { 2 }{ 6 } \) = \(\frac { 4 }{ 6 } \) Thus the correct answer is option d.

Question 4: Which of the following numbers is a prime number? (a) 1 (b) 11 (c) 21 (d) 51

Explanation: A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. 11 is a multiple of 1 and itself. Thus the correct answer is option b.

Question 5: A teacher has a bag of 100 unit cubes. She gives an equal number of cubes to each of the 7 groups in her class. She gives each group as many cubes as she can. How many unit cubes are left over? (a) 1 (b) 2 (c) 3 (d) 6

Explanation: Given, A teacher has a bag of 100 unit cubes. She gives an equal number of cubes to each of the 7 groups in her class. She gives each group as many cubes as she can. 100 divided by 7 is 14 r 2, so there are 2 leftover. Thus the correct answer is option b.

Question 6: Jessie sorted the coins in her bank. She made 7 stacks of 6 dimes and 8 stacks of 5 nickels. She then found 1 dime and 1 nickel. How many dimes and nickels does Jessie have in all? (a) 84 (b) 82 (c) 80 (d) 28

Explanation: Given, Jessie sorted the coins in her bank. She made 7 stacks of 6 dimes and 8 stacks of 5 nickels. She then found 1 dime and 1 nickel. 43 dimes and 41 nickles 43 + 41 = 84 Jessie has 84 dimes and nickels in all. Thus the correct answer is option a.

Answer: 4/5

Explanation: Given, Adrian’s cat ate \(\frac { 3 }{ 5 } \) of a bag of cat treats in September and \(\frac { 1 }{ 5 } \) of the same bag of cat treats in October. From the above figure, we can see that there are 4 fifth size pieces. \(\frac { 3 }{ 5 } \)+\(\frac { 1 }{ 5 } \) = \(\frac { 4 }{ 5 } \).

Answer: 3/4

Explanation: From the above figure, we can see that there are 3 one-fourth shaded parts. So, \(\frac { 1 }{ 4 } +\frac { 2 }{ 4 } =\frac { 3 }{ 4 } \)

Answer: 9/10

Explanation: From the above figure, we can see that there are 9 one-tenth shaded parts. So, \(\frac { 6 }{ 10 } +\frac { 3 }{ 10 } =\frac { 9 }{ 10 } \).

Find the sum. Use models to help. Question 4: \(\frac { 3 }{ 6 } +\frac { 3 }{ 6 } =\frac { }{ } \)

Answer: 6/6 = 1

Explanation: 3/6 and 3/6 has same numerators and same denominators so we have to add both the fractions. \(\frac { 3 }{ 6 } +\frac { 3 }{ 6 } =\frac { 6 }{ 6 } \) 6/6 = 1

Question 5: \(\frac { 1 }{ 3 } +\frac { 1 }{ 3 } =\frac { }{ } \)

Answer: 2/3

Explanation: 1/3 and 1/3 has same numerators and same denominators so we have to add both the fractions. \(\frac { 1 }{ 3 } +\frac { 1 }{ 3 } =\frac { 2 }{ 3 } \)

Question 6: \(\frac { 5 }{ 8 } +\frac { 2 }{ 8 } =\frac { }{ } \)

Answer: 7/8

Explanation: Given the expressions 5/8 and 2/8. The above fractions have the same denominators but the numerators are different. So, \(\frac { 5 }{ 8 } +\frac { 2 }{ 8 } =\frac { 7 }{ 8 } \)

Find the sum. Use models or iTools to help. Question 7: \(\frac { 5 }{ 8 } +\frac { 2 }{ 8 } =\frac { }{ } \) Answer: 7/8

Question 8: \(\frac { 2 }{ 5 } +\frac { 2 }{ 5 } =\frac { }{ } \) Answer: 4/5

Explanation: 2/5 and 2/5 have the same numerators and same denominators so we have to add both the fractions. \(\frac { 2 }{ 5 } +\frac { 2 }{ 5 } =\frac { 4 }{ 5 } \)

Question 9: \(\frac { 4 }{ 6 } +\frac { 1 }{ 6 } =\frac { }{ } \) Answer: 5/6

Explanation: Given the fractions 4/6 and 1/6. The above fractions have the same denominators but the numerators are different. \(\frac { 4 }{ 6 } +\frac { 1 }{ 6 } =\frac { 5 }{ 6 } \)

Question 10: Jason is making a fruit drink. He mixes \(\frac { 2 }{ 8 } \) quart of grape juice with \(\frac { 3 }{ 8 } \) quart of apple juice. Then he adds \(\frac { 1 }{ 8 } \) quart of lemonade. How much fruit drink does Jason make? \(\frac { }{ } \) quart. Answer: \(\frac { 6 }{ 8 } \) quart.

Explanation: Given that, Jason is making a fruit drink. He mixes \(\frac { 2 }{ 8 } \) quart of grape juice with \(\frac { 3 }{ 8 } \) quart of apple juice. Then he adds \(\frac { 1 }{ 8 } \) quart of lemonade Add all the three fractions to how much fruit drink Jason makes. 2/8 + 3/8 + 1/8 = \(\frac { 6 }{ 8 } \) quart.

Question 11: A sum has five addends. Each addend is a unit fraction. The sum is 1. What are the addends?

Answer: 1/5

Explanation: Given that, A sum has five addends. Each addend is a unit fraction. The sum is 1. 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 5/5 = 1 Thus the addend is 1/5.

Explanation: Given that, In a survey, \(\frac { 4 }{ 12 } \) of the students chose Friday and \(\frac { 5 }{ 12 } \) chose Saturday as their favorite day of the week. Add both the fractions 4/12 and 5/12 \(\frac { 4 }{ 12 } \) + \(\frac { 5 }{ 12 } \) = \(\frac { 9 }{ 12 } \)

Answer: \(\frac { 4}{ 10} \)

Explanation: the answer is 4/10 because 4/10 + 2/10= 6/10+ 4/10 = 10/10. a bit confusing 4 + 2 = 6 right the, 6 + 4 = 10 so 10/10.

Have you ever seen a stained glass window in a building or home? Artists have been designing stained glass windows for hundreds of years.

Help design the stained glass sail on the boat below.

Materials • color pencils

Look at the eight triangles in the sail. Use the guide below to color the triangles:

• \(\frac {2 }{8 } \) blue
• \(\frac {3 }{8 } \) red
• \(\frac { 2}{ 8} \) orange
• \(\frac {1 }{8 } \) yellow

Question 14: Write an Equation Write an equation that shows the fraction of triangles that are red or blue. Answer: \(\frac {3 }{8 } \) red

Question 15: What color is the greatest part of the sail? Write a fraction for that color. How do you know that fraction is greater than the other fractions? Explain. Answer: Red

Explanation: Among all the colors Red color has the greatest part of the sail.

Find the sum. Use fraction strips to help.

Answer: 3/6

Question 2: \(\frac { 4 }{ 10 } +\frac { 5 }{ 10 } =\frac { }{ } \)

Question 3: \(\frac { 1 }{ 3 } +\frac { 2 }{ 3 } =\frac { }{ } \)

Question 4: \(\frac { 2 }{ 4 } +\frac { 1 }{ 4 } =\frac { }{ } \)

Question 5: \(\frac { 2 }{ 12 } +\frac { 4 }{ 12 } =\frac { }{ } \)

Question 6: \(\frac { 1 }{ 6 } +\frac { 3 }{ 6 } =\frac { }{ } \)

Question 7: \(\frac { 3 }{ 12 } +\frac { 9 }{ 12 } =\frac { }{ } \)

Answer: 12/12

Question 8: \(\frac { 3 }{ 8 } +\frac { 4 }{ 8 } =\frac { }{ } \)

Question 9: \(\frac { 3 }{ 4 } +\frac { 1 }{ 4 } =\frac { }{ } \)

Question 9: \(\frac { 1 }{ 5 } +\frac { 2 }{ 5 } =\frac { }{ } \)

Answer: 3/5

Question 10: \(\frac { 6 }{ 10 } +\frac { 3 }{ 10 } =\frac { }{ } \)

Question 11: Lola walks \(\frac { 4 }{ 10} \) mile to her friend’s house. Then she walks \(\frac { 5 }{ 10 } \) mile to the store. How far does she walk in all?

Answer: \(\frac { 9 }{ 10 } \) mile

Explanation: Given, Lola walks \(\frac { 4 }{ 10} \) mile to her friend’s house. Then she walks \(\frac { 5 }{ 10 } \) mile to the store. \(\frac { 4 }{ 10} \) + \(\frac { 5 }{ 10 } \) = \(\frac { 9 }{ 10 } \) Therefore she walked \(\frac { 9 }{ 10 } \) mile in all.

Question 12: Evan eats \(\frac { 1 }{ 8 } \) of a pan of lasagna and his brother eats \(\frac { 2 }{ 8 } \) of it. What fraction of the pan of lasagna do they eat in all? Answer: \(\frac { 3 }{ 8 } \) of the pan

Explanation: Given, Evan eats \(\frac { 1 }{ 8 } \) of a pan of lasagna and his brother eats \(\frac { 2 }{ 8 } \) of it. \(\frac { 1 }{ 8 } \) + \(\frac { 2 }{ 8 } \) = \(\frac { 3 }{ 8 } \)

Question 13: Jacqueline buys \(\frac { 2 }{ 4 } \) yard of green ribbon and \(\frac { 1 }{ 4 } \) yard of pink ribbon. How many yards of ribbon does she buy in all?

Answer: \(\frac { 3 }{ 4 } \) yard

Explanation: Given, Jacqueline buys \(\frac { 2 }{ 4 } \) yard of green ribbon and \(\frac { 1 }{ 4 } \) yard of pink ribbon. \(\frac { 2 }{ 4 } \) + \(\frac { 1 }{ 4 } \) = \(\frac { 3 }{ 4 } \) Thus Jacqueline bought \(\frac { 3 }{ 4 } \) yards of ribbon in all.

Question 14: Shu mixes \(\frac { 2 }{ 3 } \) pound of peanuts with \(\frac { 1 }{ 3 } \) pound of almonds. How many pounds of nuts does Shu mix in all?

Answer: 3/3 pound

Explanation: Given, Shu mixes \(\frac { 2 }{ 3 } \) pound of peanuts with \(\frac { 1 }{ 3 } \) pound of almonds. \(\frac { 2 }{ 3 } \) + \(\frac { 1 }{ 3 } \) = \(\frac { 3 }{ 3 } \) Therefore Shu mix \(\frac { 3 }{ 3 } \) pounds of nuts in all.

Question 1: Mary Jane has \(\frac { 3 }{ 8 } \) of a medium pizza left. Hector has \(\frac { 2 }{ 8 } \) of another medium pizza left. How much pizza do they have altogether?

(a) \(\frac { 1 }{ 8 } \) (b) \(\frac { 4 }{ 8 } \) (c) \(\frac { 5 }{ 8 } \) (d) \(\frac { 6 }{ 8 } \)

Answer: \(\frac { 5 }{ 8 } \)

Explanation: Given, Mary Jane has \(\frac { 3 }{ 8 } \) of a medium pizza left. Hector has \(\frac { 2 }{ 8 } \) of another medium pizza left. To find how much pizza do they have altogether we have to add both the fractions. \(\frac { 3 }{ 8 } \) + \(\frac { 2 }{ 8 } \) = \(\frac { 5 }{ 8 } \) Therefore Mary Jane and Hector has \(\frac { 5 }{ 8 } \) pizza altogether. Thus the correct answer is option c.

Question 2: Jeannie ate \(\frac { 1 }{ 4 } \) of an apple. Kelly ate \(\frac { 2 }{ 4 } \) of the apple. How much did they eat in all?

(a) \(\frac { 1 }{ 8 } \) (b) \(\frac { 2 }{ 8 } \) (c) \(\frac { 3 }{ 8 } \) (d) \(\frac { 3 }{ 4 } \)

Explanation: Given, Jeannie ate \(\frac { 1 }{ 4 } \) of an apple. Kelly ate \(\frac { 2 }{ 4 } \) of the apple. \(\frac { 1 }{ 4 } \) + \(\frac { 2 }{ 4 } \) = \(\frac { 3 }{ 4 } \) Thus the correct answer is option d.

Question 3: Karen is making 14 different kinds of greeting cards. She is making 12 of each kind. How many greeting cards is she making?

(a) 120 (b) 132 (c) 156 (d) 168

Answer: 168

Explanation: Given, Karen is making 14 different kinds of greeting cards. She is making 12 of each kind. To find how many greeting cards she is making we have to multiply 14 and 12. 14 × 12 = 168. Thus the correct answer is option d.

Question 4: Jefferson works part-time and earns $1,520 in four weeks. How much does he earn each week?

(a) $305 (b) $350 (c) $380 (d) $385

Answer: $380

Explanation: Jefferson works part-time and earns $1,520 in four weeks. 1520 – 4 weeks ? – 1 week 1520/4 = $380 Thus the correct answer is option c.

Question 5: By installing efficient water fixtures, the average American can reduce water use to about 45 gallons of water per day. Using such water fixtures, about how many gallons of water would the average American use in December?

(a) about 1,200 gallons (b) about 1,500 gallons (c) about 1,600 gallons (d) about 2,000 gallons

Answer: about 1,500 gallons

Explanation: Given, By installing efficient water fixtures, the average American can reduce water use to about 45 gallons of water per day. 1 day – 45 gallons 31 days – ? 45 × 31 = 1395 gallons The number near to 1395 is 1500 gallons. Thus the correct answer is option b.

Question 6: Collin is making a bulletin board and note center. He is using square cork tiles and square dry-erase tiles. One of every 3 squares will be a cork square. If he uses 12 squares for the center, how many will be cork squares?

(a) 3 (b) 4 (c) 6 (d) 8

Explanation: Given that, Collin is making a bulletin board and note center. He is using square cork tiles and square dry-erase tiles. One of every 3 squares will be a cork square. 12/3 = 4 Thus the correct answer is option b.

Explanation: Given that, Lisa needs 4/5 pounds of shrimp to make shrimp salad. She has 1/5 pound of shrimp. The denominators have the same numbers and numerators have different numbers. 4/5 – 3/5 = 1/5 Thus Lisa needs 1/5 pounds more shrimp.

Use the model to find the difference.

Answer: 1/6

Explanation: Given two fractions 3/6 and 2/6 Denominators are same but the numerators are different. 3/6 – 2/6 = 1/6

Answer: 3/10

Explanation: Given two fractions 8/10 and 5/10 Denominators are the same but the numerators are different. 8/10 – 5/10 = 3/10

Subtract. Use models to help.

Question 4: \(\frac { 5 }{ 8 } – \frac { 2 }{ 8 } = \frac { }{ } \)

Answer: 3/8

Question 5: \(\frac { 7 }{ 12 } – \frac { 2 }{ 12 } = \frac { }{ } \)

Answer: 5/12

Question 6: \(\frac { 3 }{4 } – \frac { 2 }{ 4 } = \frac { }{ } \)

Answer: 1/4

Question 7: \(\frac { 2 }{ 3 } – \frac { 1 }{ 3 } = \frac { }{ } \)

Answer: 1/3

Question 8: \(\frac { 7 }{ 8 } – \frac { 5 }{ 8 } = \frac { }{ } \)

Answer: 2/8

Question 9: Explain how you could find the unknown addend in \(\frac { 2 }{ 6 } \) + _____ = 1 without using a model. Answer: 4/6

Explanation: 1 can be written in the fraction form as 6/6 2/6 + x = 6/6 x = 6/6 – 2/6 x = 4/6

Answer: 10/12

a. What do you need to know?

Answer: We need to find the fraction of the pie did they eat on the second night.

b. How can you find the number of pieces eaten on the second night?

Answer: We can find the number of pieces eaten on the second night by dividing the number of eaten pieces by the total number of pieces.

c. Explain the steps you used to solve the problem. Complete the sentences. After the first night, _______ pieces were left. After the second night, _______ pieces were left. So, _______ of the pie was eaten on the second night.

Answer: After the first night, 9 pieces were left. After the second night, 2 pieces were left. So, 10 of the pie was eaten on the second night.

Question 11: Make Connection Between Models Judi ate \(\frac { 7}{8} \) of a small pizza and Jack ate \(\frac { 2}{ 8 } \) of a second small pizza. How much more of a pizza did Judi eat? \(\frac { }{ } \) Answer: \(\frac {5}{8} \)

Explanation: Given, Make Connection Between Models Judi ate \(\frac { 7}{8} \) of a small pizza and Jack ate \(\frac { 2}{ 8 } \) of a second small pizza. \(\frac {7}{8} \) – \(\frac {2}{8} \) = \(\frac {5}{8} \) Therefore Judi eat \(\frac {5}{8} \) of a pizza.

Explanation: Given, Keiko sewed \(\frac { 3}{4} \) yard of lace on her backpack. Pam sewed \(\frac { 1}{4} \) yard of lace on her backpack. \(\frac {3}{4} \) – \(\frac {1}{4} \) = \(\frac {2}{4} \)

Explanation: Given the fraction, 4/5 and 1/5 The denominators of both the fractions are the same so subtract the numerators. 4/5 – 1/5 = 3/5

Question 2: \(\frac { 3}{ 4 } – \frac { 1}{ 4 } = \frac { —}{ — } \)

Answer: 2/4

Explanation: Given the fractions \(\frac { 3}{ 4 } \) and [/latex] \frac { 1}{ 4 } [/latex] The denominators of both the fractions are the same so subtract the numerators. \(\frac { 3}{ 4 } – \frac { 1}{ 4 } = \frac { 2 }{ 4 } \)

Question 3: \(\frac { 5}{ 6 } – \frac { 1}{ 6 } = \frac { —}{ — } \)

Answer: 4/6

Explanation: Given the fractions \(\frac { 5 }{ 6 } \) and [/latex] \frac { 1 }{ 6 } [/latex] The denominators of both the fractions are the same so subtract the numerators. \(\frac { 5}{ 6 } – \frac { 1}{ 6 } = \frac { 4 }{ 6 } \)

Question 4: \(\frac { 7}{ 8 } – \frac { 1}{ 8 } = \frac { —}{ — } \)

Answer: 6/8

Explanation: Given the fractions \(\frac { 7 }{ 8 } \) and [/latex] \frac { 1 }{ 8 } [/latex] The denominators of both the fractions are the same so subtract the numerators. \(\frac { 7}{ 8 } – \frac { 1}{ 8 } = \frac { 6 }{ 8 } \)

Question 5: \(\frac { 1}{ 3 } – \frac { 2}{ 3 } = \frac { —}{ — } \)

Explanation: Given the fractions \(\frac { 1 }{ 3 } \) and [/latex] \frac { 2 }{ 3 } [/latex] The denominators of both the fractions are the same so subtract the numerators. \(\frac { 1}{ 3 } – \frac { 2}{ 3 } = \frac { 1}{ 3 } \)

Question 6: \(\frac { 8}{ 10 } – \frac { 2}{ 10 } = \frac { —}{ — } \)

Answer: 6/10

Explanation: Given the fractions \(\frac { 8 }{ 10 } \) and [/latex] \frac { 2 }{ 10 } [/latex] The denominators of both the fractions are the same so subtract the numerators. \(\frac { 8}{ 10 } – \frac { 2}{ 10 } = \frac { 6 }{ 10 } \)

Question 7: \(\frac { 3}{ 4 } – \frac { 1}{ 4 } = \frac { —}{ — } \)

Explanation: Given the fractions \(\frac { 3 }{ 4 } \) and [/latex] \frac { 1 }{ 4 } [/latex] The denominators of both the fractions are the same so subtract the numerators. \(\frac { 3}{ 4 } – \frac { 1}{ 4 } = \frac { 2 }{ 4 } \)

Question 8: \(\frac { 7}{ 6 } – \frac {5}{ 6 } = \frac { —}{ — } \)

Answer: 2/6

Explanation: Given the fractions \(\frac { 7 }{ 6 } \) and [/latex] \frac { 5 }{ 6 } [/latex] The denominators of both the fractions are the same so subtract the numerators. \(\frac { 7}{ 6 } – \frac {5}{ 6 } = \frac { 2 }{ 6 } \)

Answer: 5/8 pound

Explanation: Given that, Ena is making trail mix. pretzels = 7/8 Raisins = 2/8 To find the number of more pounds of pretzels than raisins she buy we have to subtract both the fractions. 7/8 – 2/8 = 5/8

Question 10: How many more pounds of granola than banana chips does she buy? \(\frac { —}{ — } \)

Answer: 2/8 pound

Explanation: Granola = 5/8 Banana Chips = 3/8 To find How many more pounds of granola than banana chips does she buy we have to subtract both the fractions. 5/8 – 3/8 = 2/8 pounds

Question 1: Lee reads for \(\frac { 3}{ 4} \) hour in the morning and \(\frac {2}{ 4} \) hour in the afternoon. How much longer does Lee read in the morning than in the afternoon? (a) 5 hours (b) \(\frac { 5}{ 4} \) (c) \(\frac { 4}{ 4} \) (d) \(\frac { 1}{ 4} \)

Answer: \(\frac { 1}{ 4} \)

Explanation: Given, Lee reads for \(\frac { 3}{ 4} \) hour in the morning and \(\frac {2}{ 4} \) hour in the afternoon. \(\frac { 3}{ 4} \) – \(\frac {2}{ 4} \) = \(\frac { 1}{ 4} \) Lee read \(\frac { 1}{ 4} \) hour in the morning than in the afternoon. Thus the correct answer is option d.

