problem solving 3 digit subtraction lesson 6 6 answer key

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Break Apart Ones to Add - Lesson 4.1

Group Tens as Hundreds - Lesson 2.1

Explore 3 Digit Numbers - Lesson 2.2

Model 3 Digit Numbers - Lesson 2.3

Hundreds, Tens, and Hundreds - Lesson 2.4

​Place Value to 1,000 - Lesson 2.5

​ Number Names - Lesson 2.6

Different Forms of Numbers - Lesson 2.7

Algebra - Different Ways to Show Numbers - 2.8

Count On and Count Back by 10 and 100 - 2.9

Algebra - Number Patterns - Lesson 2.10

​Problem Solving - Compare Numbers - Lesson 2.11

Algebra - Compare Numbers - Lesson 2.12

​Chapter 2 Review for Test - Numbers to 1,000

Draw to Represent 3-Digit Addition - Lesson 6.1

Break Apart 3-Digit Addends - Lesson 6.2

3-Digit Addition - Regrouping Ones - Lesson 6.3

3-Digit Addition - Regrouping Tens - Lesson 6.4

​3-Digit Addition - Regroup Ones and Tens - L. 6.5

Problem Solving: 3-Digit Subtraction - Lesson 6.6

3-Digit Subtraction: Regroup Tens - Lesson 6.7

3-Digit Subtraction: Regroup Hundreds - Lesson 6.8

Subtraction: Regroup Ones and Tens - Lesson 6.9

Use Double Facts - Lesson 3.1 ​

Practice Addition Facts - Lesson 3.2

Algebra - Make a Ten to Add - Lesson 3.3

Algebra - Add 3 Addends - Lesson 3.4

Algebra - Relate Addition and Subtraction - Lesson 3.5

Practice Subtraction Facts - Lesson 3.6

Use Ten to Subtract - Lesson 3.7

Algebra - Use Drawings to Represent Problems - L. 3.8

Algebra - Use Equations to Represent Problems - L. 3.9

Problem Solving - Equal Groups - Lesson 3.10

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One Dollar - Lesson 7.5

Amounts Greater than $1 - Lesson 7.6

​ Problem Solving With Money - Lesson 7.7

Lesson 1.1 - Even and Odd Numbers

Lesson 1.2 - Representing Even Numbers

​Lesson 1.3 - Understanding Place Value

Lesson 1.4 - Expanded Form

Lesson 1.5 - Different Ways to Write Numbers

Lesson 1.6 - Different Names for Numbers

Lesson 1.7 - Problem Solving - Tens and Ones

Lesson 1.8 - Counting Patterns Within 100

Lesson 1.9 - Counting Patterns Within 1000

Review For Test - Chapter 1

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Subtraction: 3-Digit Numbers

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Go Math Grade 2 Answer Key Chapter 6 3-Digit Addition and Subtraction

Go math grade 2 chapter 6 answer key 3-digit addition and subtraction concepts, 3-digit addition and subtraction show what you know.

Explanation: There are 5 tens if we subtract 3 tens only 2 tens will remain.Therefore 50‐30 =20.

Explanation: There are 7 tens if we subtract 2 tens only 5 tens will remain.Therefore 70‐20 =50.

Explanation: In the above picture there are 7 tens and 9 ones.So, 54+25=79

Explanation: In the above picture there are 4 tens and 13 ones.13 ones is 1 tens and 3 ones.Finally there are 5 tens and 3 ones.So, 35+18=83

Explanation: In the above picture there are 14 tens and 9 ones.14 tens means 1 hundreds and 4 tens.Finally there are 1 hundreds, 4 tens and 9 ones.So, 82+67=149.

Explanation: In the above picture there are 10 tens and 10 ones.10 tens means 1 hundreds and 10 ones means 1 tens.Finally there are 1 hundreds and 1 tens. So, 29+81=110

Explanation: In the above picture there are 2 hundreds, 5 tens and 3 ones.So, the number is 253.

Explanation: In the above picture there are 3 hundreds, 5 tens and 1 ones.So, the number is 351.

3-Digit Addition and Subtraction Vocabulary Builder

Question 2. Write an addition sentence that has a sum of 20. ______ Answer: 10+10=20

Explanation: There are 10 ones and 10 ones in the above picture.10 ones means 1 tens.Finally there are 2 tens.So, 10+10=20.

Question 3. Write a subtraction sentence that has a difference of 10. ________ Answer: 20-10=10

Explanation: There are 2 tens in above picture if we subtract 1 tens from it we get 1 tens.So, 20‐10=10.

3-Digit Addition and Subtraction Game 2-Digit Shuffle

• number cards 10–50

Play with a partner.

• Shuffle the number cards. Place them face down in a pile.
• Take two cards. Say the sum of the two numbers.
• Your partner checks your sum.
• If your sum is correct, place a counter on a button. If you regrouped to solve, place a counter on another button.
• Take turns. Cover all the buttons. The player with more counters on the board wins.

3-Digit Addition and Subtraction Vocabulary Game

How to Play

• Take turns to play.
• Choose a math word from the Word Box. Do not say the word.
• Set the timer for 1 minute.
• Draw pictures and numbers to give clues about the math word.
• The first player to guess the word gets 1 point. If he or she use the word in a sentence, they get 1 more point. That player gets the next turn.
• The first player to score 5 points wins.

The Write Way Reflect Choose one idea. Write about it on the lines below.

• Tell how to solve this problem. 42 – 25 = _____
• Write a paragraph that uses at least three of these words. addends digit sum hundred regroup

Lesson 6.1 Draw to Represent 3-Digit Addition

Essential Question How do you draw quick pictures to show adding 3-digit numbers?

Listen and Draw

Share and Show

Explanation: In the above picture there are 4 hundreds, 6 tens and 9 ones.So, the number is 469.

Explanation: In the above picture there are 5 hundreds, 5 tens and 8 ones.So, the number is 558.

On Your Own

4 hundreds 4 tens and 9 ones is 449.

Explanation: In the above picture there are 4 hundreds, 4 tens and 9 ones.So, the number is 449.

3 hundreds 8 tens and 2 onea is 382

Explanation: In the above picture there are 3 hundreds, 8 tens and 2 ones.So, the number is 382.