Answer: \(\frac { 5}{ 6} – \frac { 3}{ 6} = \frac { 2}{ 6} \)

Explanation: From the above figure we can say that \(\frac { 5}{ 6} – \frac { 3}{ 6} = \frac { 2}{ 6} \) Thus the correct answer is option c.

Question 3: A city received 2 inches of rain each day for 3 days. The meteorologist said that if the rain had been snow, each inch of rain would have been 10 inches of snow. How much snow would that city have received in the 3 days?

(a) 20 inches (b) 30 inches (c) 50 inches (d) 60 inches

Answer: 60 inches

Explanation: Given, A city received 2 inches of rain each day for 3 days. 2 × 3 inches = 6 inches The meteorologist said that if the rain had been snow, each inch of rain would have been 10 inches of snow. 6 × 10 inches = 60 inches Therefore the city has received 60 inches of snow in 3 days. Thus the correct answer is option d.

Question 4: At a party there were four large submarine sandwiches, all the same size. During the party, \(\frac { 2}{ 3} \) of the chicken sandwich, \(\frac { 3}{ 4} \) of the tuna sandwich, \(\frac { 7}{ 12} \) of the roast beef sandwich, and \(\frac { 5}{ 6} \) of the veggie sandwich were eaten. Which sandwich had the least amount left?

(a) chicken (b) tuna (c) roast beef (d) veggie

Answer: veggie

Explanation: Given, At a party there were four large submarine sandwiches, all the same size. During the party, \(\frac { 2}{ 3} \) of the chicken sandwich, \(\frac { 3}{ 4} \) of the tuna sandwich, \(\frac { 7}{ 12} \) of the roast beef sandwich, and \(\frac { 5}{ 6} \) of the veggie sandwich were eaten. Compare the fractions \(\frac { 2}{ 3} \), \(\frac { 3}{ 4} \) , \(\frac { 7}{ 12} \) and \(\frac { 5}{ 6} \). Among all the fractions veggie has the least fraction. Thus the correct answer is option d.

Question 5: Deena uses \(\frac { 3}{ 8} \) cup milk and \(\frac { 2}{ 8} \) cup oil in a recipe. How much liquid does she use in all?

(a) \(\frac {1}{ 8} \) cup (b) \(\frac {5}{ 8} \) cup (c) \(\frac {6}{ 8} \) cup (d) 5 cups

Answer: \(\frac {5}{ 8} \) cup

Explanation: Given, Deena uses \(\frac { 3}{ 8} \) cup milk and \(\frac { 2}{ 8} \) cup oil in a recipe. \(\frac { 3}{ 8} \) + \(\frac { 2}{ 8} \) = \(\frac {5}{ 8} \) cup Therefore she used \(\frac {5}{ 8} \) cup of milk in all. Thus the correct answer is option b.

Question 6: In the car lot, \(\frac { 4}{ 12} \) of the cars are white and \(\frac { 3}{ 12} \) of the cars are blue. What fraction of the cars in the lot are either white or blue? (a) \(\frac { 1}{ 12} \) (b) \(\frac { 7}{ 24} \) (c) \(\frac { 7}{ 12} \) (d) 7

Answer: \(\frac { 7}{ 12} \)

Explanation: Given, In the car lot, \(\frac { 4}{ 12} \) of the cars are white and \(\frac { 3}{ 12} \) of the cars are blue. \(\frac { 4}{ 12} \) + \(\frac { 3}{ 12} \) = \(\frac { 7}{ 12} \) Thus the correct answer is option c.

Question 1: 9 twelfth-size parts − 5 twelfth-size parts = \(\frac { —}{ — } \)

Answer: 4/12

Explanation: 9 twelfth-size parts − 5 twelfth-size parts 9 × \(\frac { 1 }{ 12 } \) = \(\frac { 9 }{ 12 } \) 5 × \(\frac { 1 }{ 12 } \) = \(\frac { 5 }{ 12 } \) The denominators of both the fractions are the same so subtract the numerators. \(\frac { 9 }{ 12 } \) – \(\frac { 5 }{ 12 } \) = \(\frac { 4 }{ 12 } \)

Question 2: \(\frac { 3}{ 12} + \frac {8}{ 12 } = \frac { —}{ — } \)

Answer: 11/12

Explanation: Given the fractions, \(\frac { 3 }{ 12 } \) and \(\frac { 8 }{ 12 } \) Add both the fractions The denominators of both the fractions are the same so add the numerators. \(\frac { 3}{ 12} + \frac {8}{ 12 } = \frac { 11 }{ 12 } \)

Question 3: \(\frac { 1}{ 3 } + \frac {1}{ 3 } = \frac { —}{ — } \)

Explanation: Given the fractions, \(\frac { 1 }{ 3 } \) and \(\frac { 1 }{ 3 } \) Add both the fractions The denominators of both the fractions are the same so add the numerators. \(\frac { 1}{ 3 } + \frac {1}{ 3 } = \frac { 2 }{ 3 } \)

Question 4: \(\frac { 3}{ 4 } – \frac {1}{ 4 } = \frac { —}{ — } \)

Explanation: Given the fractions, \(\frac { 3 }{ 4 } \) and \(\frac { 1 }{ 4 } \) Subtract both the fractions The denominators of both the fractions are the same so Subtract the numerators. \(\frac { 3}{ 4 } – \frac {1}{ 4 } = \frac { 2 }{ 4 } \)

Question 5: \(\frac { 2}{ 6 } + \frac {2}{ 6 } = \frac { —}{ — } \)

Explanation: Given the fractions, \(\frac { 2 }{ 6 } \) and \(\frac { 2 }{ 6 } \) Add both the fractions The denominators of both the fractions are the same so add the numerators. \(\frac { 2}{ 6 } + \frac {2}{ 6 } = \frac { 4 }{ 6 } \)

Question 6: \(\frac { 3}{ 8 } – \frac {1}{ 8 } = \frac { —}{ — } \)

Explanation: Given the fractions, \(\frac { 3 }{ 8 } \) and \(\frac { 1 }{ 8 } \) Subtract both the fractions The denominators of both the fractions are the same so Subtract the numerators. \(\frac { 3}{ 8 } – \frac {1}{ 8 } = \frac { 2 }{ 8 } \)

Question 7: \(\frac { 6}{ 10 } – \frac {2}{ 10 } = \frac { —}{ — } \)

Answer: 4/10

Explanation: Given the fractions, \(\frac { 6 }{ 10 } \) and \(\frac { 2 }{ 10 } \) Subtract both the fractions The denominators of both the fractions are the same so Subtract the numerators. \(\frac { 6}{ 10 } – \frac {2}{ 10 } = \frac { 4 }{ 10 } \)

Question 8: \(\frac { 1}{ 2 } – \frac {1}{2 } = \frac { —}{ — } \)

Explanation: Given the fractions, \(\frac { 1 }{ 2 } \) and \(\frac { 1 }{ 2 } \) Subtract both the fractions The denominators of both the fractions are the same so Subtract the numerators. \(\frac { 1}{ 2 } – \frac {1}{2 } \) = 0

Question 9: \(\frac {5}{ 6 } – \frac {4}{ 6 } = \frac { —}{ — } \)

Explanation: Given the fractions, \(\frac { 5 }{ 6 } \) and \(\frac { 4 }{ 6 } \) Subtract both the fractions The denominators of both the fractions are the same so Subtract the numerators. \(\frac {5}{ 6 } – \frac {4}{ 6 } = \frac { 1 }{ 6 } \)

Question 10: \(\frac { 4}{ 5 } – \frac {2}{ 5 } = \frac { —}{ — } \)

Answer: 2/5

Explanation: Given the fractions, \(\frac { 4 }{ 5 } \) and \(\frac { 2 }{ 5 } \) Subtract both the fractions The denominators of both the fractions are the same so Subtract the numerators. \(\frac { 4}{ 5 } – \frac {2}{ 5 } = \frac { 2 }{ 5 } \)

Question 11: \(\frac { 1}{ 4 } + \frac {1}{ 4 } = \frac { —}{ — } \)

Explanation: Given the fractions, \(\frac { 1 }{ 4 } \) and \(\frac { 1 }{ 4 } \) Add both the fractions The denominators of both the fractions are the same so add the numerators. \(\frac { 1}{ 4 } + \frac {1}{ 4 } = \frac { 2 }{ 4 } \)

Question 12: \(\frac { 9}{ 10 } – \frac {5}{ 10 } = \frac { —}{ — } \)

Explanation: Given the fractions, \(\frac { 9 }{ 10 } \) and \(\frac { 5 }{ 10 } \) Subtract both the fractions The denominators of both the fractions are the same so Subtract the numerators. \(\frac { 9}{ 10 } – \frac {5}{ 10 } = \frac { 4 }{ 10 } \)

Question 13: \(\frac { 1}{ 12 } + \frac {7}{ 12 } = \frac { —}{ — } \)

Answer: 8/12

Explanation: Given the fractions, \(\frac { 1 }{ 12 } \) and \(\frac { 7 }{ 12 } \) Add both the fractions The denominators of both the fractions are the same so add the numerators. \(\frac { 1}{ 12 } + \frac {7}{ 12 } = \frac { 8 }{ 12 } \)

Question 14: Christopher mixes \(\frac { 3}{ 8} \) gallon of red paint with \(\frac { 5}{ 8} \) gallon of blue paint to make purple paint. He uses \(\frac { 2}{8} \) gallon of the purple paint. How much purple paint is left? \(\frac { —}{ — } \) gallon

Answer: \(\frac { 6 }{ 8 } \) gallon

Explanation: Given, Christopher mixes \(\frac { 3}{ 8} \) gallon of red paint with \(\frac { 5}{ 8} \) gallon of blue paint to make purple paint. He uses \(\frac { 2}{8} \) gallon of the purple paint. \(\frac { 3}{ 8} \) + \(\frac { 5}{ 8} \) = \(\frac { 8 }{ 8 } \) \(\frac { 8 }{ 8 } \) – \(\frac { 2 }{ 8 } \) = \(\frac { 6 }{ 8 } \) gallon

Question 15: A city worker is painting a stripe down the center of Main Street. Main Street is \(\frac { 8}{ 10} \) mile long. The worker painted \(\frac { 4}{ 10} \) mile of the street. Explain how to find what part of a mile is left to paint. \(\frac { —}{ — } \) mile

Answer: \(\frac { 4 }{ 10 } \) mile

Explanation: Given, A city worker is painting a stripe down the center of Main Street. Main Street is \(\frac { 8}{ 10} \) mile long. The worker painted \(\frac { 4}{ 10} \) mile of the street. \(\frac { 8 }{ 10 } \) – \(\frac { 4 }{ 10 } \) = \(\frac { 4 }{ 10 } \) mile

Question 16: Sense or Nonsense? Brian says that when you add or subtract fractions with the same denominator, you can add or subtract the numerators and keep the same denominator. Is Brian correct? Explain.

Answer: correct

Explanation: The statement of Brian is correct because when you add or subtract fractions with the same denominator, you can add or subtract the numerators and keep the same denominator.

Question 17: The length of a rope was \(\frac { 6}{8} \) yard. Jeff cut the rope into 3 pieces. Each piece is a different length measured in eighths of a yard. What is the length of each piece of rope?

Answer: \(\frac { 2}{8} \)

Explanation: Given, The length of a rope was \(\frac { 6}{8} \) yard. Jeff cut the rope into 3 pieces. Each piece is a different length measured in eighths of a yard. Divide \(\frac { 6}{8} \) into 3 pieces. \(\frac { 6}{8} \) ÷ 3 = \(\frac { 2}{8} \)

Question 18: For 18a–18d, choose Yes or No to show if the sum or difference is correct.

a. \(\frac { 3}{ 5 } – \frac {1}{ 5 } = \frac {4 }{5 } \) (i) yes (ii) no

Explanation: The denominators of both the fractions are the same so Subtract the numerators. \(\frac { 3}{ 5 } – \frac {1}{ 5 } = \frac {2 }{5 } \) Thus the above statement is not correct.

b. \(\frac { 1}{ 4 } – \frac {2}{4 } = \frac {3 }{8 } \) (i) yes (ii) no

Explanation: The denominators of both the fractions are the same so Subtract the numerators. \(\frac { 1}{ 4 } – \frac {2}{4 } = \frac {1 }{4 } \) Thus the above statement is not correct.

c. \(\frac { 5}{ 8} – \frac {4}{ 8 } = \frac {1 }{8 } \) (i) yes (ii) no

Answer: yes

Explanation: The denominators of both the fractions are the same so Subtract the numerators. \(\frac { 5}{ 8} – \frac {4}{ 8 } = \frac {1 }{8 } \) Thus the above statement is correct.

d. \(\frac { 4}{ 9 } – \frac {2}{ 9 } = \frac {6 }{9 } \) (i) yes (ii) no Answer: no

Explanation: The denominators of both the fractions are the same so Subtract the numerators. d. \(\frac { 4}{ 9 } – \frac {2}{ 9 } = \frac {2 }{9 } \) Thus the above statement is not correct.

Answer: Jane’s Answer Makes Sense. Because the numerators are the same but the denominators are different. So, in order to add the fractions first, they have to make the denominators equal. 1/4 + 1/8 = 2/8 + 1/8 = 3/8

Find the sum or difference.

Explanation: The denominators of both the fractions are the same so add the numerators. \(\frac{4}{12}\) + \(\frac{8}{12}\) = \(\frac{12}{12}\)

Question 2. \(\frac{3}{6}-\frac{1}{6}\) = \(\frac{□}{□}\)

Explanation: The denominators of both the fractions are the same so Subtract the numerators. \(\frac{3}{6}\) – \(\frac{1}{6}\) = \(\frac{2}{6}\)

Question 3. \(\frac{4}{5}-\frac{3}{5}\) = \(\frac{□}{□}\)

Explanation: The denominators of both the fractions are the same so Subtract the numerators. \(\frac{4}{5}\) – \(\frac{3}{5}\) = \(\frac{1}{5}\)

Question 4. \(\frac{6}{10}+\frac{3}{10}\) = \(\frac{□}{□}\)

Explanation: The denominators of both the fractions are the same so add the numerators. \(\frac{6}{10}+\frac{3}{10}\) = \(\frac{9}{10}\)

Question 5. 1 – \(\frac{3}{8}\) = \(\frac{□}{□}\)

Answer: 5/8

Explanation: The denominators of both the fractions are the same so Subtract the numerators. 1 – \(\frac{3}{8}\) = \(\frac{8}{8}\) – \(\frac{3}{8}\) = \(\frac{5}{8}\)

Question 6. \(\frac{1}{4}+\frac{2}{4}\) = \(\frac{□}{□}\)

Explanation: The denominators of both the fractions are the same so add the numerators. \(\frac{1}{4}+\frac{2}{4}\) = \(\frac{3}{4}\)

Question 7. \(\frac{9}{12}-\frac{5}{12}\) = \(\frac{□}{□}\)

Explanation: The denominators of both the fractions are the same so Subtract the numerators. \(\frac{9}{12}-\frac{5}{12}\) = \(\frac{4}{12}\)

Question 8. \(\frac{5}{6}-\frac{2}{6}\) = \(\frac{□}{□}\)

Explanation: The denominators of both the fractions are the same so Subtract the numerators. \(\frac{5}{6}-\frac{2}{6}\) = \(\frac{3}{6}\)

Question 9. \(\frac{2}{3}+\frac{1}{3}\) = \(\frac{□}{□}\)

Answer: 3/3 = 1

Explanation: The denominators of both the fractions are the same so add the numerators. \(\frac{2}{3}+\frac{1}{3}\) = \(\frac{3}{3}\) = 1

Problem Solving

Question 10. Guy finds how far his house is from several locations and makes the table shown. How much farther away from Guy’s house is the library than the cafe? \(\frac{□}{□}\)

Answer: \(\frac{5}{10}\) mile

Explanation: The distance from Guy’s house to the library is \(\frac{9}{10}\) mile The distance from Guy’s house to the cafe is \(\frac{4}{10}\) mile To find how much farther away from Guy’s house is the library than the cafe subtract both the fractions. \(\frac{9}{10}\) – \(\frac{4}{10}\) = \(\frac{5}{10}\) mile

Question 11. If Guy walks from his house to school and back, how far does he walk? \(\frac{□}{□}\)

Answer: 10/10 mile

Explanation: The distance from Guy’s house to school = \(\frac{5}{10}\) mile From school to house \(\frac{5}{10}\) mile \(\frac{5}{10}\) + \(\frac{5}{10}\) = \(\frac{10}{10}\) mile

Question 1. Mr. Angulo buys \(\frac{5}{8}\) pound of red grapes and \(\frac{3}{8}\)pound of green grapes. How many pounds of grapes did Mr. Angulo buy in all? Options: a. \(\frac{1}{8}\) pound b. \(\frac{2}{8}\) pound c. 1 pound d. 2 pounds

Answer: 1 pound

Explanation: Given that, Mr. Angulo buys \(\frac{5}{8}\) pound of red grapes and \(\frac{3}{8}\)pound of green grapes. \(\frac{5}{8}\) + \(\frac{3}{8}\) = \(\frac{8}{8}\) = 1 Thus the correct answer is option c.

Answer: \(\frac{7}{8}\) – \(\frac{2}{8}\) = \(\frac{5}{8}\)

Explanation: By seeing the above figure we can say that, the equation of the model is \(\frac{7}{8}\) – \(\frac{2}{8}\) = \(\frac{5}{8}\) Thus the correct answer is option d.

Spiral Review

Question 3. There are 6 muffins in a package. How many packages will be needed to feed 48 people if each person has 2 muffins? Options: a. 4 b. 8 c. 16 d. 24

Explanation: There are 6 muffins in a package. Number of people = 48 48/6 = 8 Also given that each person gets 2 muffins. 8 × 2 = 16 Thus the correct answer is option c.

Question 4. Camp Oaks gets 32 boxes of orange juice and 56 boxes of apple juice. Each shelf in the cupboard can hold 8 boxes of juice. What is the least number of shelves needed for all the juice boxes? Options: a. 4 b. 7 c. 11 d. 88

Explanation: Given, Camp Oaks gets 32 boxes of orange juice and 56 boxes of apple juice. Each shelf in the cupboard can hold 8 boxes of juice. First, add the boxes of orange juice and apple juice. 32 + 56 = 88 boxes of juice Now divide 88 by 8 88/8 = 11 Thus the correct answer is option c.

Question 5. A machine makes 18 parts each hour. If the machine operates 24 hours a day, how many parts can it make in one day Options: a. 302 b. 332 c. 362 d. 432

Answer: 432

Explanation: Given, A machine makes 18 parts each hour. Multiply the number of parts with the number of hours. 18 × 24 = 432 parts in a day. Thus the correct answer is option d.

Answer: \(\frac{5}{6}\) – \(\frac{4}{6}\) = \(\frac{1}{6}\)

Explanation: By observing the figure we can say that the equation is \(\frac{5}{6}\) – \(\frac{4}{6}\) = \(\frac{1}{6}\). Thus the correct answer is option a.

Question 1. A ___________ always has a numerator of 1. ________________

Answer: unit fraction

Explanation: A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer.

Write the fraction as a sum of unit fractions.

Question 2. Type below: ____________

Answer: 1/3 + 1/3 + 1/3

Explanation: A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. The unit fraction of 3/3 is 1/3 + 1/3 + 1/3

Question 3. Type below: ____________

Answer: 1/12 + 1/12 + 1/12 + 1/12

A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. The unit fraction of 4/12 is 1/12 + 1/12 + 1/12 + 1/12.

Explanation: By using the above model we can write the equation 3/5 – 2/5 = 1/5

Explanation: By using the above model we can write the equation 5/6 – 1/6 = 4/6

Use the model to solve the equation.

Explanation: The denominators of both the fractions are the same so add the numerators. \(\frac{3}{8}+\frac{2}{8}\) = \(\frac{5}8}\)

Question 7. \(\frac{4}{10}+\frac{5}{10}\) = \(\frac{□}{□}\)

Explanation: The denominators of both the fractions are the same so add the numerators. \(\frac{4}{10}+\frac{5}{10}\) = \(\frac{9}{10}\)

Question 8. \(\frac{9}{12}-\frac{7}{12}\) = \(\frac{□}{□}\)

Answer: 2/12

Explanation: The denominators of both the fractions are the same so subtract the numerators. \(\frac{9}{12}-\frac{7}{12}\) = \(\frac{2}{12}\)

Answer: 3/3

Explanation: The denominators of both the fractions are the same so add the numerators. \(\frac{2}{3}+\frac{1}{3}\) = \(\frac{3}{3}\)

Question 10. \(\frac{1}{5}+\frac{3}{5}\) = \(\frac{□}{□}\)

Explanation: The denominators of both the fractions are the same so add the numerators. \(\frac{1}{5}+\frac{3}{5}\) = \(\frac{4}{5}\)

Question 11. \(\frac{2}{6}+\frac{2}{6}\) = \(\frac{□}{□}\)

Explanation: The denominators of both the fractions are the same so add the numerators. \(\frac{2}{6}+\frac{2}{6}\) = \(\frac{4}{6}\)

Question 12. \(\frac{4}{4}-\frac{2}{4}\) = \(\frac{□}{□}\)

Explanation: The denominators of both the fractions are the same so subtract the numerators. \(\frac{4}{4}-\frac{2}{4}\) = \(\frac{2}{4}\)

Question 13. \(\frac{7}{8}-\frac{4}{8}\) = \(\frac{□}{□}\)

Explanation: The denominators of both the fractions are the same so subtract the numerators. \(\frac{7}{8}-\frac{4}{8}\) = \(\frac{3}{8}\)

Question 14. Tyrone mixed \(\frac{7}{12}\) quart of red paint with \(\frac{1}{12}\) quart of yellow paint. How much paint does Tyrone have in the mixture? \(\frac{□}{□}\) quart

Answer: 8/12 quart

Explanation: Given that, Tyrone mixed \(\frac{7}{12}\) quart of red paint with \(\frac{1}{12}\) quart of yellow paint. Add both the fraction of paints. \(\frac{7}{12}\) + \(\frac{1}{12}\) = \(\frac{8}{12}\) quart Therefore Tyrone has \(\frac{8}{12}\) quart in the mixture.

Question 15. Jorge lives \(\frac{6}{8}\) mile from school and \(\frac{2}{8}\) mile from a ballpark. How much farther does Jorge live from school than from the ballpark? \(\frac{□}{□}\) mile

Answer: 4/8 mile

Explanation: Given, Jorge lives \(\frac{6}{8}\) mile from school and \(\frac{2}{8}\) mile from a ballpark. Subtract both the fractions. \(\frac{6}{8}\) – \(\frac{2}{8}\) = \(\frac{4}{8}\) Therefore Jorge live \(\frac{4}{8}\) mile from school than from the ballpark.

Question 16. Su Ling started an art project with 1 yard of felt. She used \(\frac{2}{6}\) yard on Tuesday and \(\frac{3}{6}\) yard on Wednesday. How much felt does Su Ling have left? \(\frac{□}{□}\) yard

Answer: 1/6 yard

Explanation: Given, Su Ling started an art project with 1 yard of felt. She used \(\frac{2}{6}\) yard on Tuesday and \(\frac{3}{6}\) yard on Wednesday. \(\frac{3}{6}\) – \(\frac{2}{6}\) = \(\frac{1}{6}\) yard Therefore, Su Ling \(\frac{1}{6}\) yard left.

Question 17. Eloise hung artwork on \(\frac{2}{5}\) of a bulletin board. She hung math papers on \(\frac{1}{5}\) of the same bulletin board. What part of the bulletin board has artwork or math papers? \(\frac{□}{□}\)

Explanation: Given, Eloise hung artwork on \(\frac{2}{5}\) of a bulletin board. She hung math papers on \(\frac{1}{5}\) of the same bulletin board. \(\frac{2}{5}\) + \(\frac{1}{5}\) = \(\frac{3}{5}\) \(\frac{3}{5}\) part of the bulletin board has artwork or math papers.

Write the unknown numbers. Write mixed numbers above the number line and fractions greater than one below the number line.

Write the mixed number as a fraction.

Question 2. 1 \(\frac{1}{8}\) = \(\frac{□}{□}\)

Answer: 9/8

Explanation: Given the expression, 1 \(\frac{1}{8}\) Convert from the mixed fraction to the improper fraction. 1 \(\frac{1}{8}\) = (1 × 8 + 1)/8 = 9/8

Question 3. 1 \(\frac{3}{5}\) = \(\frac{□}{□}\)

Answer: \(\frac{8}{5}\)

Explanation: Given the expression, 1 \(\frac{3}{5}\) Convert from the mixed fraction to the improper fraction. 1 \(\frac{3}{5}\) = (5 × 1 + 3)/5 = \(\frac{8}{5}\)

Question 4. 1 \(\frac{2}{3}\) = \(\frac{□}{□}\)

Answer: 5/3

Explanation: Given the expression, 1 \(\frac{2}{3}\) Convert from the mixed fraction to the improper fraction. 1 \(\frac{2}{3}\) = (3 × 1 + 2)/3 = \(\frac{5}{3}\)

Write the fraction as a mixed number.

Question 5. \(\frac{11}{4}\) = _____ \(\frac{□}{□}\)

Answer: 2 \(\frac{3}{4}\)

Explanation: Given the expression, \(\frac{11}{4}\) Convert from the improper fraction to the mixed fraction. \(\frac{11}{4}\) = 2 \(\frac{3}{4}\)

Question 6. \(\frac{6}{5}\) = _____ \(\frac{□}{□}\)

Answer: 1 \(\frac{1}{5}\)

Explanation: Given the expression, \(\frac{6}{5}\) Convert from the improper fraction to the mixed fraction. \(\frac{6}{5}\) = 1 \(\frac{1}{5}\)

Question 7. \(\frac{13}{10}\) = _____ \(\frac{□}{□}\)

Answer: 1 \(\frac{3}{10}\)

Explanation: Given the expression, \(\frac{13}{10}\) Convert from the improper fraction to the mixed fraction. \(\frac{13}{10}\) = 1 \(\frac{3}{10}\)

Question 8. 2 \(\frac{7}{10}\) = \(\frac{□}{□}\)

Answer: \(\frac{27}{10}\)

Explanation: Given the expression, 2 \(\frac{7}{10}\) Convert from the mixed fraction to the improper fraction. 2 \(\frac{7}{10}\) = \(\frac{27}{10}\)

Question 9. 3 \(\frac{2}{3}\) = \(\frac{□}{□}\)

Answer: \(\frac{11}{3}\)

Explanation: Given the expression, 3 \(\frac{2}{3}\) Convert from the mixed fraction to the improper fraction. 3 \(\frac{2}{3}\) = \(\frac{11}{3}\)

Question 10. 4 \(\frac{2}{5}\) = \(\frac{□}{□}\)

Answer: \(\frac{22}{5}\)

Explanation: Given the expression, 4 \(\frac{2}{5}\) Convert from the mixed fraction to the improper fraction. 4 \(\frac{2}{5}\) = \(\frac{22}{5}\)

Use Repeated Reasoning Algebra Find the unknown numbers.

Question 11. \(\frac{13}{7}\) = 1 \(\frac{■}{7}\) ■ = _____

Answer: 1 \(\frac{6}{7}\)

Explanation: Given the expression, \(\frac{13}{7}\) Convert from the mixed fraction to the improper fraction. \(\frac{13}{7}\) = 1 \(\frac{6}{7}\)

Question 12. ■ \(\frac{5}{6}\) = \(\frac{23}{6}\) ■ = _____

Explanation: Given the expression, ■ \(\frac{5}{6}\) = \(\frac{23}{6}\) ■ \(\frac{5}{6}\) × 6 = 23 ■ ×  = 23 – 5 ■ = 18/6 ■ = 3

Question 13. \(\frac{57}{11}\) = ■ \(\frac{■}{11}\) _____ \(\frac{□}{□}\)

Answer: 5 \(\frac{2}{11}\)

Explanation: Given the expression, \(\frac{57}{11}\) = ■ \(\frac{■}{11}\) Convert from the improper fraction to the mixed fraction. \(\frac{57}{11}\) = 5 \(\frac{2}{11}\)

Question 14. Pen has \(\frac{1}{2}\)-cup and \(\frac{1}{8}\)-cup measuring cups. What are two ways he could measure out 1 \(\frac{3}{4}\) cups of flour? Type below: _________________

Answer: 3 \(\frac{1}{2}\)-cups and 2 \(\frac{1}{8}\)-cup

Explanation: Pen has \(\frac{1}{2}\)-cup and \(\frac{1}{8}\)-cup measuring cups. 1 \(\frac{3}{4}\) = \(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) = 1 \(\frac{3}{4}\) = 3 \(\frac{1}{2}\)-cups + 2 \(\frac{1}{8}\)-cup

Question 15. Juanita is making bread. She needs 3 \(\frac{1}{2}\) cups of flour. Juanita only has a \(\frac{1}{4}\)-cup measuring cup. How many \(\frac{1}{4}\) cups of flour will Juanita use to prepare the bread? _____ \(\frac{1}{4}\) cups of flour

Answer: 14 \(\frac{1}{4}\) cups of flour

Explanation: Juanita is making bread. She needs 3 \(\frac{1}{2}\) cups of flour. Juanita only has a \(\frac{1}{4}\)-cup measuring cup. 3 \(\frac{1}{2}\) = \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) Therefore she needs 14 \(\frac{1}{4}\) cups of flour.

Question 16. Reason Quantitatively Cal is making energy squares. How many \(\frac{1}{2}\) cups of peanut butter are used in the recipe? _____ \(\frac{1}{2}\) cups of peanut butter

Answer: 3 \(\frac{1}{2}\) cups of peanut butter

Explanation: Given that 1 \(\frac{1}{2}\) cups of peanut butter are used in the recipe. We have to find how many \(\frac{1}{2}\) cups of peanut butter are used in the recipe. \(\frac{1}{2}\) + \(\frac{1}{2}\)  + \(\frac{1}{2}\) Therefore 3 \(\frac{1}{2}\) cups of peanut butter are used in the recipe.

Question 17. Suppose Cal wants to make 2 times as many energy squares as the recipe makes. How many cups of bran cereal should he use? Write your answer as a mixed number and as a fraction greater than 1 in simplest form. Type below: ____________

Answer: Take the amount of bran Cal is using and multiply it by 2 Given that 3 \(\frac{1}{4}\) cups of bran cereal is used in the recipe. 3 \(\frac{1}{4}\) × 2 = \(\frac{13}{4}\) × 2 = \(\frac{13}{2}\) = 6 \(\frac{1}{2}\) Thus 6 \(\frac{1}{2}\) cups of bran cereal he should use.

Question 18. Cal added 2 \(\frac{3}{8}\) cups of raisins. Write this mixed number as a fraction greater than 1 in the simplest form. \(\frac{□}{□}\)

Answer: \(\frac{19}{8}\)

Explanation: Given, Cal added 2 \(\frac{3}{8}\) cups of raisins. Convert from the mixed fraction to the improper fraction. 2 \(\frac{3}{8}\) = \(\frac{19}{8}\)

Question 19. Jenn is preparing brown rice. She needs 1 \(\frac{1}{2}\) cups of brown rice and 2 cups of water. Jenn has only a \(\frac{1}{8}\)– cup measuring cup. How many \(\frac{1}{8}\) cups each of rice and water will Jenn use to prepare the rice? brown rice: ________ \(\frac{1}{8}\) cups water: _________ \(\frac{1}{8}\) cups

Answer: Number of water cups = 16 Number of brown rice cups = 12

Explanation: Brown rice needed = 1 1/2 cups = 3/2 cups Water needed = 2 cups Measuring cups = 1/8 No. of cups used of water = 2/1/8 = 16 No. of cups used of rice = 3/2/1/8 = 12 cups

Question 2. 4 \(\frac{1}{3}\) \(\frac{□}{□}\)

Answer: \(\frac{13}{3}\)

Explanation: \(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{1}{3}\) = \(\frac{13}{3}\)

Question 3. 1 \(\frac{2}{5}\) \(\frac{□}{□}\)

Answer: \(\frac{7}{5}\)

Explanation: \(\frac{5}{5}\) + \(\frac{2}{5}\) = \(\frac{7}{5}\)

Question 4. 3 \(\frac{3}{2}\) \(\frac{□}{□}\)

Answer: \(\frac{9}{2}\)

Explanation: \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{1}{2}\) = \(\frac{9}{2}\)

Question 5. 4 \(\frac{1}{8}\) \(\frac{□}{□}\)

Answer: \(\frac{33}{8}\)

Explanation: \(\frac{8}{8}\) + \(\frac{8}{8}\) + \(\frac{8}{8}\) + \(\frac{8}{8}\) + \(\frac{1}{8}\) = \(\frac{33}{8}\)

Question 6. 1 \(\frac{7}{10}\) \(\frac{□}{□}\)

Answer: \(\frac{17}{10}\)

Explanation: \(\frac{10}{10}\) + \(\frac{7}{10}\) = \(\frac{17}{10}\)

Question 7. 5 \(\frac{1}{2}\) \(\frac{□}{□}\)

Answer: \(\frac{11}{2}\)

Explanation: \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{1}{2}\) = \(\frac{11}{2}\)

Question 8. 2 \(\frac{3}{8}\) \(\frac{□}{□}\)

Explanation: \(\frac{8}{8}\) + \(\frac{8}{8}\) + \(\frac{3}{8}\)

Question 9. \(\frac{31}{6}\) ______ \(\frac{□}{□}\)

Answer: 5 \(\frac{1}{6}\)

Explanation: \(\frac{6}{6}\) + \(\frac{6}{6}\) + \(\frac{6}{6}\) + \(\frac{6}{6}\) + \(\frac{6}{6}\) + \(\frac{1}{6}\) 1 + 1 + 1 + 1 + 1 + \(\frac{1}{6}\) = 5 \(\frac{1}{6}\)

Question 10. \(\frac{20}{10}\) ______ \(\frac{□}{□}\)

Explanation: \(\frac{10}{10}\) + \(\frac{10}{10}\) = 1 + 1 = 2

Question 11. \(\frac{15}{8}\) ______ \(\frac{□}{□}\)

Answer: 1 \(\frac{7}{8}\)

Explanation: \(\frac{8}{8}\) + \(\frac{7}{8}\) 1 + \(\frac{7}{8}\) = 1 \(\frac{7}{8}\)

Question 12. \(\frac{13}{6}\) ______ \(\frac{□}{□}\)

Answer: 2 \(\frac{1}{6}\)

Explanation: \(\frac{6}{6}\) + \(\frac{6}{6}\) + \(\frac{1}{6}\) = 1 + 1 + \(\frac{1}{6}\) = 2 \(\frac{1}{6}\)

Question 13. \(\frac{23}{10}\) ______ \(\frac{□}{□}\)

Answer: 2 \(\frac{3}{10}\)

Explanation: \(\frac{10}{10}\) + \(\frac{10}{10}\) + \(\frac{3}{10}\) 1 + 1 + \(\frac{3}{10}\) = 2 \(\frac{3}{10}\)

Question 14. \(\frac{19}{5}\) ______ \(\frac{□}{□}\)

Answer: 3 \(\frac{4}{5}\)

Explanation: \(\frac{5}{5}\) + \(\frac{5}{5}\) + \(\frac{5}{5}\) + \(\frac{4}{5}\) 1 + 1 + 1 + \(\frac{4}{5}\) = 3 \(\frac{4}{5}\)

Question 15. \(\frac{11}{3}\) ______ \(\frac{□}{□}\)

Answer: 3 \(\frac{2}{3}\)

Explanation: \(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{2}{3}\) = 1 + 1 + 1 \(\frac{2}{3}\) = 3 \(\frac{2}{3}\)

Question 16. \(\frac{9}{2}\) ______ \(\frac{□}{□}\)

Answer: 4 \(\frac{1}{2}\)

Explanation: \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{1}{2}\) = 1 + 1 + 1 + 1 + \(\frac{1}{2}\) = 4 \(\frac{1}{2}\)

Question 17. A recipe calls for 2 \(\frac{2}{4}\) cups of raisins, but Julie only has a \(\frac{1}{4}\) -cup measuring cup. How many \(\frac{1}{4}\) cups does Julie need to measure out 2 \(\frac{2}{4}\) cups of raisins? She needs ______ \(\frac{1}{4}\) cups

Answer: 10 \(\frac{1}{4}\) cups

Explanation: Given, A recipe calls for 2 \(\frac{2}{4}\) cups of raisins, but Julie only has a \(\frac{1}{4}\) -cup measuring cup. \(\frac{4}{4}\) + \(\frac{4}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) = 10 \(\frac{1}{4}\) cups

Question 18. If Julie needs 3 \(\frac{1}{4}\) cups of oatmeal, how many \(\frac{1}{4}\) cups of oatmeal will she use? She will use ______ \(\frac{1}{4}\) cups of oatmeal

Answer: 13 \(\frac{1}{4}\) cups of oatmeal

Explanation: \(\frac{4}{4}\) + \(\frac{4}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) = 13 \(\frac{1}{4}\) Therefore Julie needs 13 \(\frac{1}{4}\) cups of oatmeal.

Question 1. Which of the following is equivalent to \(\frac{16}{3}\) ? Options: a. 3 \(\frac{1}{5}\) b. 3 \(\frac{2}{5}\) c. 5 \(\frac{1}{3}\) d. 5 \(\frac{6}{3}\)

Answer: 5 \(\frac{1}{3}\)

Explanation: Convert from improper fraction to the mixed fraction. \(\frac{16}{3}\) = \(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{1}{3}\) = 5 \(\frac{1}{3}\) Thus the correct answer is option c.

Question 2. Stacey filled her \(\frac{1}{2}\)cup measuring cup seven times to have enough flour for a cake recipe. How much flour does the cake recipe call for? Options: a. 3 cups b. 3 \(\frac{1}{2}\) cups c. 4 cups d. 4 \(\frac{1}{2}\) cups

Answer: 3 \(\frac{1}{2}\) cups

Explanation: Given, Stacey filled her \(\frac{1}{2}\)cup measuring cup seven times to have enough flour for a cake recipe. \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{1}{2}\) 1 + 1 + 1 + \(\frac{1}{2}\) = 3 \(\frac{1}{2}\) cups Thus the correct answer is option b.