Problem Solving • Applications

Explanation: Add 145 and 122. There are 2 hundreds, 6 tens and 7 ones in the above picture.So, the sum of 145 and 122 is 267. 2 hundred 6 tens 7 ones.

Draw to Represent 3-Digit Addition Homework & Practice 6.1

Explanation: Add 227 and 341. In the above picture add the hundreds, tens and ones.There are 5 hundreds,6 tens and 8 ones.So the sum of 227 and 341 is 568. 5 hundreds 6 tens 8 ones.

Explanation: Add the shells in the above picture.There are 3 rows of shells and each row has 4 shells each.So, there are 12 shells in all. 1 tens and 2 ones.

Explanation: Add the number of pens kara counts.Add the tens and ones.There are 7 tens and 18 ones.So, the number of pens kara counted is 7 tens and 18 ones ie 8 tens and 8 ones.Therefore the sum of 32,25,7 and 24 is 88. 8 tens and 8 ones.

Explanation: In the above picture 39 is removed from 46.So, the difference of 46 and 39 is 7. 7 ones.

Explanation: In the above picture 34 is removed from 55.So, the difference of 55 and 34 is 21. 2 tens 1 ones.

Lesson 6.2 Break Apart 3-Digit Addends

Essential Question How do you break apart addends to add hundreds, tens, and then ones?

Write the number. Draw a quick picture for the number. Then write the number in different ways. _______ ______ hundreds ______ tens _____ ones _____ + _____ + ______ Answer: 258 2 hundreds 5 tens 8 ones 200+50+8

_______ ______ hundreds ______ tens _____ ones _____ + _____ + ______ Answer: 325 3 hundreds 2 tens 5 ones 300+20+8

MATHEMATICAL PRACTICES Make Connections What number can be written as 400 + 20 + 9? Answer: 400+20+9 =4 hundreds 2 tens and 9 ones 400+20+9=429

Model and Draw

Explanation: Add 538 and 216.Add the hundreds, tens and ones from the above picture.There are 7 hundreds,4 tens and 14 ones.So, the sum of 538 and 216 is 754. 7 hundreds 5 tens 4 ones.

Explanation: Add 321 and 457.Add the hundreds, tens and ones from the above picture.There are 7 hundreds,7 tens and 8 ones.So, the sum of 321 and 457 is 778 7 hundreds 7 tens 8 ones.

Explanation: Add 744 and 162.Add the hundreds, tens and ones from the above picture.There are 8 hundreds,1 tens and 6 ones.So, the sum of 744 and 162 is 906. 9 hundreds 0 tens 6 ones.

Explanation: Add 254 and 536.Add the hundreds, tens and ones from the above picture.There are 7 hundreds,8 tens and 10 ones.So, the sum of 254 and 536 is 790. 7 hundreds 9 tens 0 ones.

Explanation: Add 425 and 232.Add the hundreds, tens and ones from the above picture.There are 5 hundreds,5 tens and 7 ones.So, the sum of 538 and 216 is 557. 5 hundreds 5 tens 7 ones.

Explanation: Add 849 and 123.Add the hundreds, tens and ones from the above picture.There are 9 hundreds,6 tens and 12 ones.So, the sum of 538 and 216 is 972. 9 hundreds 7 tens 2 ones.

Explanation: Add 158,100 and 231.Add the hundreds, tens and ones from the above picture.There are 4 hundreds,8 tens and 9 ones.So, the sum of 158,100 and 231 is 489. 4 hundreds 8 tens 9 ones.

Explanation: As in the above example add hundreds,tens and ones seperately and the sum of hundreds,tens and ones is 786. 7 hundreds 8 tens 6 ones

Explanation: Add 376 and 316.Add the hundreds, tens and ones from the above picture.There are 6 hundreds,8 tens and 12 ones.So, the sum of 376 and 316 is 692. 6 hundreds 9 tens 2 ones.

TAKE HOME ACTIVITY • Write 347 + 215. Have your child break apart the numbers and then find the sum.

Break Apart 3-Digit Addends Homework & Practice 6.2

Explanation: There are 126 crayons in a bucket and the teacher adds 144 more to the bucket.To find the totqal number of crayons in the bucket, Add 126 and 144.Add the hundreds, tens and ones from the above picture.There are 2 hundreds,7 tens and 0 ones.So, the sum of 126 and 144 is 270.Therefore there are total 260 crayons in the bucket. 2 hundreds 6 tens 0 ones.

Explanation: Add 324 and 231.Add the hundreds, tens and ones from the above picture.There are 5 hundreds,5 tens and 5 ones.So, the sum of 324 and 231 is 555. 5 hundreds 5 tens 5 ones.

Explanation: Add 218 and 145.Add the hundreds, tens and ones from the above picture.There are 3 hundreds,5 tens and 13 ones.So, the sum of 218 and 145 is 363. 3 hundreds 6 tens 3 ones.

Explanation: Add 664 and 223.Add the hundreds, tens and ones from the above picture.There are 8 hundreds,8 tens and 7 ones.So, the sum of 664 and 223 is 887. 8 hundreds 8 tens 7 ones.

Explanation: Ang found 19 berries and Barry found 21 berries.Add 19 and 21.There are 3 tens and 10 ones in the above picture.So, the sum of 19 and 21 is 40. 4 tens and 0 ones.

Question: Write a subtraction fact related to 9 + 6 = ______ Answer: 20-5=15

Explanation: In the above question the sum of 9 and 6 is 15.So, the subtraction fact for 15 is 20-5=15.

Explanation: There are 25 goldfish and 33 betta fish.Add 25 and 33.Add the tens and ones from the above picture.There are 5 tens and 8 ones.So the sum of

Lesson 6.3 3-Digit Addition: Regroup Ones

Essential Question When do you regroup ones in addition?

Explanation: To find the sum of 213 and 356.There are 5 hundreds,6 tens and 9 ones in the above picture.So. the sum of 213 and 356 is 569.5 hundreds 6 tens 9 ones.

Explanation: In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 328 and 134 is 462.

Explanation: In the above picture the ones,tens and hundreds are added seperately without regrouping.The sum of 445 and 23 is 468.

Explanation: In the above picture the ones,tens and hundreds are added seperately without regrouping.The sum of 526 and 103 is 629.