Question 3. Becki put some stamps into her stamp collection book. She put 14 stamps on each page. If she completely filled 16 pages, how many stamps did she put in the book? Options: a. 224 b. 240 c. 272 d. 275

Answer: 224

Explanation: Becki put some stamps into her stamp collection book. She put 14 stamps on each page. If she completely filled 16 pages Multiply 14 with 16 pages. 14 × 16 = 224 pages Thus the correct answer is option a.

Question 4. Brian is driving 324 miles to visit some friends. He wants to get there in 6 hours. How many miles does he need to drive each hour? Options: a. 48 miles b. 50 miles c. 52 miles d. 54 miles

Answer: 54 miles

Explanation: Brian is driving 324 miles to visit some friends. He wants to get there in 6 hours. Divide the number of miles by hours. 324/6 = 54 miles Thus the correct answer is option d.

Question 5. During a bike challenge, riders have to collect various colored ribbons. Each \(\frac{1}{2}\) mile they collect a red ribbon, each \(\frac{1}{8}\) mile they collect a green ribbon, and each \(\frac{1}{4}\) mile they collect a blue ribbon. Which colors of ribbons will be collected at the \(\frac{3}{4}\) mile marker? Options: a. red and green b. red and blue c. green and blue d. red, green, and blue

Answer: green and blue

Explanation: Given, During a bike challenge, riders have to collect various colored ribbons. Each \(\frac{1}{2}\) mile they collect a red ribbon, each \(\frac{1}{8}\) mile they collect a green ribbon, and each \(\frac{1}{4}\) mile they collect a blue ribbon. Green and Blue colors of ribbons will be collected at the \(\frac{3}{4}\) mile marker. Thus the correct answer is option c.

Question 6. Stephanie had \(\frac{7}{8}\) pound of bird seed. She used \(\frac{3}{8}\) pound to fill a bird feeder. How much bird seed does Stephanie have left? Options: a. \(\frac{3}{8}\) pound b. \(\frac{4}{8}\) pound c. 1 pound d. \(\frac{10}{8}\) pound

Answer: \(\frac{4}{8}\) pound

Explanation: Given, Stephanie had \(\frac{7}{8}\) pound of bird seed. She used \(\frac{3}{8}\) pound to fill a bird feeder. \(\frac{7}{8}\) – \(\frac{3}{8}\) = \(\frac{4}{8}\) pound Thus the correct answer is option b.

Write the sum as a mixed number with the fractional part less than 1.

Question 1. 1 \(\frac{1}{6}\) +3 \(\frac{3}{6}\) ———————– _______ \(\frac{□}{□}\)

Answer: 4 \(\frac{2}{3}\)

Explanation: 1 \(\frac{1}{6}\) +3 \(\frac{3}{6}\) 4 \(\frac{4}{6}\) = 4 \(\frac{2}{3}\)

Question 2. 1 \(\frac{4}{5}\) +7 \(\frac{2}{5}\) ———————– _______ \(\frac{□}{□}\)

Answer: 9 \(\frac{1}{5}\)

Explanation: 1 \(\frac{4}{5}\) +7 \(\frac{2}{5}\) 8 \(\frac{6}{5}\) = 9 \(\frac{1}{5}\)

Question 3. 2 \(\frac{1}{2}\) +3 \(\frac{1}{2}\) ———————– _______

Explanation: 2 \(\frac{1}{2}\) +3 \(\frac{1}{2}\) 5 \(\frac{2}{2}\) = 6

Find the difference.

Question 4. 3 \(\frac{7}{12}\) -2 \(\frac{5}{12}\) ———————– _______ \(\frac{□}{□}\)

Answer: 1 \(\frac{1}{6}\)

Explanation: 3 \(\frac{7}{12}\) -2 \(\frac{5}{12}\) 1 \(\frac{2}{12}\) = 1 \(\frac{1}{6}\)

Question 5. 4 \(\frac{2}{3}\) -3 \(\frac{1}{3}\) ———————– _______ \(\frac{□}{□}\)

Answer: 1 \(\frac{1}{3}\)

Explanation: 4 \(\frac{2}{3}\) -3 \(\frac{1}{3}\) 1 \(\frac{1}{3}\)

Question 6. 6 \(\frac{9}{10}\) -3 \(\frac{7}{10}\) ———————– _______ \(\frac{□}{□}\)

Answer: 3 \(\frac{1}{5}\)

Explanation: 6 \(\frac{9}{10}\) -3 \(\frac{7}{10}\) 3 \(\frac{2}{10}\)

Question 7. 7 \(\frac{4}{6}\) +4 \(\frac{3}{6}\) ———————– _______ \(\frac{□}{□}\)

Answer: 12 \(\frac{1}{6}\)

Explanation: 7 \(\frac{4}{6}\) +4 \(\frac{3}{6}\) 12 \(\frac{1}{6}\)

Question 8. 8 \(\frac{1}{3}\) +3 \(\frac{2}{3}\) ———————– _______ \(\frac{□}{□}\)

Explanation: 8 \(\frac{1}{3}\) +3 \(\frac{2}{3}\) 11 \(\frac{3}{3}\) = 12

Question 9. 5 \(\frac{4}{8}\) +3 \(\frac{5}{8}\) ———————– _______ \(\frac{□}{□}\)

Answer: 9 \(\frac{1}{8}\)

Explanation: 5 \(\frac{4}{8}\) +3 \(\frac{5}{8}\) 9 \(\frac{1}{8}\)

Question 10. 5 \(\frac{5}{12}\) +4 \(\frac{2}{12}\) ———————– _______ \(\frac{□}{□}\)

Answer: 9 \(\frac{7}{12}\)

Explanation: 5 \(\frac{5}{12}\) +4 \(\frac{2}{12}\) 9 \(\frac{7}{12}\)

Question 11. 5 \(\frac{7}{8}\) -2 \(\frac{3}{8}\) ———————– _______ \(\frac{□}{□}\)

Answer: 3 \(\frac{1}{2}\)

Explanation: 5 \(\frac{7}{8}\) -2 \(\frac{3}{8}\) 3 \(\frac{1}{2}\)

Question 12. 5 \(\frac{7}{12}\) -4 \(\frac{1}{12}\) ———————– _______ \(\frac{□}{□}\)

Answer: 1 \(\frac{1}{2}\)

Explanation: 5 \(\frac{7}{12}\) -4 \(\frac{1}{12}\) 1 \(\frac{1}{2}\)

Question 13. 3 \(\frac{5}{10}\) -1 \(\frac{3}{10}\) ———————– _______ \(\frac{□}{□}\)

Answer: 2 \(\frac{1}{5}\)

Explanation: 3 \(\frac{5}{10}\) -1 \(\frac{3}{10}\) 2 \(\frac{1}{5}\)

Question 14. 7 \(\frac{3}{4}\) -2 \(\frac{2}{4}\) ———————– _______ \(\frac{□}{□}\)

Answer: 5 \(\frac{1}{4}\)

Explanation: 7 \(\frac{3}{4}\) -2 \(\frac{2}{4}\) 5 \(\frac{1}{4}\)

Practice: Copy and Solve Find the sum or difference.

Question 15. \(1 \frac{3}{8}+2 \frac{7}{8}\) = _______ \(\frac{□}{□}\)

Answer: 4 \(\frac{1}{4}\)

Explanation: First add the whole numbers 1 + 2 = 3 3/8 + 7/8 = 10/8 Convert from improper fraction to the mixed fraction 10/8 = 5/4 = 1 1/4 3 + 1 1/4 = 4 1/4

Question 16. \(6 \frac{5}{8}\) – 4 = _______ \(\frac{□}{□}\)

Answer: 2 \(\frac{5}{8}\)

Explanation: \(6 \frac{5}{8}\) – 4 Subtract the whole numbers 6 – 4 = 2 = 2 \(\frac{5}{8}\)

Question 17. \(9 \frac{1}{2}+8 \frac{1}{2}\) = _______

Explanation: 9 \(\frac{1}{2}\) + 8 \(\frac{1}{2}\) 18

Question 18. \(6 \frac{3}{5}+4 \frac{3}{5}\) = _______ \(\frac{□}{□}\)

Answer: 11 \(\frac{1}{5}\)

Explanation: 6 \(\frac{3}{5}\) + 4 \(\frac{3}{5}\) 11 \(\frac{1}{5}\)

Question 19. \(8 \frac{7}{10}-\frac{4}{10}\) = _______ \(\frac{□}{□}\)

Answer: 8 \(\frac{3}{10}\)

Explanation: 8 \(\frac{7}{10}\)  – \(\frac{4}{10}\) 8 \(\frac{3}{10}\)

Question 20. \(7 \frac{3}{5}-6 \frac{3}{5}\) = _______

Explanation: 7 \(\frac{3}{5}\) + 6 \(\frac{3}{5}\) 1

Solve. Write your answer as a mixed number.

Question 21. Make Sense of Problems The driving distance from Alex’s house to the museum is 6 \(\frac{7}{10}\) miles. What is the round-trip distance? _______ \(\frac{□}{□}\) miles

Answer: 13 \(\frac{2}{5}\) miles

Explanation: Given that, The driving distance from Alex’s house to the museum is 6 \(\frac{7}{10}\) miles. To find the round-trip distance we have to multiply the driving distance with 2. 6 \(\frac{7}{10}\) × 2 = 13 \(\frac{4}{10}\) = 13 \(\frac{2}{5}\) miles

Question 22. The driving distance from the sports arena to Kristina’s house is 10 \(\frac{9}{10}\) miles. The distance from the sports arena to Luke’s house is 2 \(\frac{7}{10}\) miles. How much greater is the driving distance between the sports arena and Kristina’s house than between the sports arena and Luke’s house? _______ \(\frac{□}{□}\) miles

Answer: 8 \(\frac{1}{5}\) miles

Explanation: Given, The driving distance from the sports arena to Kristina’s house is 10 \(\frac{9}{10}\) miles. The distance from the sports arena to Luke’s house is 2 \(\frac{7}{10}\) miles. 10 \(\frac{9}{10}\) –  2 \(\frac{7}{10}\) First, subtract the whole numbers and then subtract the fractions 10 – 2 = 8 \(\frac{9}{10}\) – \(\frac{7}{10}\) = \(\frac{1}{5}\) = 8 \(\frac{1}{5}\) miles

Question 23. Pedro biked from his house to the nature preserve, a distance of 23 \(\frac{4}{5}\) miles. Sandra biked from her house to the lake, a distance of 12 \(\frac{2}{5}\) miles. How many miles less did Sandra bike than Pedro? _______ \(\frac{□}{□}\) miles

Answer: 11 \(\frac{2}{5}\) miles

Explanation: Pedro biked from his house to the nature preserve, a distance of 23 4/5 miles. Converting 23 4/5 miles to an improper fraction, it becomes 119/5 miles. Sandra biked from her house to the lake, a distance of 12 2/5 miles. Converting 12 2/5 miles to an improper fraction, it becomes 62/5 miles. Therefore, the difference in the number of miles biked by Sandra and Pedro is 119/5 – 62/5 = 57/5 = 11 2/5 miles

Question 24. During the Martinez family trip, they drove from home to a ski lodge, a distance of 55 \(\frac{4}{5}\) miles, and then drove an additional 12 \(\frac{4}{5}\) miles to visit friends. If the family drove the same route back home, what was the distance traveled during their trip? _______ \(\frac{□}{□}\) miles

Answer: 68 \(\frac{3}{5}\) miles

Explanation: Given, During the Martinez family trip, they drove from home to a ski lodge, a distance of 55 \(\frac{4}{5}\) miles, and then drove an additional 12 \(\frac{4}{5}\) miles to visit friends. 55 \(\frac{4}{5}\) + 12 \(\frac{4}{5}\) = 67 \(\frac{8}{5}\) = 68 \(\frac{3}{5}\) miles

Question 25. For 25a–25d, select True or False for each statement. a. 2 \(\frac{3}{8}\) + 1 \(\frac{6}{8}\) is equal to 4 \(\frac{1}{8}\). i. True ii. False

Answer: True

Explanation: Given the statement 2 \(\frac{3}{8}\) + 1 \(\frac{6}{8}\) is equal to 4 \(\frac{1}{8}\). First add the whole numbers 2 + 1 = 3 \(\frac{3}{8}\) + \(\frac{6}{8}\) = \(\frac{9}{8}\) Convert the improper fraction to the mixed fraction. \(\frac{9}{8}\) = 1 \(\frac{1}{8}\) 3 +1 \(\frac{1}{8}\) = 4 \(\frac{1}{8}\). Thus the above statement is true.

Question 25. b. 1 \(\frac{1}{6}\) + 1 \(\frac{4}{12}\) is equal to 2 \(\frac{2}{12}\). i. True ii. False

Answer: False

Explanation: 1 \(\frac{1}{6}\) + 1 \(\frac{4}{12}\) is equal to 2 \(\frac{2}{12}\). First add the whole numbers 1 + 1 = 2 \(\frac{1}{6}\) = \(\frac{2}{12}\)

\(\frac{2}{12}\) + \(\frac{4}{12}\) = \(\frac{6}{12}\) = 2 \(\frac{6}{12}\) Thus the above statement is false.

Question 25. c. 5 \(\frac{5}{6}\) – 2 \(\frac{4}{6}\) is equal to 1 \(\frac{3}{6}\). i. True ii. False

Explanation: 5 \(\frac{5}{6}\) – 2 \(\frac{4}{6}\) is equal to 1 \(\frac{3}{6}\). 5 – 2 = 3 \(\frac{5}{6}\) – \(\frac{4}{6}\) = \(\frac{1}{6}\) = 3 \(\frac{1}{6}\) Thus the above statement is false.

Question 25. d. 5 \(\frac{5}{8}\) – 3 \(\frac{2}{8}\) is equal to 2 \(\frac{3}{8}\). i. True ii. False

Explanation: 5 \(\frac{5}{8}\) – 3 \(\frac{2}{8}\) is equal to 2 \(\frac{3}{8}\) First, subtract the whole numbers 5 – 3 = 2 \(\frac{5}{8}\) – \(\frac{2}{8}\) = \(\frac{3}{8}\) = 2 \(\frac{3}{8}\) Thus the above statement is true.

Find the sum. Write the sum as a mixed number, so the fractional part is less than 1.

Question 2. 4 \(\frac{1}{2}\) +2 \(\frac{1}{2}\) _______ \(\frac{□}{□}\)

4 \(\frac{1}{2}\) +2 \(\frac{1}{2}\) 6 \(\frac{2}{2}\) = 6 + 1 = 7

Question 3. 2 \(\frac{2}{3}\) +3 \(\frac{2}{3}\) _______ \(\frac{□}{□}\)

Answer: 6 \(\frac{1}{3}\)

Explanation: 2 \(\frac{2}{3}\) +3 \(\frac{2}{3}\) 5 \(\frac{4}{3}\) = 5 + 1 \(\frac{1}{3}\) = 6 \(\frac{1}{3}\)

Question 4. 6 \(\frac{4}{5}\) +7 \(\frac{4}{5}\) _______ \(\frac{□}{□}\)

Answer: 14 \(\frac{3}{5}\)

Explanation: 6 \(\frac{4}{5}\) +7 \(\frac{4}{5}\) 13 \(\frac{8}{5}\) 13 + 1 \(\frac{3}{5}\) = 14 \(\frac{3}{5}\)

Question 5. 9 \(\frac{3}{6}\) +2 \(\frac{2}{6}\) _______ \(\frac{□}{□}\)

Answer: 11 \(\frac{5}{6}\)

Explanation: 9 \(\frac{3}{6}\) +2 \(\frac{2}{6}\) 11 \(\frac{5}{6}\)

Question 6. 8 \(\frac{4}{12}\) +3 \(\frac{6}{12}\) _______ \(\frac{□}{□}\)

Answer: 11 \(\frac{10}{12}\)

Explanation: 8 \(\frac{4}{12}\) +3 \(\frac{6}{12}\) 11 \(\frac{10}{12}\)

Question 7. 4 \(\frac{3}{8}\) +1 \(\frac{5}{8}\) _______ \(\frac{□}{□}\)

Explanation: 4 \(\frac{3}{8}\) +1 \(\frac{5}{8}\) 5 \(\frac{8}{8}\) = 5 + 1 = 6

Question 8. 9 \(\frac{5}{10}\) +6 \(\frac{3}{10}\) _______ \(\frac{□}{□}\)

Answer: 15 \(\frac{8}{10}\)

Explanation: 9 \(\frac{5}{10}\) +6 \(\frac{3}{10}\) 15 \(\frac{8}{10}\)

Question 9. 6 \(\frac{7}{8}\) -4 \(\frac{3}{8}\) _______ \(\frac{□}{□}\)

Answer: 2 \(\frac{4}{8}\)

Explanation: 6 \(\frac{7}{8}\) -4 \(\frac{3}{8}\) 2 \(\frac{4}{8}\)

Question 10. 4 \(\frac{2}{3}\) -3 \(\frac{1}{3}\) _______ \(\frac{□}{□}\)

Question 11. 6 \(\frac{4}{5}\) -3 \(\frac{3}{5}\) _______ \(\frac{□}{□}\)

Explanation: 6 \(\frac{4}{5}\) -3 \(\frac{3}{5}\) 3 \(\frac{1}{5}\)

Question 12. 7 \(\frac{3}{4}\) -2 \(\frac{1}{4}\) _______ \(\frac{□}{□}\)

Answer: 5 \(\frac{1}{2}\)

Explanation: 7 \(\frac{3}{4}\) -2 \(\frac{1}{4}\) 5 \(\frac{2}{4}\) = 5 \(\frac{1}{2}\)

Question 13. James wants to send two gifts by mail. One package weighs 2 \(\frac{3}{4}\) pounds. The other package weighs 1 \(\frac{3}{4}\) pounds. What is the total weight of the packages? _______ \(\frac{□}{□}\)

Explanation: 2 \(\frac{3}{4}\) + 1 \(\frac{3}{4}\) 4 \(\frac{1}{2}\)

Question 14. Tierra bought 4 \(\frac{3}{8}\) yards blue ribbon and 2 \(\frac{1}{8}\) yards yellow ribbon for a craft project. How much more blue ribbon than yellow ribbon did Tierra buy? _______ \(\frac{□}{□}\)

Answer: 2 \(\frac{1}{4}\)

Explanation: Given, 4 \(\frac{3}{8}\) -2 \(\frac{1}{8}\)  2 \(\frac{1}{4}\)

Question 1. Brad has two lengths of copper pipe to fit together. One has a length of 2 \(\frac{5}{12}\) feet and the other has a length of 3 \(\frac{7}{12}\) feet. How many feet of pipe does he have in all? Options: a. 5 feet b. 5 \(\frac{6}{12}\) feet c. 5 \(\frac{10}{12}\) feet d. 6 feet

Answer: 5 feet

Explanation: Given, Brad has two lengths of copper pipe to fit together. One has a length of 2 \(\frac{5}{12}\) feet and the other has a length of 3 \(\frac{7}{12}\) feet. Add both the lengths 2 \(\frac{5}{12}\) + 3 \(\frac{7}{12}\) = 5 \(\frac{12}{12}\) = 5 feet Thus the correct answer is option a.

Question 2. A pattern calls for 2 \(\frac{1}{4}\) yards of material and 1 \(\frac{1}{4}\) yards of lining. How much total fabric is needed? Options: a. 2 \(\frac{2}{4}\) yards b. 3 yards c. 3 \(\frac{1}{4}\) yards d. 3 \(\frac{2}{4}\) yards

Answer: 3 \(\frac{2}{4}\) yards

Explanation: Given, A pattern calls for 2 \(\frac{1}{4}\) yards of material and 1 \(\frac{1}{4}\) yards of lining. 2 \(\frac{1}{4}\) + 1 \(\frac{1}{4}\) = 3 + \(\frac{1}{4}\) + \(\frac{1}{4}\) = 3 \(\frac{2}{4}\) yards Thus the correct answer is option d.