Explanation: In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 348 and 19 is 367.

Explanation: In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 628 and 347 is 975.

Explanation: In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 562 and 329 is 891.

Explanation: In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 147 and 125 is 272.

Explanation: In the above picture the ones,tens and hundreds are added seperately without regrouping.The sum of 326 and 200 is 526.

Explanation: In the above picture the ones,tens and hundreds are added seperately without regrouping.The sum of 140 and 235is 375.

Explanation: In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 249 and 318 is 567.

TAKE HOME ACTIVITY • Ask your child to explain why he or she regrouped in only some of the problems in this lesson.

3-Digit Addition: Regroup Ones Homework & Practice 6.3

Explanation: In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 148 and 234 is 382.

Explanation: In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 321 and 318 is 639.

Explanation: In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 414 and 179 is 593.

Explanation: In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 602 and 258 is 860.

Explanation: In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 258 and 135 is 393.

Explanation: In the above picture the ones,tens and hundreds are added seperately without regrouping.The sum of 136 and 212 is 348.

Explanation: In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 435 and 146 is 581.

Explanation: In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 436 and 306 is 742.

Explanation: In the above picture there are 9 ones.Subtract 4 ones from ir.There are 5 ones remained after subracting.Therefore the difference of 9 and 4 is 5.

Explanation: In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 243 and 132 is 375.

Lesson 6.4 3-Digit Addition: Regroup Tens

Essential Question When do you regroup tens in addition?

MATHEMATICAL PRACTICES Explain how your quick pictures show what happened in the problem. Answer:

Question 15. GO DEEPER Who sold more pieces of fruit? _______________ How many more? _______ more pieces of fruit Answer:

TAKE HOME ACTIVITY • Have your child choose a new combination of two fruits on this page and find the total number of pieces of the two types of fruit.

3-Digit Addition: Regroup Tens Homework & Practice 6.4

Problem Solving Solve. Write or draw to explain. Question 7. There are 142 blue toy cars and 293 red toy cars at the toy store. How many toy cars are there? _______ toy cars Answer:

Question 8. WRITE Find the sum of 362 + 265. Explain why you did or did not regroup. Answer:

Question 5. Francis had 8 toy cars, then his brother gave him 9 more. How many toy cars does Francis have now? 8 + 9 = ______ cars Answer:

Lesson 6.5 Addition: Regroup Ones and Tens

Essential Question How do you know when to regroup in addition?

Explanation: Add the tens digits  and hundreds digits in the above sums.

Explanation: Add the tens digits and the hundreds digits in the above sums.

MATHEMATICAL PRACTICES Analyze Were some problems easier to solve than other problems? Explain. Answer:

Explanation: 4 ones+ 9 ones=13 ones 1 ten + 8 tens +2 tens=11 tens 1 hundred + 1 hundred + 3 hundreds=5 hundreds.

Explanation: 6 ones+ 8 ones=14 ones 1 ten + 4 tens +7 tens=12 tens 1 hundred + 5 hundred + 2 hundreds=8 hundreds.

Explanation: 7 ones+ 3 ones=10 ones 1 ten + 2 tens +5 tens=11 tens 3 hundreds + 3 hundreds=6 hundreds.

Explanation: 4 ones+ 2 ones=6 ones 3 tens +5 tens=8 tens 2 hundred + 1 hundreds=3 hundreds.

Explanation: 5 ones+ 2 ones=7 ones 7 tens +7 tens=14 tens 1 hundred + 3 hundreds + 2 hundreds=6 hundreds.

Explanation: 9 ones+ 3 ones=12 ones 1 ten + 8 tens +2 tens=11 tens 1 hundred + 1 hundred + 6 hundreds=8 hundreds.

Explanation: 4 ones+ 1 one=5 ones 7 tens +8 tens=15 tens 1 hundred + 5 hundreds + 2 hundreds=8 hundreds.

Explanation: 6 ones+ 3 ones=9 ones 1 ten + 8 tens =9 tens 4 hundreds + 4 hundreds=8 hundreds.

Explanation: 6 ones+ 7 ones=13 ones 1 ten + 4 tens +9 tens=14 tens 1 hundred + 3 hundreds + 5 hundreds=9 hundreds.

Explanation: 5 ones+ 3 ones=8 ones 6 tens +8 tens=14 tens 1 hundred + 3 hundreds + 2 hundreds=6 hundreds.

Explanation: 7 ones+ 9 ones=16 ones 1 ten + 4 tens +0 tens=5 tens 6 hundred + 1 hundreds=5 hundreds.

Explanation: 6 ones+ 6 ones=12 ones 1 ten + 4 tens +5 tens=10 tens 1 hundred + 5 hundreds + 3 hundreds=9 hundreds.

Explanation: 5 ones+ 9 ones=14 ones 1 ten + 5 tens +3 tens=9 tens 4 hundreds + 1 hundred=5 hundreds.

Explanation: 3 ones+ 5 ones=8 ones 6 tens +4 tens=10 tens 1 hundred + 5 hundreds + 2 hundreds=8 hundreds.

Explanation: 6 ones+ 4 ones=10 ones 1 ten + 3 tens +8 tens=12 tens 1 hundred + 2 hundreds + 4 hundreds=7 hundreds.

Addition: Regroup Ones and Tens Homework & Practice 6.5

Explanation: 7 ones+ 5 ones=12 ones 1 ten + 4 tens +3 tens=8 tens 5 hundreds + 4 hundreds=9 hundreds.

Explanation: 7 ones+ 4 ones=11 ones 1 ten + 6 tens +8 tens=15 tens 1 hundred + 3 hundreds + 2 hundreds=6 hundreds.

Explanation: 5 ones+ 6 ones=11 ones 1 ten + 8 tens +5 tens=14 tens 1 hundred + 4 hundred + 4 hundreds=5 hundreds.

Explanation: 7 ones+ 6 ones=13 ones 1 ten + 8 tens +0 tens=9 tens 1 hundred + 3 hundreds=4 hundreds.

Explanation: 7 ones+ 8 ones=15 ones 1 ten + 4 tens +2 tens=7 tens 6 hundreds + 1 hundred=7 hundreds.

Explanation: Saul and luisa has 167 points each on a computer game.Add points of both saul and luisa.There are 3 hundreds 2 tens and 14 ones.So, the sum of 167 and 167 is 3 hundred 3 tens and 4 ones. 7 ones+ 7 ones=14 ones 1 ten + 6 tens +6 tens=13 tens 1 hundred + 1 hundred + 1 hundred=3 hundreds.

Explanation: 5 ones+ 9 ones=14 ones 1 ten + 7 tens +4 tens=12 tens 1 hundred + 2 hundreds + 2 hundreds=5 hundreds.

Explanation: 8 ones+ 2 ones=10 ones 1 ten + 4 tens +7 tens=12 tens 1 hundred + 3 hundreds + 2 hundreds=6 hundreds.

Explanation: 3 ones+ 7 ones=10 ones 1 ten + 2 tens +1 tens=11 tens 1 hundred + 2 hundreds=3 hundreds.

Spiral Review Question 3. Which addition fact has the same sum as 9 + 4. 10 + _____ Answer: 9+4=13 10+3=13

Explanation: The sumof 9 and 4 is 13.So, if we add 3 to 10 we get the same sum 13.Therefore the addition fact that has the same sum as 9+4 is 10+3.

Explanation: 2 ones+ 5 ones + 6 ones=13 ones 1 ten + 3 tens +1 tens +4 tens=9 tens

Question 6. Tom had 25 pretzels. He gave away 12 pretzels. How many pretzels does Tom have left? 25 – 12 = ______ pretzels Answer:

Explanation: There are 25 blocks in the above picture.Subtract 1 tens and 2 ones from the above picture.Therefore 13 blocks are left. So, the difference of 25 and 12 is 13.

3-Digit Addition and Subtraction Mid-Chapter Checkpoint

Concepts and Skills

Explanation: Add 567 and 324.Add the hundreds, tens and ones from the above picture.There are 8 hundreds,8 tens and 11 ones.So, the sum of 567 and 324 is 363. 8 hundreds 9 tens 1 ones

write the  sum .

Explanation: 8 ones+ 6 ones=14 ones 1 ten + 4 tens +4 tens=9 tens 2 hundreds + 3 hundreds=5 hundreds.

Explanation: 0 ones+ 4 ones=4 ones 1 ten +6 tens=11 tens 6 hundreds + 2 hundreds=8 hundreds.

Explanation: 1 ones+ 7 ones=8 ones 9 tens +3 tens=12 tens 1 hundred + 3 hundreds + 5 hundreds=9 hundreds.

Explanation: 8 ones+ 9 ones=17 ones 1 ten + 4 tens +1 tens=6 tens 1 hundred + 1 hundred=2 hundreds.

Lesson 6.6 Problem Solving • 3-Digit Subtraction

Essential Question How can making a model help when solving subtraction problems?

There were 436 people at the art show. 219 people went home. How many people stayed at the art show?

Show how to solve the problem. Make a model. Then draw a quick picture of your model. ______ people

HOME CONNECTION • Your child used a model and a quick picture to represent and solve a subtraction problem.

Question 2. 245 children go to the face-painting event. 114 of the children are boys. How many of the children are girls? _______ girls Answer:

MATHEMATICAL PRACTICES Explain how you solved the first problem on this page. Answer:

TAKE HOME ACTIVITY • Ask your child to choose one of the problems in this lesson and solve it in a different way.

Problem Solving • 3-Digit Subtraction Homework & Practice 6.6

Make a model to solve. Then draw a quick picture of your model. Question 1. On Saturday, 770 people went to the snack shop. On Sunday, 628 people went. How many more people went to the snack shop on Saturday than on Sunday? ______ more people Answer:

Question 2. There were 395 lemon ice cups at the snack shop. People bought 177 lemon ice cups. How many lemon ice cups are still at the snack shop? ______ cups Answer:

Question 3. There were 576 bottles of water at the snack shop. People bought 469 bottles of water. How many bottles of water are at the snack shop now? _______ bottles Answer:

Question 4. WRITE Draw quick pictures to show how to subtract 314 and 546. Answer:

Lesson Check Question 1. There are 278 math and science books. 128 of them are math books. How many science books are there? ______ books Answer:

Question 2. A book has 176 pages. Mr. Roberts has read 119 pages. How many pages does he have left to read? _____ pages Answer:

Spiral Review Question 3. What is the sum? 1 + 6 + 2 = _____ Answer:

Question 4. What is the difference? 54 – 8 = _____ Answer:

Lesson 6.7 3-Digit Subtraction: Regroup Tens

Essential Question When do you regroup tens in subtraction?

MATHEMATICAL PRACTICES Describe what to do when there are not enough ones to subtract from. Answer:

Question 7. GO DEEPER A bookstore has 148 books about people and 136 books about places. Some books were sold. Now there are 137 books left. How many books were sold? _______ books Answer:

3-Digit Subtraction: Regroup Tens Homework & Practice 6.7

Problem Solving Solve. Write or draw to explain. Question 5. There were 985 pencils. Some pencils were sold. Then there were 559 pencils left. How many pencils were sold? ______ pencils Answer:

Question 6. WRITE Choose one exercise from above. Draw quick pictures to check your work. Answer:

Spiral Review Question 3. What is the difference? 45 – 7 = _____ Answer:

Question 4. Leroy has 11 cubes. Jane has 15 cubes. How many cubes do they have altogether? ______ cubes Answer:

Question 5. Mina puts 5 flowers in each vase. How many flowers will she put in 3 vases? ______ flowers Answer:

Question 6. Mr. Hill had 428 pencils. He gave away 150 pencils. How many pencils did he keep? ______ pencils Answer:

Lesson 6.8 3-Digit Subtraction: Regroup Hundreds

Essential Question When do you regroup hundreds in subtraction?

MATHEMATICAL PRACTICES Describe what to do when there are not enough tens to subtract from. Answer:

MATHEMATICAL PRACTICE Make Arguments Question 9. Choose one exercise above. Describe the subtraction that you did. Be sure to tell about the values of the digits in the numbers. ______________________ _______________________ Answer:

TAKE HOME ACTIVITY • Have your child explain how to find the difference for 745 − 341.