Question 3. Shanice has 23 baseball trading cards of star players. She agrees to sell them for $16 each. How much will she get for the cards? Options: a. $258 b. $358 c. $368 d. $468

Answer: $368

Explanation: Given, Shanice has 23 baseball trading cards of star players. She agrees to sell them for $16 each. To find how much will she get for the cards 23 × 16 = 368 Therefore she will get $368 for the cards. Thus the correct answer is option c.

Question 4. Nanci is volunteering at the animal shelter. She wants to spend an equal amount of time playing with each dog. She has 145 minutes to play with all 7 dogs. About how much time can she spend with each dog? Options: a. about 10 minutes b. about 20 minutes c. about 25 minutes d. about 26 minutes

Answer: about 20 minutes

Explanation: Given, Nanci is volunteering at the animal shelter. She wants to spend an equal amount of time playing with each dog. She has 145 minutes to play with all 7 dogs. 145/7 = 20.7 Therefore she can spend about 20 minutes with each dog. Thus the correct answer is option b.

Question 5. Frieda has 12 red apples and 15 green apples. She is going to share the apples equally among 8 people and keep any extra apples for herself. How many apples will Frieda keep for herself? Options: a. 3 b. 4 c. 6 d. 7

Explanation: Given, Frieda has 12 red apples and 15 green apples. She is going to share the apples equally among 8 people and keep any extra apples for herself. 12 + 15 = 27 27/8 27 – 24 = 3 Thus Frieda keep for herself 3 apples. Thus the correct answer is option a.

Question 6. The Lynch family bought a house for $75,300. A few years later, they sold the house for $80,250. How much greater was the selling price than the purchase price? Options: a. $4,950 b. $5,050 c. $5,150 d. $5,950

Answer: $4,950

Explanation: Given, The Lynch family bought a house for $75,300. A few years later, they sold the house for $80,250. $80,250 – $75,300 = $4,950 Thus the correct answer is option a.

Question 1. Rename both mixed numbers as fractions. Find the difference. 3 \(\frac{3}{6}\) = \(\frac{■}{6}\) −1 \(\frac{4}{6}\) = – \(\frac{■}{6}\) —————————————- _______ \(\frac{□}{□}\)

Answer: 1 \(\frac{5}{6}\)

Explanation: Convert from mixed fractions to the improper fractions. 3 \(\frac{3}{6}\) = \(\frac{21}{6}\) 1 \(\frac{4}{6}\) = \(\frac{10}{6}\) \(\frac{21}{6}\) – \(\frac{10}{6}\) \(\frac{11}{6}\) Convert from improper fractions to the mixed fractions. \(\frac{11}{6}\) = 1 \(\frac{5}{6}\)

Question 2. 1 \(\frac{1}{3}\) − \(\frac{2}{3}\) ——————— \(\frac{□}{□}\)

Answer: \(\frac{2}{3}\)

Explanation: Convert from mixed fractions to improper fractions. 1 \(\frac{1}{3}\) = \(\frac{4}{3}\) \(\frac{4}{3}\) – \(\frac{2}{3}\) \(\frac{2}{3}\)

Question 3. 4 \(\frac{7}{10}\) − 1 \(\frac{9}{10}\) ——————— ______ \(\frac{□}{□}\)

Answer: 2 \(\frac{8}{10}\)

Explanation: Convert from mixed fractions to improper fractions. 4 \(\frac{7}{10}\) = \(\frac{47}{10}\) 1 \(\frac{9}{10}\) = \(\frac{19}{10}\) \(\frac{47}{10}\) – \(\frac{19}{10}\) \(\frac{28}{10}\) = 2 \(\frac{8}{10}\)

Question 4. 3 \(\frac{5}{12}\) − \(\frac{8}{12}\) ——————— _____ \(\frac{□}{□}\)

Answer: 2 \(\frac{9}{12}\)

Explanation: Convert from mixed fractions to improper fractions. 3 \(\frac{5}{12}\) = \(\frac{41}{12}\) \(\frac{41}{12}\) − \(\frac{8}{12}\) 2 \(\frac{9}{12}\)

Question 5. 8 \(\frac{1}{10}\) − 2 \(\frac{9}{10}\) ——————— \(\frac{□}{□}\)

Answer: 5 \(\frac{1}{5}\)

Explanation: Convert from mixed fractions to improper fractions. 8 \(\frac{1}{10}\) = \(\frac{81}{10}\) 2 \(\frac{9}{10}\) = \(\frac{29}{10}\) \(\frac{81}{10}\) –\(\frac{29}{10}\) \(\frac{52}{10}\) = 5 \(\frac{1}{5}\)

Question 6. 2 − 1 \(\frac{1}{4}\) ——————— \(\frac{□}{□}\)

Answer: \(\frac{3}{4}\)

Explanation: Convert from mixed fractions to improper fractions. 1 \(\frac{1}{4}\) = \(\frac{5}{4}\) 2 − 1 \(\frac{1}{4}\) \(\frac{3}{4}\)

Question 7. 4 \(\frac{1}{5}\) − 3 \(\frac{2}{5}\) ——————— \(\frac{□}{□}\)

Answer: \(\frac{4}{5}\)

Explanation: Convert from mixed fractions to improper fractions. 4 \(\frac{1}{5}\) = \(\frac{21}{5}\) 3 \(\frac{2}{5}\) = \(\frac{17}{5}\) \(\frac{21}{5}\) –\(\frac{17}{5}\) \(\frac{4}{5}\)

Practice: Copy and Solve Find the difference.

Question 8. \(4 \frac{1}{6}-2 \frac{5}{6}\) _____ \(\frac{□}{□}\)

Explanation: Convert from mixed fractions to improper fractions. 4 \(\frac{1}{6}\) = \(\frac{25}{6}\) 2 \(\frac{5}{6}\) = \(\frac{17}{6}\) \(\frac{25}{6}\) –\(\frac{17}{6}\) \(\frac{8}{6}\) = 1 \(\frac{1}{3}\)

Question 9. \(6 \frac{9}{12}-3 \frac{10}{12}\) _____ \(\frac{□}{□}\)

Answer: 2 \(\frac{11}{12}\)

Explanation: Convert from mixed fractions to improper fractions. 6 \(\frac{9}{12}\) – 3 \(\frac{10}{12}\) 2 \(\frac{11}{12}\)

Question 10. \(3 \frac{3}{10}-\frac{7}{10}\) _____ \(\frac{□}{□}\)

Answer: 2 \(\frac{3}{5}\)

Explanation: Convert from mixed fractions to improper fractions. 3 \(\frac{3}{10}\) = \(\frac{33}{10}\) \(\frac{33}{10}\) – \(\frac{7}{10}\) 2 \(\frac{3}{5}\)

Question 11. 4 – 2 \(\frac{3}{5}\) _____ \(\frac{□}{□}\)

Answer: 1 \(\frac{2}{5}\)

Explanation: Convert from mixed fractions to improper fractions. 2 \(\frac{3}{5}\) = \(\frac{13}{5}\) 4 –\(\frac{13}{5}\)  1 \(\frac{2}{5}\)

Question 12. Lisa mixed 4 \(\frac{2}{6}\) cups of orange juice with 3 \(\frac{1}{6}\) cups of pineapple juice to make fruit punch. She and her friends drank 3 \(\frac{4}{6}\) cups of the punch. How much of the fruit punch is left? _____ \(\frac{□}{□}\) cups

Answer: 3 \(\frac{5}{6}\) cups

Explanation: Given, Lisa mixed 4 \(\frac{2}{6}\) cups of orange juice with 3 \(\frac{1}{6}\) cups of pineapple juice to make fruit punch. She and her friends drank 3 \(\frac{4}{6}\) cups of the punch. Convert from mixed fractions to improper fractions. 4 \(\frac{2}{6}\) + 3 \(\frac{1}{6}\) 7 \(\frac{3}{6}\) Now subtract 3 \(\frac{4}{6}\) from 7 \(\frac{3}{6}\). 7 \(\frac{3}{6}\) -3 \(\frac{4}{6}\) 3 \(\frac{5}{6}\)

Rename the fractions to solve.

Question 13. Analyze Relationships Trumpets and cornets are brass instruments. Fully stretched out, the length of a trumpet is 5 \(\frac{1}{4}\) feet and the length of a cornet is 4 \(\frac{2}{4}\) feet. The trumpet is how much longer than the cornet? \(\frac{□}{□}\) feet

Answer: \(\frac{3}{4}\) feet

Explanation: Given, Trumpets and cornets are brass instruments. Fully stretched out, the length of a trumpet is 5 \(\frac{1}{4}\) feet and the length of a cornet is 4 \(\frac{2}{4}\) feet. 5 \(\frac{1}{4}\) – 4 \(\frac{2}{4}\) First subtract the whole numbers 5 – 4 = 1 \(\frac{1}{4}\) – \(\frac{2}{4}\) = \(\frac{1}{4}\) 1 – \(\frac{1}{4}\) = \(\frac{3}{4}\) feet Therefore trumpet is \(\frac{3}{4}\) feet longer than the cornet.

Question 14. Tubas, trombones, and French horns are brass instruments. Fully stretched out, the length of a tuba is 18 feet, the length of a trombone is 9 \(\frac{11}{12}\) feet, and the length of a French horn is 17 \(\frac{1}{12}\) feet. The tuba is how much longer than the French horn? The French horn is how much longer than the trombone? Type below: _____________

Answer: First, convert the fractions to decimals making the trombone 8.93 feet and the french horn 17.21 feet. The tuba would be 0.79 feet longer than the french horn, and the french horn would be 8.23 feet longer than the trombone. However, if you need the answer to remain a fraction, the tuba would be 11/14 feet longer than a french horn, and a french horn would be 8 3/14 feet longer than a trombone.

Question 15. The pitch of a musical instrument is related to its length. In general, the greater the length of a musical instrument, the lower its pitch. Order the brass instruments identified on this page from lowest pitch to the highest pitch. ____________ ____________ ____________

Answer: Tuba French Horn Trombone

Explanation: By seeing the above answer we can write the order of the brass instruments from the lowest pitch to the highest pitch. The order is tuba, french horn, and trombone.

Question 16. Alicia had 3 \(\frac{1}{6}\)yards of fabric. After making a tablecloth, she had 1 \(\frac{3}{6}\) yards of fabric. Alicia said she used 2 \(\frac{3}{6}\) yards of fabric for the tablecloth. Do you agree? Explain. ______

Answer: Yes

Explanation: An easier way to do this is to make the fractions improper fractions. 3 1/6 can be rewritten as 19/6. 1 4/6 can be rewritten as 10/6. Multiply the denominator by the number at its side, and add it to the numerator. 2 3/6 is 15/6. Subtract 10/6 from 19/6. 19/6-10/6=9/6. 9/6 is not 15/6, therefore she did not use 2 3/6 yards of fabric.

Question 2. 6 – 3 \(\frac{2}{5}\) _______ \(\frac{□}{□}\)

Explanation: First subtract the whole numbers 6 – 3 = 3 Next subtract the fractions, 3 – \(\frac{2}{5}\) = 2 \(\frac{3}{5}\)

Question 3. 5 \(\frac{1}{4}\) – 2 \(\frac{3}{4}\) _______ \(\frac{□}{□}\)

Answer: 2 \(\frac{1}{2}\)

Explanation: First subtract the whole numbers 5 – 2 = 3 Next subtract the fractions, \(\frac{1}{4}\) – \(\frac{3}{4}\) = – \(\frac{1}{2}\) 3 – \(\frac{1}{2}\) = 2 \(\frac{1}{2}\)

Question 4. 9 \(\frac{3}{8}\) – 8 \(\frac{7}{8}\) _______ \(\frac{□}{□}\)

Answer: \(\frac{1}{2}\)

Explanation: First subtract the whole numbers 9 – 8 = 1 Next subtract the fractions, \(\frac{3}{8}\) – \(\frac{7}{8}\) = – \(\frac{4}{8}\) = – \(\frac{1}{2}\) = 1 – \(\frac{1}{2}\) = \(\frac{1}{2}\)

Question 5. 12 \(\frac{3}{10}\) – 7 \(\frac{7}{10}\) _______ \(\frac{□}{□}\)

Answer: 4 \(\frac{3}{5}\)

Explanation: First subtract the whole numbers 12 – 7 = 5 Next subtract the fractions, \(\frac{3}{10}\) – \(\frac{7}{10}\) = – \(\frac{4}{10}\) 5 – \(\frac{4}{10}\) 5 – \(\frac{2}{5}\) = 4 \(\frac{3}{5}\)

Question 6. 8 \(\frac{1}{6}\) – 3 \(\frac{5}{6}\) _______ \(\frac{□}{□}\)

Answer: 4 \(\frac{1}{3}\)

Explanation: First subtract the whole numbers 8 – 3 = 5 Next subtract the fractions, \(\frac{1}{6}\) – \(\frac{5}{6}\) = – \(\frac{2}{3}\) 5 – \(\frac{2}{3}\) = 4 \(\frac{1}{3}\)

Question 7. 7 \(\frac{3}{5}\) – 4 \(\frac{4}{5}\) _______ \(\frac{□}{□}\)

Answer: 2 \(\frac{4}{5}\)

Explanation: First subtract the whole numbers 7 – 4 = 3 Next subtract the fractions, \(\frac{3}{5}\) – \(\frac{4}{5}\) = – \(\frac{1}{5}\) 3 – \(\frac{1}{5}\) = 2 \(\frac{4}{5}\)

Question 8. 10 \(\frac{1}{2}\) – 8 \(\frac{1}{2}\) _______ \(\frac{□}{□}\)

Explanation: First subtract the whole numbers 10 – 8 = 2 \(\frac{1}{2}\) – \(\frac{1}{2}\) = 0

Question 9. 7 \(\frac{1}{6}\) – 2 \(\frac{5}{6}\) _______ \(\frac{□}{□}\)

Explanation: First subtract the whole numbers 7 – 2 = 5 Next subtract the fractions, \(\frac{1}{6}\) – \(\frac{5}{6}\) = – \(\frac{4}{6}\) 5 – \(\frac{4}{6}\) = 4 \(\frac{1}{3}\)

Question 10. 9 \(\frac{3}{12}\) – 4 \(\frac{7}{12}\) _______ \(\frac{□}{□}\)

Answer: 2 \(\frac{2}{3}\)

Explanation: First subtract the whole numbers 9 – 4 = 5 Next subtract the fractions, \(\frac{3}{12}\) – \(\frac{7}{12}\) = – \(\frac{4}{12}\) = – \(\frac{1}{3}\) 5 – \(\frac{1}{3}\) = 2 \(\frac{2}{3}\)

Question 11. 9 \(\frac{1}{10}\) – 8 \(\frac{7}{10}\) _______ \(\frac{□}{□}\)

Answer: \(\frac{2}{5}\)

Explanation: First subtract the whole numbers 9 – 8 = 1 Next subtract the fractions, \(\frac{1}{10}\) – \(\frac{7}{10}\) = – \(\frac{6}{10}\) 1 – \(\frac{3}{5}\) = \(\frac{2}{5}\)

Question 12. 9 \(\frac{1}{3}\) – \(\frac{2}{3}\) _______ \(\frac{□}{□}\)

Answer: 8 \(\frac{2}{3}\)

Explanation: 9 \(\frac{1}{3}\) – \(\frac{2}{3}\) 8 \(\frac{2}{3}\)

Question 13. 3 \(\frac{1}{4}\) – 1 \(\frac{3}{4}\) _______ \(\frac{□}{□}\)

3 \(\frac{1}{4}\) – 1 \(\frac{3}{4}\) 1 \(\frac{1}{2}\)

Question 14. 4 \(\frac{5}{8}\) – 1 \(\frac{7}{8}\) _______ \(\frac{□}{□}\)

Explanation: First subtract the whole numbers 4 – 1 = 3 Next subtract the fractions, \(\frac{5}{8}\) – \(\frac{7}{8}\) = – \(\frac{1}{4}\) 3 – \(\frac{1}{4}\) = 2 \(\frac{3}{4}\)

Question 15. 5 \(\frac{1}{12}\) – 3 \(\frac{8}{12}\) _______ \(\frac{□}{□}\)

Answer: 1 \(\frac{5}{12}\)

Explanation: First subtract the whole numbers 5 – 3 = 2 Next subtract the fractions, \(\frac{1}{12}\) – \(\frac{8}{12}\) = – \(\frac{7}{12}\) 2 – \(\frac{7}{12}\) = 1 \(\frac{5}{12}\)

Question 16. 7 – 1 \(\frac{3}{5}\) _______ \(\frac{□}{□}\)

Answer: 5 \(\frac{2}{5}\)

Explanation: 7 – 1 \(\frac{3}{5}\) 5 \(\frac{2}{5}\)

Question 17. Alicia buys a 5-pound bag of rocks for a fish tank. She uses 1 \(\frac{1}{8}\) pounds for a small fish bowl. How much is left? _______ \(\frac{□}{□}\)

Answer: 3 \(\frac{7}{8}\)

Explanation: Given, Alicia buys a 5-pound bag of rocks for a fish tank. She uses 1 \(\frac{1}{8}\) pounds for a small fish bowl. First subtract the whole numbers 5 – 1 = 4 4 – 1 \(\frac{1}{8}\) = 3 \(\frac{7}{8}\)

Question 18. Xavier made 25 pounds of roasted almonds for a fair. He has 3 \(\frac{1}{2}\) pounds left at the end of the fair. How many pounds of roasted almonds did he sell at the fair? _______ \(\frac{□}{□}\)

Answer: 21 \(\frac{1}{2}\)

Explanation: Given, Xavier made 25 pounds of roasted almonds for a fair. He has 3 \(\frac{1}{2}\) pounds left at the end of the fair. First subtract the whole numbers 25 – 3 = 22 22 – \(\frac{1}{2}\) = 21 \(\frac{1}{2}\)

Question 1. Reggie is making a double-layer cake. The recipe for the first layer calls for 2 \(\frac{1}{4}\) cups sugar. The recipe for the second layer calls for 1 \(\frac{1}{4}\) cups sugar. Reggie has 5 cups of sugar. How much will he have left after making both recipes? Options: a. 1 \(\frac{1}{4}\) cups b. 1 \(\frac{2}{4}\) cups c. 2 \(\frac{1}{4}\) cups d. 2 \(\frac{2}{4}\) cups

Answer: 1 \(\frac{2}{4}\) cups

Explanation: Given, Reggie is making a double-layer cake. The recipe for the first layer calls for 2 \(\frac{1}{4}\) cups sugar. The recipe for the second layer calls for 1 \(\frac{1}{4}\) cups sugar. Reggie has 5 cups of sugar. 2 \(\frac{1}{4}\) + 1 \(\frac{1}{4}\) = 3 \(\frac{1}{2}\) 5 – 3 \(\frac{1}{2}\) = 1 \(\frac{2}{4}\) cups Thus the correct answer is option b.

Question 2. Kate has 4 \(\frac{3}{8}\) yards of fabric and needs 2 \(\frac{7}{8}\) yards to make a skirt. How much extra fabric will she have left after making the skirt? Options: a. 2 \(\frac{4}{8}\) yards b. 2 \(\frac{2}{8}\) yards c. 1 \(\frac{4}{8}\) yards d. 1 \(\frac{2}{8}\) yards

Answer: 1 \(\frac{4}{8}\) yards

Explanation: Given, Kate has 4 \(\frac{3}{8}\) yards of fabric and needs 2 \(\frac{7}{8}\) yards to make a skirt. First, subtract the whole numbers 4 – 2 = 2 Next, subtract the fractions, \(\frac{3}{8}\) – \(\frac{7}{8}\) = – \(\frac{4}{8}\) 2 – \(\frac{4}{8}\) = 1 \(\frac{4}{8}\) yards Thus the correct answer is option c.

Question 3. Paulo has 128 glass beads to use to decorate picture frames. He wants to use the same number of beads on each frame. If he decorates 8 picture frames, how many beads will he put on each frame? Options: a. 6 b. 7 c. 14 d. 16

Explanation: Given, Paulo has 128 glass beads to use to decorate picture frames. He wants to use the same number of beads on each frame 128/8 = 16 Thus the correct answer is option d.

Question 4. Madison is making party favors. She wants to make enough favors so each guest gets the same number of favors. She knows there will be 6 or 8 guests at the party. What is the least number of party favors Madison should make? Options: a. 18 b. 24 c. 30 d. 32

Explanation: Given, Madison is making party favors. She wants to make enough favors so each guest gets the same number of favors. She knows there will be 6 or 8 guests at the party. To find the least number of party favors, we have to consider the number of guests. In this case, there are two possibilities—6 or 8. For 6: 6, 12, 18, 24 (Add 6 to each number) For 8: 8, 16, 24 (Add 8 to each number) Now in both series, the least number (that is in common) is 24. Hence, Madison should make at least 24 party favors. Thus the correct answer is option b.

Question 5. A shuttle bus makes 4 round-trips between two shopping centers each day. The bus holds 24 people. If the bus is full on each one-way trip, how many passengers are carried by the bus each day? Options: a. 96 b. 162 c. 182 d. 192

Explanation: Given, A shuttle bus makes 4 round-trips between two shopping centers each day. The bus holds 24 people. 4 × 24 = 96 Thus the correct answer is option a.

Question 6. To make a fruit salad, Marvin mixes 1 \(\frac{3}{4}\) cups of diced peaches with 2 \(\frac{1}{4}\) cups of diced pears. How many cups of peaches and pears are in the fruit salad? Options: a. 4 cups b. 3 \(\frac{2}{4}\) cups c. 3 \(\frac{1}{4}\) cups d. 3 cups

Answer: 4 cups

Explanation: Given, To make a fruit salad, Marvin mixes 1 \(\frac{3}{4}\) cups of diced peaches with 2 \(\frac{1}{4}\) cups of diced pears. 1 \(\frac{3}{4}\) + 2 \(\frac{1}{4}\) = 4 cups Thus the correct answer is option a.

Question 1. Complete. Name the property used. \(\left(3 \frac{4}{10}+5 \frac{2}{10}\right)+\frac{6}{10}\) ______ \(\frac{□}{□}\)

Answer: The property used is associative property. 9 \(\frac{2}{10}\)

Explanation: The associative property states that you can add or multiply regardless of how the numbers are grouped. Given, \(\left(3 \frac{4}{10}+5 \frac{2}{10}\right)+\frac{6}{10}\) First add the whole numbers in the group. (3 \(\frac{4}{10}\) + 5 \(\frac{2}{10}\)) + \(\frac{6}{10}\) 3 + 5 = 8 8 + \(\frac{4}{10}\) + \(\frac{2}{10}\) + \(\frac{6}{10}\) Now add the fractions 8 + \(\frac{6}{10}\) + \(\frac{6}{10}\) 8 + \(\frac{12}{10}\) Convert from improper fractions to the mixed fractions. \(\frac{12}{10}\) = 1 \(\frac{2}{10}\) 8 + 1 \(\frac{2}{10}\) = 9 \(\frac{2}{10}\) Thus \(\left(3 \frac{4}{10}+5 \frac{2}{10}\right)+\frac{6}{10}\) = 9 \(\frac{2}{10}\)

Use the properties and mental math to find the sum.

Question 2. \(\left(2 \frac{7}{8}+3 \frac{2}{8}\right)+1 \frac{1}{8}\) ______ \(\frac{□}{□}\)

Answer: 7 \(\frac{1}{4}\)

Explanation: The associative property states that you can add or multiply regardless of how the numbers are grouped. Given \(\left(2 \frac{7}{8}+3 \frac{2}{8}\right)+1 \frac{1}{8}\) First add the whole numbers in the group. (2 \(\frac{7}{8}\) + 3 \(\frac{2}{8}\)) + 1 \(\frac{1}{8}\) 2 + 3 = 5 5 + \(\frac{7}{8}\) + \(\frac{2}{8}\) + 1 \(\frac{1}{8}\) 5 + \(\frac{9}{8}\) + 1 \(\frac{1}{8}\) 6 + \(\frac{10}{8}\) = 7 \(\frac{1}{4}\) Thus \(\left(2 \frac{7}{8}+3 \frac{2}{8}\right)+1 \frac{1}{8}\) = 7 \(\frac{1}{4}\)

Question 3. \(1 \frac{2}{5}+\left(1+\frac{3}{5}\right)\) ______

Explanation: The associative property states that you can add or multiply regardless of how the numbers are grouped. Given, \(1 \frac{2}{5}+\left(1+\frac{3}{5}\right)\) First add the whole numbers in the group. 1 + \(\frac{3}{5}\) = 1 \(\frac{3}{5}\) 1 \(\frac{2}{5}\) + 1 \(\frac{3}{5}\) 1 + 1 + \(\frac{5}{5}\) 1 + 1 + 1 = 3 Thus \(1 \frac{2}{5}+\left(1+\frac{3}{5}\right)\) = 3

Question 4. \(5 \frac{3}{6}+\left(5 \frac{5}{6}+4 \frac{3}{6}\right)\) ______ \(\frac{□}{□}\)

Answer: 15 \(\frac{5}{6}\)

Explanation: The associative property states that you can add or multiply regardless of how the numbers are grouped. Given, \(5 \frac{3}{6}+\left(5 \frac{5}{6}+4 \frac{3}{6}\right)\) First add the whole numbers in the group. 5 + 4 = 9 \(\frac{5}{6}\) + \(\frac{3}{6}\) = \(\frac{8}{6}\) 5 \(\frac{3}{6}\) + 9 \(\frac{8}{6}\) 5 \(\frac{3}{6}\) + 10 \(\frac{2}{6}\) = 15 \(\frac{5}{6}\) Thus \(5 \frac{3}{6}+\left(5 \frac{5}{6}+4 \frac{3}{6}\right)\) = 15 \(\frac{5}{6}\)

Question 5. \(\left(1 \frac{1}{4}+1 \frac{1}{4}\right)+2 \frac{3}{4}\) ______ \(\frac{□}{□}\)

Explanation: The associative property states that you can add or multiply regardless of how the numbers are grouped. Given, \(\left(1 \frac{1}{4}+1 \frac{1}{4}\right)+2 \frac{3}{4}\) First add the whole numbers in the group. (1 \(\frac{1}{4}\) + 1 \(\frac{1}{4}\)) + 2 \(\frac{3}{4}\) 1 + 1 = 2 2 \(\frac{1}{4}\) + \(\frac{1}{4}\) + 2 \(\frac{3}{4}\) 2 \(\frac{1}{2}\) + 2 \(\frac{3}{4}\) Add the whole numbers 2 + 2 = 4 4 \(\frac{1}{2}\) + \(\frac{3}{4}\) = 5 \(\frac{1}{4}\) Thus \(\left(1 \frac{1}{4}+1 \frac{1}{4}\right)+2 \frac{3}{4}\) = 5 \(\frac{1}{4}\)

Question 6. \(\left(12 \frac{4}{9}+1 \frac{2}{9}\right)+3 \frac{5}{9}\) ______ \(\frac{□}{□}\)

Answer: 17 \(\frac{2}{9}\)

Explanation: The associative property states that you can add or multiply regardless of how the numbers are grouped. Given, \(\left(12 \frac{4}{9}+1 \frac{2}{9}\right)+3 \frac{5}{9}\) First add the whole numbers in the group. 12 + 1 = 13 Add the fraction in the group. \(\frac{4}{9}\) + \(\frac{2}{9}\) + 3 \(\frac{5}{9}\) = 13 \(\frac{6}{9}\) + 3 \(\frac{5}{9}\) = 16 \(\frac{11}{9}\) = 17 \(\frac{2}{9}\) Thus \(\left(12 \frac{4}{9}+1 \frac{2}{9}\right)+3 \frac{5}{9}\) = 17 \(\frac{2}{9}\)

Question 7. \(\left(\frac{3}{12}+1 \frac{8}{12}\right)+\frac{9}{12}\) ______ \(\frac{□}{□}\)

Explanation: The associative property states that you can add or multiply regardless of how the numbers are grouped. Given, \(\left(\frac{3}{12}+1 \frac{8}{12}\right)+\frac{9}{12}\) First add the fractions in the group. \(\frac{3}{12}\) + \(\frac{8}{12}\) = \(\frac{11}{12}\) 1 \(\frac{11}{12}\) + \(\frac{9}{12}\) = 1 \(\frac{20}{12}\) = 2 \(\frac{2}{3}\) Thus \(\left(\frac{3}{12}+1 \frac{8}{12}\right)+\frac{9}{12}\) = 2 \(\frac{2}{3}\)

Question 8. \(\left(45 \frac{1}{3}+6 \frac{1}{3}\right)+38 \frac{2}{3}\) ______ \(\frac{□}{□}\)

Answer: 90 \(\frac{1}{3}\)

Explanation: Given, \(\left(45 \frac{1}{3}+6 \frac{1}{3}\right)+38 \frac{2}{3}\) First add the whole numbers in the group. 45 + 6 = 51 (51 \(\frac{1}{3}\) + \(\frac{1}{3}\)) + 38 \(\frac{2}{3}\) 51 \(\frac{2}{3}\) + 38 \(\frac{2}{3}\) = 89 \(\frac{4}{3}\) = 90 \(\frac{1}{3}\) Thus \(\left(45 \frac{1}{3}+6 \frac{1}{3}\right)+38 \frac{2}{3}\) = 90 \(\frac{1}{3}\)

Question 9. \(\frac{1}{2}+\left(103 \frac{1}{2}+12\right)\) ______ \(\frac{□}{□}\)

Answer: 116

Explanation: Given, \(\frac{1}{2}+\left(103 \frac{1}{2}+12\right)\) First add the whole numbers in the group. 103 + \(\frac{1}{2}\) + 12 = 115 \(\frac{1}{2}\) 115 \(\frac{1}{2}\) + \(\frac{1}{2}\) = 116 Thus \(\frac{1}{2}+\left(103 \frac{1}{2}+12\right)\) = 116

Question 10. \(\left(3 \frac{5}{10}+10\right)+11 \frac{5}{10}\) ______

Explanation: Given, \(\left(3 \frac{5}{10}+10\right)+11 \frac{5}{10}\) First add the whole numbers in the group. 3 + 10 = 13 13 + \(\frac{5}{10}\) + 11 \(\frac{5}{10}\) Add the whole numbers 13 + 11 = 24 24 + \(\frac{5}{10}\) + \(\frac{5}{10}\) = 25 Thus \(\left(3 \frac{5}{10}+10\right)+11 \frac{5}{10}\) = 25

Question 11. Pablo is training for a marathon. He ran 5 \(\frac{4}{8}\) miles on Friday, 6 \(\frac{5}{8}\) miles on Saturday, and 7 \(\frac{4}{8}\) miles on Sunday. How many miles did he run on all three days? ______ \(\frac{□}{□}\) miles

Answer: 19 \(\frac{5}{8}\) miles

Explanation: Given, Pablo is training for a marathon. He ran 5 \(\frac{4}{8}\) miles on Friday, 6 \(\frac{5}{8}\) miles on Saturday, and 7 \(\frac{4}{8}\) miles on Sunday. Add all the fractions to find how many miles he runs on all three days. 5 \(\frac{4}{8}\) + 6 \(\frac{5}{8}\) + 7 \(\frac{4}{8}\) First add the whole numbers 5 + 6 + 7 = 18 18 + \(\frac{4}{8}\) + \(\frac{5}{8}\) + \(\frac{4}{8}\) = 18 + \(\frac{13}{8}\) = 19 \(\frac{5}{8}\) miles Therefore Pablo runs 19 \(\frac{5}{8}\) miles on all three days.

Question 12. At lunchtime, Dale’s Diner served a total of 2 \(\frac{2}{6}\) pots of vegetable soup, 3 \(\frac{5}{6}\) pots of chicken soup, and 4 \(\frac{3}{6}\) pots of tomato soup. How many pots of soup were served in all? ______ \(\frac{□}{□}\) pots

Answer: 10 \(\frac{2}{3}\) pots

Explanation: Given, At lunchtime, Dale’s Diner served a total of 2 \(\frac{2}{6}\) pots of vegetable soup, 3 \(\frac{5}{6}\) pots of chicken soup, and 4 \(\frac{3}{6}\) pots of tomato soup. 2 \(\frac{2}{6}\) + 3 \(\frac{5}{6}\) + 4 \(\frac{3}{6}\) First add the whole numbers 2 + 3 + 4 = 9 Next add the fractions. \(\frac{2}{6}\) + \(\frac{5}{6}\) + \(\frac{3}{6}\) = \(\frac{10}{6}\) 9 + \(\frac{10}{6}\) = 10 \(\frac{2}{3}\) pots Therefore 10 \(\frac{2}{3}\) pots of soup were served in all.

Question 13. Which property of addition would you use to regroup the addends in Expression A? ______ property

Answer: Associative Property

Explanation: The associative property states that you can add or multiply regardless of how the numbers are grouped. Expression A is \(\frac{1}{8}\) + (\(\frac{7}{8}\) + \(\frac{4}{8}\)) The denominators of all three fractions are the same. So, the property for expression A is Associative Property.

Question 14. Which two expressions have the same value? ________ and _________

Answer: A and C

Explanation: Expression A is \(\frac{1}{8}\) + (\(\frac{7}{8}\) + \(\frac{4}{8}\)) \(\frac{1}{8}\) + (\(\frac{11}{8}\) = \(\frac{12}{8}\) Expression B is 1/2 + 2 1/2 + 4/2 = 5/2 Expression C is \(\frac{3}{7}\) + (\(\frac{1}{2}\) + \(\frac{4}{7}\)) \(\frac{1}{2}\) + \(\frac{4}{7}\) = \(\frac{7}{14}\) + \(\frac{8}{14}\) = \(\frac{15}{14}\) \(\frac{15}{14}\) + \(\frac{3}{7}\) = \(\frac{15}{14}\) + \(\frac{6}{14}\) = \(\frac{21}{14}\) Thus the expressions A and C has the same value.

Question 16. Costumes are being made for the high school musical. The table at the right shows the amount of fabric needed for the costumes of the male and female leads. Alice uses the expression \(7 \frac{3}{8}+1 \frac{5}{8}+2 \frac{4}{8}\) to find the total amount of fabric needed for the costume of the female lead. To find the value of the expression using mental math, Alice used the properties of addition. \(7 \frac{3}{8}+1 \frac{5}{8}+2 \frac{4}{8}=\left(7 \frac{3}{8}+1 \frac{5}{8}\right)+2 \frac{4}{8}\) Alice added 7 + 1 and was able to quickly add \(\frac{3}{8}\) and \(\frac{5}{8}\) to the sum of 8 to get 9. She added 2 \(\frac{4}{8}\) to 9, so her answer was 11 \(\frac{4}{8}\). So, the amount of fabric needed for the costume of the female lead actor is 11 \(\frac{4}{8}\) yards. Write a new problem using the information for the costume for the male lead actor. Pose a Problem                     Solve your problem. Check your solution. Type below: _____________

Answer: Alice used the expressions 1 2/8 + 2 3/8 + 5 6/8 to find the total amount of frabric needed for the costume of the male lead. What is the total amount of fabric needed for the costume? Answer: Alice wrote the expressions as (1 2/8 + 5 6/8) + 2 3/8 and simplified it by adding the whole number parts and the fraction parts in the parentheses. Then she added the mixed number: 1 + 5 + 1 + 2 3/8 = 9 3/8. So, the male leads costume needed 9 3/8 yards of fabric.

Question 16. Identify Relationships Explain how using the properties of addition makes both problems easier to solve. Type below: ____________

Answer: The properties make the properties the easier to solve because you can rearrange the mixed numbers so that their fraction parts add to 1.

Question 2. \(10 \frac{1}{8}+\left(3 \frac{5}{8}+2 \frac{7}{8}\right)\) _______ \(\frac{□}{□}\)

Answer: 16 \(\frac{5}{8}\)

Explanation: Given, \(10 \frac{1}{8}+\left(3 \frac{5}{8}+2 \frac{7}{8}\right)\) First add the whole numbers in the bracket. 3 + 2 = 5 10 \(\frac{1}{8}\) + 5 + \(\frac{5}{8}\) + \(\frac{7}{8}\) 10 \(\frac{1}{8}\) + 5 + \(\frac{12}{8}\) 10 + 5 = 15 15 + \(\frac{1}{8}\) + \(\frac{12}{8}\) 15 + \(\frac{13}{8}\) 16 \(\frac{5}{8}\) \(10 \frac{1}{8}+\left(3 \frac{5}{8}+2 \frac{7}{8}\right)\) = 16 \(\frac{5}{8}\)

Question 3. \(8 \frac{1}{5}+\left(3 \frac{2}{5}+5 \frac{4}{5}\right)\) _______ \(\frac{□}{□}\)

Answer: 17 \(\frac{2}{5}\)

Explanation: \(8 \frac{1}{5}+\left(3 \frac{2}{5}+5 \frac{4}{5}\right)\) 8 \(\frac{1}{5}\) + 3 \(\frac{2}{5}\) + 5 \(\frac{4}{5}\) 3 + 5 = 8 8 \(\frac{1}{5}\) + 8 + \(\frac{2}{5}\) + \(\frac{4}{5}\) 8 \(\frac{1}{5}\) + 8 + \(\frac{6}{5}\) 8 + 8 = 16 16 + \(\frac{1}{5}\) + \(\frac{6}{5}\) 16 + \(\frac{7}{5}\) 17 \(\frac{2}{5}\) \(8 \frac{1}{5}+\left(3 \frac{2}{5}+5 \frac{4}{5}\right)\) = 17 \(\frac{2}{5}\)

Question 4. \(6 \frac{3}{4}+\left(4 \frac{2}{4}+5 \frac{1}{4}\right)\) _______ \(\frac{□}{□}\)

Answer: 16 \(\frac{1}{2}\)

Explanation: \(6 \frac{3}{4}+\left(4 \frac{2}{4}+5 \frac{1}{4}\right)\) First add the whole numbers in the bracket. 6 \(\frac{3}{4}\) + 4 \(\frac{2}{4}\) + 5 \(\frac{1}{4}\) 4 + 5 = 9 6 \(\frac{3}{4}\) + 9 \(\frac{3}{4}\) 6 + 9 = 15 15 + \(\frac{3}{4}\) + \(\frac{3}{4}\) 16 \(\frac{1}{2}\) \(6 \frac{3}{4}+\left(4 \frac{2}{4}+5 \frac{1}{4}\right)\) = 16 \(\frac{1}{2}\)

Question 5. \(\left(6 \frac{3}{6}+10 \frac{4}{6}\right)+9 \frac{2}{6}\) _______ \(\frac{□}{□}\)

Answer: 26 \(\frac{3}{6}\)

Explanation: \(\left(6 \frac{3}{6}+10 \frac{4}{6}\right)+9 \frac{2}{6}\) 6 \(\frac{3}{6}\) + 10 \(\frac{4}{6}\) + 9 \(\frac{2}{6}\) First add the whole numbers in the bracket. 6 + 10 = 16 16 + \(\frac{3}{6}\) + \(\frac{4}{6}\) + 9 \(\frac{2}{6}\) 16 + \(\frac{7}{6}\) + 9 \(\frac{2}{6}\) 16 + 9 = 25 25 + \(\frac{7}{6}\) + \(\frac{2}{6}\) 25 + \(\frac{9}{6}\) = 26 \(\frac{3}{6}\) \(\left(6 \frac{3}{6}+10 \frac{4}{6}\right)+9 \frac{2}{6}\) = 26 \(\frac{3}{6}\)