3-Digit Subtraction: Regroup Hundreds Homework & Practice 6.8

Problem Solving Solve. Write or draw to explain. Question 5. There were 537 people in the parade. 254 of these people were playing an instrument. How many people were not playing an instrument? _______ people Answer:

Question 6. WRITE Write the subtraction problem for 838 – 462 and find the difference. Then draw quick pictures to check your difference. Answer:

Spiral Review Question 3. What is the difference? 52 – 15 = ______ Answer:

Question 4. Wallace has 8 crayons and Alma has 7. How many do the have together? 8 + 7 = _____ crayons Answer:

Lesson 6.9 Subtraction: Regroup Hundreds and Tens

Essential Question How do you know when to regroup in subtraction?

Explanation: Subtract the tens amd hundreds from the above sums to find the difference.

MATHEMATICAL PRACTICES Were some problems easier to solve than other problems? Explain. Answer: Yes some problems wre easy to solve than the other problems as theur was no need of any regrouping for some problems.

Explanation: Regroup 2 tens 1 ones as 1 tens 11 ones.Subtract the ones. Regroup 4 hundreds 1 tens as 3 hundreds 11 tens.Subtract the tens Subtract the hundreds.

Explanation: Subtract the ones. Regroup 1 hundreds 7 tens as 1 hundreds 17 tens.Subtract the tens Subtract the hundreds.

Explanation: Regroup 4 tens 6 ones as 3 tens 16 ones.Subtract the ones. Regroup 5 hundreds 3 tens as 4 hundreds 13 tens.Subtract the tens Subtract the hundreds.

Explanation: Subtract the hundreds,tens and ones as there is no need of regrouping.

Explanation: Regroup 4 tens 7 ones as 3 tens 17 ones.Subtract the ones. Regroup 7 hundreds 3 tens as 6 hundreds 13 tens.Subtract the tens Subtract the hundreds.

Explanation: Subtract the ones. Regroup 9 hundreds 3 tens as 8 hundreds 13 tens.Subtract the tens Subtract the hundreds.

Explanation: Regroup 4 tens 2 ones as 3 tens 12 ones.Subtract the ones. Subtract the tens Subtract the hundreds.

Explanation: Subtract the ones. Regroup 4 hundreds 6 tens as 3 hundreds 16 tens.Subtract the tens Subtract the hundreds.

Explanation: Regroup 5 tens 5 ones as 4 tens 15 ones.Subtract the ones. Regroup 4 hundreds 1 tens as 3 hundreds 1 tens.Subtract the tens Subtract the hundreds.

Explanation: Subtract the ones. Regroup 6 hundreds 5 tens as 5 hundreds 15 tens.Subtract the tens Subtract the hundreds.

Explanation: Regroup 2 tens 1 ones as 1 tens 11 ones.Subtract the ones. Regroup 5 hundreds 1 tens as 4 hundreds 11 tens.Subtract the tens Subtract the hundreds.

Explanation: Regroup 5 tens 8 ones as 4 tens 18 ones.Subtract the ones. Subtract the tens Subtract the hundreds.

Explanation: Regroup 4 tens 2 ones as 3 tens 12 ones.Subtract the ones. Regroup 5 hundreds 3 tens as 4 hundreds 13 tens.Subtract the tens Subtract the hundreds.

Explanation: Subtract the ones. Regroup 8 hundreds 2 tens as 7 hundreds 12 tens.Subtract the tens Subtract the hundreds.

Explanation: Regroup 4 tens 7 ones as 3 tens 17 ones.Subtract the ones. Regroup 9 hundreds 3 tens as 8 hundreds 13 tens.Subtract the tens Subtract the hundreds.

Explanation: The missing numbers in the first sum are 5 and 5 because only when the numbers are 5 tens and 5 ones if we regroup them they become 4 tens and 15 ones. The missing numbers in the second sum are 8, 3 and 6 because only when the numbers are 8 hundreds and 3 tens if we regroup them they become 7 hundreds and 13 ones.And 6 ones because if we subtract only 6 ones from 7 ones we get the answer as 1 ones.

Explanation: As shown in the above picture the difference between 270 and 300 is 30, 800 and 300 is 500 and 843 and 800 is 43.So, when we add 30,500 and 43 is sum wiil be 573.Therefore the difference between 543 and 270 is 573.

Explanation: Regroup 7 tens 1 ones as 6 tens 11 ones.Subtract the ones. Subtract the tens Subtract the hundreds.

Explanation: Regroup 2 tens 7 ones as 1 tens 17 ones.Subtract the ones. Regroup 4 hundreds 1 tens as 3 hundreds 11 tens.Subtract the tens Subtract the hundreds.

Explanation: Subtract the ones. Regroup 4 hundreds 7 tens as 3 hundreds 17 tens.Subtract the tens Subtract the hundreds.

Subtraction: Regroup Hundreds and Tens Homework & Practice 6.9

Explanation: Regroup 1 tens 6 ones as 0 tens 16 ones.Subtract the ones. Regroup 8 hundreds 0 tens as 7 hundreds 10 tens.Subtract the tens Subtract the hundreds.

Explanation: Regroup 0 tens 2 ones as 9 tens 12 ones.Subtract the ones. Regroup 9 hundreds 9 tens as 8 hundreds 19 tens.Subtract the tens Subtract the hundreds.

Explanation: Regroup 9 tens 6 ones as 8 tens 16 ones.Subtract the ones. Subtract the tens Subtract the hundreds.

Explanation: Regroup 3 tens 2 ones as 2 tens 12 ones.Subtract the ones. Regroup 4 hundreds 2 tens as 3 hundreds 12 tens.Subtract the tens Subtract the hundreds.

Explanation: Regroup 3 tens 5 ones as 2 tens 15 ones.Subtract the ones. Regroup 7 hundreds 2 tens as 6 hundreds 12 tens.Subtract the tens Subtract the hundreds.

Explanation: Subtract the ones. Regroup 3 hundreds 4 tens as 2hundreds 14 tens.Subtract the tens Subtract the hundreds.

Explanation: Regroup 3 tens 6 ones as 2 tens 16 ones.Subtract the ones. Regroup 3 hundreds 2 tens as 2 hundreds 12 tens.Subtract the tens Subtract the hundreds.

Explanation: 6 ones + 3 ones=19 ones 1 tens +4 tens + 3 tens=7 tens 2 hundreds + 5 hundreds=7 hundreds. 7 hundreds 7 tens 9 ones.

Explanation: Regroup 3 tens 8 ones as 2 tens 18 ones.Subtract the ones. Subtract the tens

Question 5. What is the difference? 17 – 9 = _____ Answer:

Question 6. Lisa had 15 daisies. She gave away 7 daisies. Then she found 3 more daisies. How many daisies does Lisa have now? 15 – 7 + 3 = ______ Answer:

Lesson 6.10 Regrouping with Zeros

Essential Question How do you regroup when there are zeros in the number you start with?

MATHEMATICAL PRACTICES Describe another way that you could solve the problem. Answer:

Question 14. MATHEMATICAL PRACTICE Analyze Claire has 250 pennies. Some are in a box and some are in her bank. There are more than 100 pennies in each place. How many pennies could be in each place? _____ pennies in a box _______ pennies in her bank Explain how you solved the problem. ________________ _________________ Answer:

TAKE HOME ACTIVITY • Ask your child to explain how he or she solved one of the problems in this lesson.

Regrouping with Zeros Homework & Practice 6.10

Problem Solving Solve. Question 7. There are 303 students. There are 147 girls. How many boys are there? _______ boys Answer:

Question 8. WRITE Write the subtraction problem 604 – 357. Describe how you will subtract to find the difference. _______________ ________________ Answer:

Question 5. What is the difference? 10 – 2 = _____ Answer:

3-Digit Addition and Subtraction Review/Test

Question 1. Mr. Kent’s art class used 234 craft sticks. Ms. Reed’s art class used 358 craft sticks. How many craft sticks did the two classes use? ______ craft sticks Answer:

Question 5. Mrs. Preston had 513 leaves. She gave 274 leaves to her students. Draw to show how you found your answer. How many leaves does she still have? ______ leaves Answer:

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Math Expressions Grade 1 Unit 3 Lesson 6 Answer Key Subtraction Strategies

Solve the questions in Math Expressions Grade 1 Homework and Remembering Answer Key Unit 3 Lesson 6 Answer Key Subtraction Strategies to attempt the exam with higher confidence. https://mathexpressionsanswerkey.com/math-expressions-grade-1-unit-3-lesson-6-answer-key/

Math Expressions Common Core Grade 1 Unit 3 Lesson 6 Answer Key Subtraction Strategies

Math Expressions Grade 1 Unit 3 Lesson 6 Homework

Count to solve.

Math Expressions Grade 1 Unit 3 Lesson 6 Answer Key Question 1. 6 – 4 = __ Answer: 6 – 4 = 2 Explanation: The subtraction of given two numbers is 2 counted on to solve

Grade 1 Unit 3 Lesson 6 Answer Key Math Expressions Question 2. 10 – 7 = __ Answer: 10 – 7 = 3 Explanation: The subtraction of given two numbers is 3 counted on to solve

Unit 3 Lesson 6 Answer Key Math Expressions Grade 1 Question 3. 8 – 3 = ___ Answer: 8 – 3 = 5 Explanation: The subtraction of given two numbers is 5 counted on to solve

Solve the story problem.

Show your work. Use drawings, numbers, or words.

Math Expressions Grade 1 Unit 3 Lesson 6 Remembering

Write the 10-partners and the switched partners.

Underline the greater number. Count on from that number.

Explanation: Counted on from that number Underlined the greater number Written the equation

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Subtracting 3-Digit from 3-Digit Numbers With Some Regrouping (49 Questions) (A)

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Step 1: Start with Division Vocabulary

Step 2: introduce long division layout, step 3: demonstrate with an examples, step 4: practice without bringing down zeros, step 5: teach bringing down zeros, step 6: explain problems with remainders.

Long division can be challenging for kids because it involves many steps and new vocabulary, making it easy to lose track of the process. This complexity often confuses students, especially when bringing down digits or handling remainders. Teaching long division step by step helps kids understand it better. This guide on “ how to teach long division to kids ” will provide clear steps to simplify learning for kids, making it less overwhelming.

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What Should My Child Know Before Learning Long Division?

Before diving into teaching long division, children must have a solid foundation in several key areas. These pre-requisites ensure that they are prepared for the complexities of long division:

• Understanding Multiplication: Kids should be comfortable with multiplication facts up to 12. This knowledge is fundamental because long division requires frequent multiplication to check and subtract products during the division steps.

Here are some fun activities to brush up your child’s understanding of multiplication facts:

• Basic Division Concepts: Ensure children understand the concept of division as sharing or grouping equally. They should be able to perform simple division tasks without remainders, using numbers that are easy to handle.

Here are some fun activities to brush up your child’s understanding of division facts:

• Familiarity with Subtraction: Subtraction is a significant part of the long division process, used to find the difference after multiplying the divisor. Children should be confident in subtracting large numbers, as they will need to do this repeatedly in each step of long division.

Assess how well your kids are versed with subtraction with these fun subtraction games :

• Number Sense: Good number sense , or an understanding of how numbers work and relate to each other, helps children anticipate the results of multiplication and division, making the process of long division smoother and more intuitive.

Ensuring kids are proficient in these areas makes teaching long division more effective, setting them up for success.

How to Teach Long Division in 6 Steps

Before learning the steps of long division, kids need to understand the key terms used throughout the process. Knowing these will help them follow long division strategies more easily.

• Dividend: This is the number being divided in the problem. In the long division layout, the dividend is written inside the long division bracket (often called the “house”).
• Divisor: The number dividing the dividend is called the divisor . The divisor is placed outside the long division bracket.
• Quotient: The quotient is the answer or the result of the division problem. This is written above the bracket, aligned with the digits of the dividend being divided.
• Remainder: If the division isn’t exact, there’s an amount left over called the remainder . The remainder is written as “R” followed by the remaining value after the division process.