Question 6. \(\left(6 \frac{2}{5}+1 \frac{4}{5}\right)+3 \frac{1}{5}\) _______ \(\frac{□}{□}\)

Answer: 11 \(\frac{2}{5}\)

Explanation: \(\left(6 \frac{2}{5}+1 \frac{4}{5}\right)+3 \frac{1}{5}\) 6 \(\frac{2}{5}\) + 1 \(\frac{4}{5}\) + 3 \(\frac{1}{5}\) First add the whole numbers in the bracket. 6 + 1 = 7 7 \(\frac{2}{5}\) + \(\frac{4}{5}\) + 3 \(\frac{1}{5}\) 7 + \(\frac{6}{5}\) + 3 \(\frac{1}{5}\) 7 + 3 = 10 10 + \(\frac{6}{5}\) + \(\frac{1}{5}\) 10 + \(\frac{7}{5}\) = 11 \(\frac{2}{5}\) Therefore \(\left(6 \frac{2}{5}+1 \frac{4}{5}\right)+3 \frac{1}{5}\) = 11 \(\frac{2}{5}\)

Question 7. \(7 \frac{7}{8}+\left(3 \frac{1}{8}+1 \frac{1}{8}\right)\) _______ \(\frac{□}{□}\)

Answer: 12 \(\frac{1}{8}\)

Explanation: \(7 \frac{7}{8}+\left(3 \frac{1}{8}+1 \frac{1}{8}\right)\) 7 \(\frac{7}{8}\) + 3 \(\frac{1}{8}\) + 1 \(\frac{1}{8}\) First add the whole numbers in the bracket. 3 + 1 = 4 7 \(\frac{7}{8}\) + 4 + \(\frac{1}{8}\) + \(\frac{1}{8}\) 7 \(\frac{7}{8}\) + 4 +\(\frac{2}{8}\) 7 + 4 = 11 11 + \(\frac{7}{8}\) + \(\frac{2}{8}\) 11 + \(\frac{9}{8}\) = 12 \(\frac{1}{8}\) Thus \(7 \frac{7}{8}+\left(3 \frac{1}{8}+1 \frac{1}{8}\right)\) = 12 \(\frac{1}{8}\)

Question 8. \(14 \frac{1}{10}+\left(20 \frac{2}{10}+15 \frac{7}{10}\right)\) _______ \(\frac{□}{□}\)

Explanation: \(14 \frac{1}{10}+\left(20 \frac{2}{10}+15 \frac{7}{10}\right)\) First add the whole numbers in the bracket. 14 \(\frac{1}{10}\) + 20 \(\frac{2}{10}\) + 15 \(\frac{7}{10}\) 20 + 15 = 35 14 \(\frac{1}{10}\) + 35 + \(\frac{2}{10}\) + \(\frac{7}{10}\) 14 \(\frac{1}{10}\) + 35 \(\frac{9}{10}\) 49 \(\frac{1}{10}\) + \(\frac{9}{10}\) 49 + 1 = 50 Thus \(14 \frac{1}{10}+\left(20 \frac{2}{10}+15 \frac{7}{10}\right)\) = 50

Question 9. \(\left(13 \frac{2}{12}+8 \frac{7}{12}\right)+9 \frac{5}{12}\) _______ \(\frac{□}{□}\)

Answer: 31 \(\frac{2}{12}\)

Explanation: \(\left(13 \frac{2}{12}+8 \frac{7}{12}\right)+9 \frac{5}{12}\) 13 \(\frac{2}{12}\) + 8 \(\frac{7}{12}\) + 9 \(\frac{5}{12}\) First add the whole numbers in the bracket. 13 + 8 = 21 21 + \(\frac{2}{12}\) + \(\frac{7}{12}\) + 9 \(\frac{5}{12}\) 21 + \(\frac{9}{12}\) + 9 \(\frac{5}{12}\) 30 + \(\frac{9}{12}\) + \(\frac{5}{12}\) = 31 \(\frac{2}{12}\) Thus \(\left(13 \frac{2}{12}+8 \frac{7}{12}\right)+9 \frac{5}{12}\) = 31 \(\frac{2}{12}\)

Question 10. Nate’s classroom has three tables of different lengths. One has a length of 4 \(\frac{1}{2}\) feet, another has a length of 4 feet, and a third has a length of 2 \(\frac{1}{2}\) feet. What is the length of all three tables when pushed end to end? _______ \(\frac{□}{□}\)

Explanation: Given, Nate’s classroom has three tables of different lengths. One has a length of 4 \(\frac{1}{2}\) feet, another has a length of 4 feet, and a third has a length of 2 \(\frac{1}{2}\) feet. 4 \(\frac{1}{2}\) + 4 + 2 \(\frac{1}{2}\) 4 + 4 + 2 = 10 \(\frac{1}{2}\) + \(\frac{1}{2}\) = 1 10 + 1 = 11 Therefore the length of all three tables when pushed end to end is 11 feet.

Question 11. Mr. Warren uses 2 \(\frac{1}{4}\) bags of mulch for his garden and another 4 \(\frac{1}{4}\) bags for his front yard. He also uses \(\frac{3}{4}\) bag around a fountain. How many total bags of mulch does Mr. Warren use? _______ \(\frac{□}{□}\)

Explanation: Given, Mr. Warren uses 2 \(\frac{1}{4}\) bags of mulch for his garden and another 4 \(\frac{1}{4}\) bags for his front yard. He also uses \(\frac{3}{4}\) bag around a fountain. 2 \(\frac{1}{4}\) + 4 \(\frac{1}{4}\) + \(\frac{3}{4}\) 2 + 4 = 6 6 + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{3}{4}\) = 7 \(\frac{1}{4}\)

Question 1. A carpenter cut a board into three pieces. One piece was 2 \(\frac{5}{6}\) feet long. The second piece was 3 \(\frac{1}{6}\) feet long. The third piece was 1 \(\frac{5}{6}\) feet long. How long was the board? Options: a. 6 \(\frac{5}{6}\) feet b. 7 \(\frac{1}{6}\) feet c. 7 \(\frac{5}{6}\) feet d. 8 \(\frac{1}{6}\) feet

Answer: c. 7 \(\frac{5}{6}\) feet

Explanation: Given, A carpenter cut a board into three pieces. One piece was 2 \(\frac{5}{6}\) feet long. The second piece was 3 \(\frac{1}{6}\) feet long. The third piece was 1 \(\frac{5}{6}\) feet long. Add three pieces. 2 \(\frac{5}{6}\) + 3 \(\frac{1}{6}\) = 5 + \(\frac{6}{6}\) = 5 + 1 = 6 6 + 1 \(\frac{5}{6}\) = 7 \(\frac{5}{6}\) feet Thus the correct answer is option c.

Question 2. Harry works at an apple orchard. He picked 45 \(\frac{7}{8}\) pounds of apples on Monday. He picked 42 \(\frac{3}{8}\) pounds of apples on Wednesday. He picked 54 \(\frac{1}{8}\) pounds of apples on Friday. How many pounds of apples did Harry pick those three days? Options: a. 132 \(\frac{3}{8}\) pounds b. 141 \(\frac{3}{8}\) pounds c. 142 \(\frac{1}{8}\) pounds d. 142 \(\frac{3}{8}\) pounds

Answer: 142 \(\frac{3}{8}\) pounds

Explanation: Given, Harry works at an apple orchard. He picked 45 \(\frac{7}{8}\) pounds of apples on Monday. He picked 42 \(\frac{3}{8}\) pounds of apples on Wednesday. He picked 54 \(\frac{1}{8}\) pounds of apples on Friday. 45 \(\frac{7}{8}\) + 42 \(\frac{3}{8}\) + 54 \(\frac{1}{8}\) Add the whole numbers first 45 + 42 + 54 = 141 141 + \(\frac{7}{8}\) + \(\frac{3}{8}\) + \(\frac{1}{8}\) 141 + 1 \(\frac{3}{8}\) = 142 \(\frac{3}{8}\) pounds Thus the correct answer is option d.

Question 3. There were 6 oranges in the refrigerator. Joey and his friends ate 3 \(\frac{2}{3}\) oranges. How many oranges were left? Options: a. 2 \(\frac{1}{3}\) oranges b. 2 \(\frac{2}{3}\) oranges c. 3 \(\frac{1}{3}\) oranges d. 9 \(\frac{2}{3}\) oranges

Answer: 9 \(\frac{2}{3}\) oranges

Explanation: Given, There were 6 oranges in the refrigerator. Joey and his friends ate 3 \(\frac{2}{3}\) oranges. 6 + 3 \(\frac{2}{3}\) = 9 \(\frac{2}{3}\) oranges Thus the correct answer is option d.

Question 4. Darlene was asked to identify which of the following numbers is prime. Which number should she choose? Options: a. 2 b. 12 c. 21 d. 39

Explanation: A prime number is an integer, or whole number, that has only two factors 1 and itself. In the above options, all are composite numbers except 2. Therefore 2 is a prime number. Thus the correct answer is option a.

Question 5. A teacher has 100 chairs to arrange for an assembly. Which of the following is NOT a way the teacher could arrange the chairs? Options: a. 10 rows of 10 chairs b. 8 rows of 15 chairs c. 5 rows of 20 chairs d. 4 rows of 25 chairs

Answer: 8 rows of 15 chairs

Explanation: A teacher has 100 chairs to arrange for an assembly. 15 × 8 = 120 So, 8 rows of 15 chairs are not the way to arrange the chairs. Thus the correct answer is option b.

Question 6. Nic bought 28 folding chairs for $16 each. How much money did Nic spend on chairs? Options: a. $196 b. $348 c. $448 d. $600

Answer: c. $448

Explanation: Given, Nic bought 28 folding chairs for $16 each. 28 × 16 = 448 Thus the correct answer is option c.

Question 1. Last week, Sia ran 1 \(\frac{1}{4}\) miles each day for 5 days and then took 2 days off. Did she run at least 6 miles last week? First, model the problem. Describe your model. Type below: _________

Answer: I will model the problem using fraction strips. I need a 1 strip for the whole and a 1/4 part for each of the 5 days. My model has a total of five 1 strops and five 1/4 parts.

Question 1. Then, regroup the parts in the model to find the number of whole miles Sia ran. Sia ran ___________ whole miles and ___________ mile. Finally, compare the total number of miles she ran to 6 miles. So, Sia ___________ run at least 6 miles last week. 6 \(\frac{1}{4}\) miles _____ 6 miles

Answer: Sia ran 6 whole miles and 1/4 mile. So, Sia did run at least 6 miles last week. 6 \(\frac{1}{4}\) miles > 6 miles

Question 2. What if Sia ran only \(\frac{3}{4}\) mile each day. Would she have run at least 6 miles last week? Explain. _____

Explanation: She would have run \(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{3}{4}\) = \(\frac{15}{4}\) or 3 \(\frac{3}{4}\) miles.

Question 3. A quarter is \(\frac{1}{4}\) dollar. Noah has 20 quarters. How much money does he have? Explain. $ _____

Explanation: Since each quarter is 1/4 dollar, each group of 4 quarters is 1 dollar. Since 4/4 + 4/4 + 4/4 + 4/4 + 4/4 = 20/4, Noah has 1 + 1 + 1 + 1 + 1 = 5 dollars

Question 4. How many \(\frac{2}{5}\) parts are in 2 wholes? _____

Explanation: \(\frac{2}{5}\)/2 = 5

Question 5. A company shipped 15,325 boxes of apples and 12,980 boxes of oranges. How many more boxes of apples than oranges did the company ship? _____ boxes

Answer: 2345 boxes

Explanation: Given, A company shipped 15,325 boxes of apples and 12,980 boxes of oranges. Subtract 12,980 from 15,325 boxes 15,325 – 12,980 = 2,345 boxes.

Question 6. Analyze A fair sold a total of 3,300 tickets on Friday and Saturday. It sold 100 more on Friday than on Saturday. How many tickets did the fair sell on Friday? _____ tickets

Answer: 1700 tickets

Explanation: Given, Analyze A fair sold a total of 3,300 tickets on Friday and Saturday. It sold 100 more on Friday than on Saturday. 3,300 – 100 = 3,200 tickets 3200/2 = 1,600 tickets It sold 1600 tickets on saturday and 1700 tickets on Friday.

Question 7. Emma walked \(\frac{1}{4}\) mile on Monday, \(\frac{2}{4}\) mile on Tuesday, and \(\frac{3}{4}\) mile on Wednesday. If the pattern continues, how many miles will she walk on Friday? Explain how you found the number of miles. \(\frac{□}{□}\) miles

Answer: \(\frac{5}{4}\) miles

Explanation: I made a table that shows each day and the distance she walked. Then I looked for a pattern. The pattern showed that she walked 1/4 mile more each day. I continued the pattern to show she walked 4/4 mile on Thursday and 5/4 miles on Friday.

Question 8. Jared painted a mug \(\frac{5}{12}\) red and \(\frac{4}{12}\) blue. What part of the mug is not red or blue? \(\frac{□}{□}\)

Answer: \(\frac{3}{12}\)

Explanation: Given, Jared painted a mug \(\frac{5}{12}\) red and \(\frac{4}{12}\) blue. We have to find What part of the mug is not red or blue that means \(\frac{3}{12}\) part is neither red nor blue.

Explanation: Given, Each day, Mrs. Hewes knits \(\frac{1}{3}\) of a scarf in the morning and \(\frac{1}{3}\) of a scarf in the afternoon. \(\frac{1}{3}\) + \(\frac{1}{3}\) = \(\frac{2}{3}\) Thus it takes 3 days to knit 2 scarves.

Read each problem and solve.

Question 2. Val walks 2 \(\frac{3}{5}\) miles each day. Bill runs 10 miles once every 4 days. In 4 days, who covers the greater distance? _________

Answer: Val

Explanation: Given, Val walks 2 \(\frac{3}{5}\) miles each day. Bill runs 10 miles once every 4 days. 2 \(\frac{3}{5}\) × 4 Convert from mixed fraction to the improper fraction. 2 \(\frac{3}{5}\) = \(\frac{13}{5}\) × 4 = 10.4 10.4 > 10 Thus Val covers the greater distance.

Question 3. Chad buys peanuts in 2-pound bags. He repackages them into bags that hold \(\frac{5}{6}\) pound of peanuts. How many 2-pound bags of peanuts should Chad buy so that he can fill the \(\frac{5}{6}\) -pound bags without having any peanuts left over? _________ 2-pound bags

Explanation: Given, Chad buys peanuts in 2-pound bags. He repackages them into bags that hold \(\frac{5}{6}\) pound of peanuts. \(\frac{5}{6}\) + \(\frac{5}{6}\) + \(\frac{5}{6}\) + \(\frac{5}{6}\) + \(\frac{5}{6}\) Thus 5 2-pound bags of peanuts are left.

Question 4. A carpenter has several boards of equal length. He cuts \(\frac{3}{5}\) of each board. After cutting the boards, the carpenter notices that he has enough pieces left over to make up the same length as 4 of the original boards. How many boards did the carpenter start with? _________

Explanation: Given, A carpenter has several boards of equal length. He cuts \(\frac{3}{5}\) of each board. After cutting the boards, the carpenter notices that he has enough pieces left over to make up the same length as 4 of the original boards. 4 of the original boards have a summed length of 20 units. 5 x 4 = 20. Since 2/5 is left from each board, you simply add them until the 2’s add to 20. So, 2 x 10 = 20. Hence, there are 10 2/5 boards. That’s just 4 of the boards that the 2/5 make up, but that should also mean that there are 10 3/5 boards as well. 30/5 + 20/5 = 50/5 = 10

Question 1. Karyn cuts a length of ribbon into 4 equal pieces, each 1 \(\frac{1}{4}\) feet long. How long was the ribbon? Options: a. 4 feet b. 4 \(\frac{1}{4}\) feet c. 5 feet d. 5 \(\frac{1}{4}\) feet

Explanation: Given, Karyn cuts a length of ribbon into 4 equal pieces, each 1 \(\frac{1}{4}\) feet long. 1 \(\frac{1}{4}\) × 4 Convert from the mixed fraction to the improper fraction. 1 \(\frac{1}{4}\) = \(\frac{5}{4}\) \(\frac{5}{4}\) × 4 = 5 feet Thus the correct answer is option c.

Question 2. Several friends each had \(\frac{2}{5}\) of a bag of peanuts left over from the baseball game. They realized that they could have bought 2 fewer bags of peanuts between them. How many friends went to the game? Options: a. 6 b. 5 c. 4 d. 2

Explanation: Given, Several friends each had \(\frac{2}{5}\) of a bag of peanuts left over from the baseball game. They realized that they could have bought 2 fewer bags of peanuts between them 2 ÷ \(\frac{2}{5}\) = 5 Thus the correct answer is option b.

Question 3. A frog made three jumps. The first was 12 \(\frac{5}{6}\) inches. The second jump was 8 \(\frac{3}{6}\) inches. The third jump was 15 \(\frac{1}{6}\) inches. What was the total distance the frog jumped? Options: a. 35 \(\frac{3}{6}\) inches b. 36 \(\frac{1}{6}\) inches c. 36 \(\frac{3}{6}\) inches d. 38 \(\frac{1}{6}\) inches

Answer: 36 \(\frac{3}{6}\) inches

Explanation: Given, A frog made three jumps. The first was 12 \(\frac{5}{6}\) inches. The second jump was 8 \(\frac{3}{6}\) inches. The third jump was 15 \(\frac{1}{6}\) inches. First add the whole numbers 12 + 8 + 15 = 35 Next add the fractions, \(\frac{5}{6}\) + \(\frac{3}{6}\) + \(\frac{1}{6}\) = 1 \(\frac{3}{6}\) 35 + \(\frac{3}{6}\) = 36 \(\frac{3}{6}\) inches Thus the correct answer is option c.

Question 4. LaDanian wants to write the fraction \(\frac{4}{6}\) as a sum of unit fractions. Which expression should he write? Options: a. \(\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}\) b. \(\frac{2}{6}+\frac{2}{6}\) c. \(\frac{3}{6}+\frac{1}{6}\) d. \(\frac{1}{6}+\frac{1}{6}+\frac{2}{6}\)

Answer: \(\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}\)

Explanation: Given, LaDanian wants to write the fraction \(\frac{4}{6}\) as a sum of unit fractions. The unit fraction for \(\frac{4}{6}\) is \(\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}\) Thus the correct answer is option a.

Question 5. Greta made a design with squares. She colored 8 out of the 12 squares blue. What fraction of the squares did she color blue? Options: a. \(\frac{1}{4}\) b. \(\frac{1}{3}\) c. \(\frac{2}{3}\) d. \(\frac{3}{4}\)

Explanation: Given, Greta made a design with squares. She colored 8 out of the 12 squares blue. \(\frac{8}{12}\) = \(\frac{2}{3}\) Thus the correct answer is option c.

Question 6. The teacher gave this pattern to the class: the first term is 5 and the rule is add 4, subtract 1. Each student says one number. The first student says 5. Victor is tenth in line. What number should Victor say? Options: a. 17 b. 19 c. 20 d. 21

Answer: given a=5 d=4-1=3 to find t10 tn=a + (n-1) d t10=5 + (10-1) 3 t10=5 + 27 t10 = 32 victor is tenth in line,therefore he should say the number 32

Explanation: Given, A painter mixed \(\frac{1}{4}\) quart of red paint with \(\frac{3}{4}\) blue paint to make purple paint. \(\frac{1}{4}\) + \(\frac{3}{4}\) = \(\frac{4}{4}\) or 1.