Setting up a long division problem correctly is an essential skill for kids to learn. Here’s how to structure it visually:

• Write the Dividend Inside: Start by placing the dividend (the number being divided) inside the long division bracket, often called the “house.” This makes it clear that this number is the one being split into smaller groups.
• Place the Divisor Outside: Write the divisor (the number doing the dividing) outside, to the left of the bracket. This shows which number will be used repeatedly to divide the dividend into smaller groups.
• Draw Lines for the Quotient: The space above the bracket is where the quotient (the result of the division) will be written. Each digit of the quotient will align above the digit or digits of the dividend that are being divided.

1: Set Up the Problem

Write 1564 under the division bar and 27 outside the division bar.

• Look at the first two digits of the dividend (15). Since 15 is less than 27, we need to include the next digit, making it 156.
• Now, determine how many times 27 can fit into 156. 27 goes into 156 a total of 5 times because 27 multiplied by 6 (the next higher number) would exceed 156.

3. Multiply

• Multiply the quotient digit found (5) by the divisor (27), which equals 135.
• Write 135 under 156.

4. Subtract

• Subtract 135 from 156, which equals 21.
• Write 21 below 135.

5. Bring Down

Bring down the next digit of the dividend (the 4 in 1564), making the new number 214.

6. Repeat the Process

• Determine how many times 27 can fit into 214. It fits 7 times (since 27 multiplied by 8 exceeds 214).
• Multiply 27 by 7 (the next quotient digit) to get 189.
• Write 189 under 214, and subtract to find the difference: 214 – 189 = 25.

7. Remainder

• Since there are no more digits to bring down, 25 is the remainder.
• The complete quotient is 57 with a remainder of 25.

After understanding the layout, kids can apply what they’ve learned by playing these games in, each focusing on different levels of difficulty: 

• Dividing 2-Digit Numbers by 1-Digit

• Dividing 3-Digit Numbers by 1-Digit

• Dividing 4-Digit Numbers by 1-Digit

• Divide 4-Digit By 2-Digit Numbers

To build a strong foundation in long division, it’s crucial for children to practice problems where they bring down each digit consecutively without the complication of zeros . This helps them focus on mastering the basic steps of division:

Sequential Bringing Down: Start with simpler numbers where each digit in the dividend needs to be brought down one at a time. This practice solidifies their understanding of the division process step by step.

Example Problems:

• 21 ÷ 3: Begin by dividing the first digit. Since 2 divided by 3 doesn’t work, we use 21. 21 divided by 3 equals 7, so 7 is written above the division bar.
• 154 ÷ 7: Start with the first digit. 1 divided by 7 is not possible, so consider the first two digits, 15. 15 divided by 7 equals 2. Write 2 above the division bar, multiply 2 by 7 (which is 14), subtract 14 from 15 to get 1, then bring down the next digit to make it 14. Continue this way.

Handling zeros can be tricky, but it’s one of the key ways to teach long division. Here’s how to approach problems involving zeros:

Example: 120 ÷ 4

• Divide: Start by dividing the first non-zero digit. Since 1 is smaller than 4, look at the first two digits, 12. Divide 12 by 4 to get 3.
• Write the Quotient: Write 3 above the long division bracket.
• Multiply and Subtract: Multiply 3 by 4 (giving 12) and subtract this from 12, leaving 0.
• Bring Down Zeros: Bring down the next digit, which is 0, making it 0. Divide this 0 by 4 to get 0. Write 0 next to the 3 in the quotient.
• Multiply and Subtract: Multiply 0 by 4 to get 0 and subtract, leaving no remainder.

In some cases, division doesn’t result in an even quotient. This means there’s an amount leftover, called a remainder. Here’s how to handle it:

Example: 29 ÷ 4

• Divide: Start by dividing the first digit, 2, by 4. Since 2 is smaller than 4, consider the first two digits, 29.
• Find the Quotient: Divide 29 by 4 to get 7. Write 7 above the long division bracket.
• Multiply and Subtract: Multiply 7 by 4, which gives 28. Subtract 28 from 29, leaving 1.
• Write the Remainder: Since there’s nothing left to bring down, write “R1” (remainder of 1) next to the 7.

Knowing how to recognize and handle remainders is one of the essential long division tricks that help kids understand why not all division problems divide evenly. 

5 Fun Ways to Teach Long Division

Practicing long division is crucial for reinforcing the steps and strategies. Here are five effective ways to help kids master this skill:

• Online Long Division Games 

Use interactive online games that challenge students to solve division problems step-by-step. These games make learning fun while providing instant feedback to help them understand mistakes.

• Long Division Worksheets

Provide worksheets that start with simpler problems and progressively increase in complexity. Use colorful designs and real-world scenarios to keep kids engaged.

Create or find flashcards that present division problems on one side and answers on the other. This simple tool is a quick way to reinforce division facts and promote speedy calculations.

• Real-Life Problems

Apply division concepts to real-world situations, like dividing treats among friends or organizing items into equal groups. This practical approach makes long division relatable.

• Group Activities

Collaborative exercises where kids work together to solve division problems encourage discussion and peer learning. This can help clarify challenging steps and foster teamwork.

Learning long division can be challenging, but kids can grasp the concept effectively with clear steps, consistent practice, and engaging resources like games and worksheets. With these strategies on how to teach long division, children will build confidence and become proficient problem-solvers at their own pace.

Frequently Asked Questions (FAQs)

What is an easy way to learn division.

An easy way to learn division is by starting with simple problems and using visual aids like counters or drawings to illustrate the process. Gradually move to more complex problems as confidence builds.

What are some tips for teaching long division to struggling students?

Break down the steps into smaller, manageable parts, and offer lots of practice with engaging resources like games and worksheets. Provide positive reinforcement to encourage their progress and address specific challenges with patience.

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Texas Go Math Grade 6 Lesson 13.3 Answer Key Multiplication and Division Inequalities with Positive Numbers

Refer to our  Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Lesson 13.3 Answer Key Multiplication and Division Inequalities with Positive Numbers.

Texas Go Math Grade 6 Lesson 13.3 Explore Activity Answer Key

Modeling One-Step Inequalities

Question 1. Analyze Relationships Is 3.25 a solution of the inequality you wrote in A ? If so, does that solution make sense for the situation? Answer: Inequality for A is the following: 3 ∙ x > 9 We can substitute 3.2 for x and check if inequality is true, so we have the following: 3 ∙ 3.25 > 9 9 ∙ 75 > 9 We got that inequality is true, so, 3.25 can be the solution. And yes, this solution makes sense for the situation.