Question 2. Ivan biked 1 \(\frac{2}{3}\) hours on Monday, 2 \(\frac{1}{3}\) hours on Tuesday, and 2 \(\frac{2}{3}\) hours on Wednesday. What is the total number of hours Ivan spent biking? Ivan spen _______ hours biking. _____ \(\frac{□}{□}\)

Answer: 6 \(\frac{2}{3}\)

Explanation: Given, Ivan biked 1 \(\frac{2}{3}\) hours on Monday, 2 \(\frac{1}{3}\) hours on Tuesday, and 2 \(\frac{2}{3}\) hours on Wednesday. 1 \(\frac{2}{3}\) + 2 \(\frac{1}{3}\) + 2 \(\frac{2}{3}\) First add the whole numbers, 1 + 2 + 2 = 5 2/3 + 1/3 + 2/3 = 5/3 Convert from improper fraction to the mixed fraction. 5/3 = 1 2/3 5 + 1 1/3  = 6 \(\frac{2}{3}\)

Question 3. Tricia had 4 \(\frac{1}{8}\) yards of fabric to make curtains. When she finished she had 2 \(\frac{3}{8}\) yards of fabric left. She said she used 2 \(\frac{2}{8}\) yards of fabric for the curtains. Do you agree? Explain. ______

Explanation: When I subtract 2 \(\frac{3}{8}\) and 4 \(\frac{1}{8}\), the answer is not 2 \(\frac{2}{8}\). The mixed number 4 \(\frac{1}{8}\) needs to be regrouped as a mixed number with a fraction greater than 1. 4 \(\frac{1}{8}\) = 3 \(\frac{9}{8}\) So, 3 \(\frac{9}{8}\) – 2 \(\frac{3}{8}\) = 1 \(\frac{6}{8}\) or 1 \(\frac{3}{4}\)

Answer: \(\frac{8}{10}\)

Explanation: Given, Miguel’s class went to the state fair. The fairground is divided into sections. Rides are in \(\frac{6}{10}\) of the fairground. Games are in \(\frac{2}{10}\) of the fairground. \(\frac{6}{10}\) + \(\frac{2}{10}\) = \(\frac{8}{10}\)

Question 4. Part B How much greater is the part of the fairground with rides than with farm exhibits? Explain how the model could be used to find the answer. \(\frac{□}{□}\)

Answer: \(\frac{5}{10}\)

Explanation: I could shade 6 sections to represent the section with the rides, and then I could cross out 1 section to represent the farm exhibits. This leaves 5 sections, so the part of the fairground with rides is 5/10 or 1/2 greater than the part with farm exhibits.

Question 5. Rita is making chili. The recipe calls for 2 \(\frac{3}{4}\) cups of tomatoes. How many cups of tomatoes, written as a fraction greater than one, are used in the recipe? _____ cups

Answer: 11/4 cups

Explanation: Given, Rita is making chili. The recipe calls for 2 \(\frac{3}{4}\) cups of tomatoes. Convert from the mixed fraction to the improper fraction. 2 \(\frac{3}{4}\) = 11/4 cups

Question 6. Lamar’s mom sells sports equipment online. She sold \(\frac{9}{10}\) of the sports equipment. Select a way \(\frac{9}{10}\) can be written as a sum of fractions. Mark all that apply. Options: a. \(\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{2}{10}\) b. \(\frac{3}{10}+\frac{2}{10}+\frac{3}{10}+\frac{1}{10}\) c. \(\frac{2}{10}+\frac{2}{10}+\frac{2}{10}+\frac{2}{10}\) d. \(\frac{4}{10}+\frac{1}{10}+\frac{1}{10}+\frac{3}{10}\) e. \(\frac{4}{10}+\frac{3}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}\) f. \(\frac{2}{10}+\frac{2}{10}+\frac{2}{10}+\frac{3}{10}\)

Answer: \(\frac{3}{10}+\frac{2}{10}+\frac{3}{10}+\frac{1}{10}\)

Explanation: a. \(\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{2}{10}\) = 6/10 ≠ 9/10 b. \(\frac{3}{10}+\frac{2}{10}+\frac{3}{10}+\frac{1}{10}\) = 9/10 c. \(\frac{2}{10}+\frac{2}{10}+\frac{2}{10}+\frac{2}{10}\) = 8/10 d. \(\frac{4}{10}+\frac{1}{10}+\frac{1}{10}+\frac{3}{10}\) = 9/10 e. \(\frac{4}{10}+\frac{3}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}\) = 10/10 ≠ 9/10 f. \(\frac{2}{10}+\frac{2}{10}+\frac{2}{10}+\frac{3}{10}\) = 9/10 Thus the suitable answers are b, d, f.

Question 7. Bella brought \(\frac{8}{10}\) gallon of water on a hiking trip. She drank \(\frac{6}{10}\) gallon of water. How much water is left? \(\frac{□}{□}\) gallons

Answer: \(\frac{2}{10}\) gallons

Explanation: Given, Bella brought \(\frac{8}{10}\) gallon of water on a hiking trip. She drank \(\frac{6}{10}\) gallon of water. To find how much water is left we have to subtract the two fractions. \(\frac{8}{10}\) – \(\frac{6}{10}\) = \(\frac{2}{10}\) gallons

Answer: \(\frac{7}{10}\)

Explanation: Given, In a survey, \(\frac{6}{10}\) of the students chose Saturday and \(\frac{1}{10}\) chose Monday as their favorite day of the week. \(\frac{6}{10}\) + \(\frac{1}{10}\) = \(\frac{7}{10}\)

Question 8. Part B How are the numerator and denominator of your answer related to the model? Explain. Type below: ___________

Answer: The numerator shows the number of parts shaded. The denominator shows the size of the parts.

Question 10. For numbers 10a–10e, select Yes or No to show if the sum or difference is correct. (a) \(\frac{2}{8}+\frac{1}{8}=\frac{3}{8}\) i. yes ii. no

Explanation: Denominators are the same but the numerators are different. So, add the numerators. \(\frac{2}{8}+\frac{1}{8}=\frac{3}{8}\) Thus the above statement is true.

Question 10. (b) \(\frac{4}{5}+\frac{1}{5}=\frac{5}{5}\) i. yes ii. no

Explanation: Denominators are the same but the numerators are different. So, add the numerators. \(\frac{4}{5}+\frac{1}{5}=\frac{5}{5}\) Thus the above statement is true.

Question 10. (c) \(\frac{4}{6}+\frac{1}{6}=\frac{5}{12}\) i. yes ii. no

Explanation: Denominators are the same but the numerators are different. So, add the numerators. \(\frac{4}{6}+\frac{1}{6}=\frac{5}{6}\) Thus the above statement is false.

Question 10. (d) \(\frac{6}{12}-\frac{4}{12}=\frac{2}{12}\) i. yes ii. no

Explanation: Denominators are the same but the numerators are different. So, subtract the numerators. \(\frac{6}{12}-\frac{4}{12}=\frac{2}{12}\) Thus the above statement is true.

Question 10. (e) \(\frac{7}{9}-\frac{2}{9}=\frac{9}{9}\) i. yes ii. no

Explanation: Denominators are the same but the numerators are different. So, subtract the numerators. \(\frac{7}{9}-\frac{2}{9}=\frac{5}{9}\) Thus the above statement is false.

Question 11. Gina has 5 \(\frac{2}{6}\) feet of silver ribbon and 2 \(\frac{4}{6}\) of gold ribbon. How much more silver ribbon does Gina have than gold ribbon? ______ \(\frac{□}{□}\) feet more silver ribbon.

Answer: 2 \(\frac{4}{6}\) feet more silver ribbon.

Explanation: Given, Gina has 5 \(\frac{2}{6}\) feet of silver ribbon and 2 \(\frac{4}{6}\) of gold ribbon. 5 \(\frac{2}{6}\) – 2 \(\frac{4}{6}\) = \(\frac{32}{6}\) – \(\frac{16}{6}\) = \(\frac{16}{6}\) Convert from improper fraction to the mixed fraction. 2 \(\frac{4}{6}\) feet more silver ribbon Therefore Gina has 2 \(\frac{4}{6}\) feet more silver ribbon than gold ribbon.

Question 12. Jill is making a long cape. She needs 4 \(\frac{1}{3}\) yards of blue fabric for the outside of the cape. She needs 3 \(\frac{2}{3}\) yards of purple fabric for the lining of the cape. Part A Jill incorrectly subtracted the two mixed numbers to find how much more blue fabric than purple fabric she should buy. Her work is shown below. \(4 \frac{1}{3}-3 \frac{2}{3}=\frac{12}{3}-\frac{9}{3}=\frac{3}{3}\) Why is Jill’s work incorrect? Type below: __________________

Answer: Jill changed only the whole number parts of the mixed number to thirds. She forgot to add the fraction part of the mixed number.

Question 12. Part B How much more blue fabric than purple fabric should Jill buy? Show your work. \(\frac{□}{□}\)

Answer: 4 \(\frac{1}{3}\) – 3 \(\frac{2}{3}\) = \(\frac{13}{3}\) – \(\frac{11}{3}\) = \(\frac{2}{3}\) Jill should buy \(\frac{2}{3}\) yard more blue fabric than purple fabric.

Explanation: Given, Russ has two jars of glue. One jar is \(\frac{1}{5}\) full. The other jar is \(\frac{2}{5}\) full. \(\frac{1}{5}\) + \(\frac{2}{5}\) = \(\frac{3}{5}\)

Answer: \(\frac{1}{4}\)

Explanation: Given that, Gertie ran \(\frac{3}{4}\) mile during physical education class. Sarah ran \(\frac{2}{4}\) mile during the same class. \(\frac{3}{4}\) – \(\frac{2}{4}\) = \(\frac{1}{4}\)

Question 15. Teresa planted marigolds in \(\frac{2}{8}\) of her garden and petunias in \(\frac{3}{8}\) of her garden. What fraction of the garden has marigolds and petunias? \(\frac{□}{□}\)

Answer: \(\frac{5}{8}\)

Explanation: Given, Teresa planted marigolds in \(\frac{2}{8}\) of her garden and petunias in \(\frac{3}{8}\) of her garden. Add both the fractions 2/8 and 3/8 to find the fraction of the garden has marigolds and petunias. \(\frac{2}{8}\) + \(\frac{3}{8}\) = \(\frac{5}{8}\)

Explanation: Each day she eats 1/2 cups of rice. But we want to know how long it will take to each 2 cups worth. so lets make an equation. 1/2 × x = 2 x = 4 Thus It will take 4 days to eat 2 cups of rice cereal.

Question 18. Three girls are selling cases of popcorn to earn money for a band trip. In week 1, Emily sold 2 \(\frac{3}{4}\) cases, Brenda sold 4 \(\frac{1}{4}\) cases, and Shannon sold 3 \(\frac{1}{2}\) cases. Part A How many cases of popcorn have the girls sold in all? Explain how you found your answer. ______ \(\frac{□}{□}\)

Answer: 10 \(\frac{1}{2}\) cases

Explanation: Given, Three girls are selling cases of popcorn to earn money for a band trip. In week 1, Emily sold 2 \(\frac{3}{4}\) cases, Brenda sold 4 \(\frac{1}{4}\) cases, and Shannon sold 3 \(\frac{1}{2}\) cases. First I add the whole numbers 2 + 4 + 3 = 9 cases. Then I add the fractions by combining 3/4 + 1/4 into one whole. So, 9 + 1 + 1/2 = 10 \(\frac{1}{2}\) cases

Question 18. Part B The girls must sell a total of 35 cases in order to have enough money for the trip. Suppose they sell the same amount in week 2 and week 3 of the sale as in week 1. Will the girls have sold enough cases of popcorn to go on the trip? Explain. ______

Explanation: Given, The girls must sell a total of 35 cases in order to have enough money for the trip. Suppose they sell the same amount in week 2 and week 3 of the sale as in week 1. If I add the sales from the 3 weeks, or 10 1/2 + 10 1/2 + 10 1/2, the sum is only 31 1/2 cases of popcorn. Thus is less than 35 cases.

Question 19. Henry ate \(\frac{3}{8}\) of a sandwich. Keith ate \(\frac{4}{8}\) of the same sandwich. How much more of the sandwich did Keith eat than Henry? \(\frac{□}{□}\) of the sandwich

Answer: \(\frac{1}{8}\) of the sandwich

Explanation: Given, Henry ate \(\frac{3}{8}\) of a sandwich. Keith ate \(\frac{4}{8}\) of the same sandwich. \(\frac{4}{8}\) – \(\frac{3}{8}\) = \(\frac{1}{8}\) of the sandwich

Question 20. For numbers 20a–20d, choose True or False for each sentence. a. \(1 \frac{4}{9}+2 \frac{6}{9}\) is equal to 4 \(\frac{1}{9}\) i. True ii. False

Explanation: \(1 \frac{4}{9}+2 \frac{6}{9}\) = 4 \(\frac{1}{9}\) First add the whole numbers 1 + 2 = 3 4/9 + 6/9 = 10/9 Convert it into the mixed fractions 10/9 = 1 \(\frac{1}{9}\) 3 + 1 \(\frac{1}{9}\) = 4 \(\frac{1}{9}\) Thus the above statement is true.

Question 20. b. \(3 \frac{5}{6}+2 \frac{3}{6}\) is equal to 5 \(\frac{2}{6}\) i. True ii. False

Explanation: First add the whole numbers 3 + 2 = 5 5/6 + 3/6 = 8/6 Convert it into the mixed fractions 8/6 = 1 \(\frac{2}{6}\) 5 + 1 \(\frac{2}{6}\) = 6 \(\frac{2}{6}\) Thus the above statement is false.

Question 20. c. \(4 \frac{5}{8}-2 \frac{4}{8}\) is equal to 2 \(\frac{3}{8}\) i. True ii. False

Explanation: \(4 \frac{5}{8}-2 \frac{4}{8}\) First subtract the whole numbers 4 – 2 = 2 5/8 – 4/8 = 1/8 = 2 \(\frac{1}{8}\) Thus the above statement is false.

Question 20. d. \(5 \frac{5}{8}-3 \frac{2}{8}\) is equal to 2 \(\frac{3}{8}\) i. True ii. False

Explanation: \(5 \frac{5}{8}-3 \frac{2}{8}\) 5 – 3 = 2 5/8 – 2/8 = 3/8 = 2 \(\frac{3}{8}\) \(5 \frac{5}{8}-3 \frac{2}{8}\) = 2 \(\frac{3}{8}\) Thus the above statement is true.

Question 21. Justin lives 4 \(\frac{3}{5}\) miles from his grandfather’s house. Write the mixed number as a fraction greater than one. 4 \(\frac{3}{5}\) = \(\frac{□}{□}\)

Answer: \(\frac{23}{5}\)

Explanation: Justin lives 4 \(\frac{3}{5}\) miles from his grandfather’s house. Convert from mixed fractions to an improper fraction. 4 \(\frac{3}{5}\) = \(\frac{23}{5}\)

Explanation: \(\frac{3}{4}\) The unit fraction of \(\frac{3}{4}\) is \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) \(\frac{3}{4}\) = 3 × \(\frac{1}{4}\) Thus the whole number is 3.

Write the fraction as a product of a whole number and a unit fraction.

Question 2. \(\frac{4}{5}\) = ______ × \(\frac{1}{5}\)

Explanation: The unit fraction for \(\frac{4}{5}\) is \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) \(\frac{4}{5}\) = 4 × \(\frac{1}{5}\) Thus the whole number is 4.

Question 3. \(\frac{3}{10}\) = ______ × \(\frac{1}{10}\)

Explanation: The unit fraction for \(\frac{3}{10}\) is \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) \(\frac{3}{10}\) = 3 × \(\frac{1}{10}\) Thus the whole number is 3.

Question 4. \(\frac{8}{3}\) = ______ × \(\frac{1}{3}\)

Explanation: The unit fraction for \(\frac{8}{3}\) is \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) \(\frac{8}{3}\) = 8 × \(\frac{1}{3}\) Thus the whole number is 8.

List the next four multiples of the unit fraction.

Question 5. \(\frac{1}{6}\) , Type below: ___________

Answer: 2/6, 3/6, 4/6, 5/6

Explanation: The next four multiples of \(\frac{1}{6}\) is \(\frac{2}{6}\) , \(\frac{3}{6}\) , \(\frac{4}{6}\) , \(\frac{5}{6}\)

Question 6. \(\frac{1}{3}\) , Type below: ___________

Answer: 2/3, 3/3, 4/3, 5/3

Explanation: The next four multiples of \(\frac{1}{3}\) is \(\frac{2}{3}\), \(\frac{3}{3}\), \(\frac{4}{3}\) and \(\frac{5}{3}\)

Question 7. \(\frac{5}{6}\) = ______ × \(\frac{1}{6}\)

Explanation: The unit fraction for \(\frac{5}{6}\) is \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) \(\frac{5}{6}\) = 5 × \(\frac{1}{6}\) Thus the whole number is 5.

Question 8. \(\frac{9}{4}\) = ______ × \(\frac{1}{4}\)

Explanation: The unit fraction for \(\frac{9}{4}\) is \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) \(\frac{9}{4}\) = 9 × \(\frac{1}{4}\) Thus the whole number is 9.

Question 9. \(\frac{3}{100}\) = ______ × \(\frac{1}{100}\)

Explanation: The unit fraction for \(\frac{3}{100}\) is \(\frac{1}{100}\) + \(\frac{1}{100}\) + \(\frac{1}{100}\) \(\frac{3}{100}\) = 3 × \(\frac{1}{100}\) Thus the whole number is 3.

Question 10. \(\frac{1}{10}\) , Type below: ___________

Answer: 2/10, 3/10, 4/10, 5/10

Explanation: The next four multiples of \(\frac{1}{10}\) is 2/10, 3/10, 4/10, 5/10

Question 11. \(\frac{1}{8}\) , Type below: ___________

Answer: 2/8, 3/8, 4/8, 5/8

Explanation: The next four multiples of \(\frac{1}{8}\) is 2/8, 3/8, 4/8, 5/8.

Question 12. Robyn uses \(\frac{1}{2}\) cup of blueberries to make each loaf of blueberry bread. Explain how many loaves of blueberry bread she can make with 2 \(\frac{1}{2}\) cups of blueberries. _____ loaves of blueberry bread

Answer: 5 loaves of blueberry bread

Explanation: Given, Robyn uses \(\frac{1}{2}\) cup of blueberries to make each loaf of blueberry bread. The unit fraction for 2 \(\frac{1}{2}\) is \(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\) =  5 loaves of blueberry bread

Question 13. Nigel cut a loaf of bread into 12 equal slices. His family ate some of the bread and now \(\frac{5}{12}\) of the loaf is left. Nigel wants to put each of the leftover slices in its own bag. How many bags does Nigel need? _____ bags

Answer: 5 bags

Explanation: Given, Nigel cut a loaf of bread into 12 equal slices. His family ate some of the bread and now \(\frac{5}{12}\) of the loaf is left. Nigel wants to put each of the leftover slices in its own bag. \(\frac{5}{12}\) = \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\) = 5 bags

Question 14. Which fraction is a multiple of \(\frac{1}{5}\)? Mark all that apply. Options: a. \(\frac{4}{5}\) b. \(\frac{5}{7}\) c. \(\frac{5}{9}\) d. \(\frac{3}{5}\)

Answer: \(\frac{4}{5}\), \(\frac{3}{5}\)

Explanation: The multiples of the \(\frac{1}{5}\) is \(\frac{4}{5}\), \(\frac{3}{5}\).

Sense or Nonsense?

Answer: The boy’s statement makes sense. Because 4/5 is not the multiple of 1/4.

Question 15. For the statement that is nonsense, write a new statement that makes sense. Type below: _________________

Answer: 4/5 is the multiple of 1/5.

Conclusion:

Just click on the links available above and practice the concepts of add and subtract fractions for homework help & standard tests. Help students to practice all chapter 7 questions from Go Math Answer Key to write the answers perfectly. For more questions just go with our Go Math Grade 4 Answer Key Chapter 7 Add and Subtract Fractions Homework Practice FL pdf article.

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