Go Math Lesson 13.3 Answer Key Grade 6 Multiplication Question 2. Represent Real-World Problems Rewrite the situation in A to represent the inequality 3x < 9. Answer: The modified situation that represents the given inequality could be: Dominic is buying school supplies. He buys 3 binders and spends less than 9$. How much did he spend on each binder?

Solve each inequality. Graph and check the solution.

Question 5. Represent Real-World Problems Write and solve a real-world problem for the inequality 4x ≤ 60. Answer: Justin buys snacks. He bought 4 packs and spent $60 or less than $60. How much costs one pack of snacks? Let x represent a price of one pack of snacks. According to given information. we have the following inequality: 4x ≤ 60 In order to solve it. We will divide it by 4 and get: \(\frac{4 x}{4} \leq \frac{60}{4}\) x ≤ 15 So, one pack of snacks costs $15 or less than $15.

Question 6. A paperweight must weigh less than 4 ounces. Brittany wants to make 6 paperweights using sand. Write and solve an inequality to find the possible weight of the sand she needs. Answer: Let x represent the possible weight of the sand Brittany needs. According to all informations, we have the following inequality: 6x < 4 We will, divide by 6 given inequality in order to solve previous inequality and get: \(\frac{6x}{6}\) < \(\frac{4}{6}\) x < \(\frac{2}{3}\) So, the weight of the sand must be less than \(\frac{2}{3}\) ounce. We will check solution substituting \(\frac{1}{3}\) for x in original inequality and get: 6 ∙ \(\frac{1}{3}\) < 4 2 < 4 So, the inequality is true. x < \(\frac{2}{3}\)

Texas Go Math Grade 6 Lesson 13.3 Guided Practice Answer Key

Solve each inequality. Graph and check the solution.  (Example 1)

Question 4. Karen divided her books and put them on 6 shelves. There were at least 14 books on each shelf. How many books did she have? Write and solve an inequality to represent this situation. (Example 2) Answer: Let x represent number of books Karen had. According to previous informations, we need to solve following inequality: \(\frac{x}{6}\) > 14 First, we will multiply by 6 both sides and get: 6(\(\frac{x}{6}\)) > 14.6 x > 84 Next thing we will do is to check the solution by substituting a value in the solution set in the original inequality. We will substitute 90 for x and get: \(\frac{90}{6}\) > 14 15 > 14 So, the inequality is true. Conclusion is that Karen had at least 84 book. x > 84

Essential Question Check-In

Question 5. Explain how to solve and check the solution to 5x < 40 using properties of inequalities. Answer: In order to solve this inequality, we need to divide both sides by 5 and get: \(\frac{5x}{5}\) < \(\frac{40}{5}\) x < 8 So, we got that set of solutions is x < 8. Now we will check the solution by substituting a value in the solution set in the original inequality. We will substitute 5 for x and get: 5 ∙ 5 < 40 25 < 40 So, the inequality is true.

Texas Go Math Grade 6 Lesson 13.3 Independent Practice Answer Key

Write and solve an inequality for each problem.

Question 7. Tamar needs to make at least $84 at work on Tuesday to afford dinner and a movie on Wednesday night. She makes $14 an hour at her job. How many hours does she need to work on Tuesday? Answer: Let x represent a number of hours Tamara needs to work on Tuesday. According to all the information in the task, we have the following inequality: 14x ≥ 84 In order to solve this inequality, we need to divide both sides by 14 and get: \(\frac{14x}{14}\) ≥ \(\frac{84}{14}\) x ≥ 6 So, Tamara needs to work at least 6 hours on Tuesday

Lesson 13.3 Answer Key Multiplication and Division Inequalities Question 8. In a litter of 7 kittens, each kitten weighs more than 3.5 ounces. Find the possible total weight of the litter. Answer: Let x represent the possible total. weight of the litter. According to all information in the task, we have the following inequality: \(\frac{x}{7}\) > 3.5 We will multiply both sides by 7 and get: 7(\(\frac{x}{7}\)) > 3.5 ∙ 7 x > 24.5 So, the possible total weight of the litter is more than 24.5 ounces.

Question 9. To cover his rectangular backyard, Will needs at least 1 70.5 square feet of sod. The length of Will’s yard is 15.5 feet. What are the possible widths of Will’s yard? Answer: Let x represent width of Will’s yard. In order to calculate it, we need to solve the following inequality: 15.5x ≥ 170.5 We wiLl divide both sides by 15.5 and get: \(\frac{15.5x}{15.5}\) ≥ \(\frac{170.5}{15.5}\) x ≥ 11 So, the width of Will’s yard need to be at least 11 feet.

Question 12. Steve pays less than $32 per day to rent his apartment. August has 31 days. What are the possible amounts Steve could pay for rent in August? Answer: Let x represent the possible amount Steve could pay for rent in August According to all informations, we have the following inequality we need to solve: \(\frac{x}{31}\) < 32 We will multiply both sides by 31 and get: 31(\(\frac{x}{31}\)) < 32 ∙ 31 x < 992 So, Steve could pay for amount in August less than 992$.

Question 13. If you were to graph the solution for exercise 12, would all points on the graph make sense for the situation? Explain. Answer: No, points which make sense for the situation will be between 992 and 0. Points with negative values do not make sense for this a real-world situation.

Question 14. Multistep Lina bought 4 smoothies at a health food store. The bill was less than $16. a. Write and solve an inequality to represent the cost of each smoothie. Answer: Let x represent the cost of each smoothie. We need to soLve the following inequaLity in order to caLculate x. 4x < 16 We need to divide both sides by 4 and get: \(\frac{4x}{4}\) < \(\frac{16}{4}\) x < 4 So, the price of each smoothie in less than 4$.

b. What values make sense for this situation? Explain. Answer: Values that makes sense for this situation are between 4 and 0. Because, no one sells nothing for price 0. So only previous values make sense for this situation.

Solve each inequality.

Question 20. Gary has enough money to buy at most 5.5 pounds of potatoes. How much money does Gary have? Answer: Let x represent sum of money Gary have. According to data from the table and informations from task, we have the following inequality: \(\frac{x}{0.50}\) ≤ 0.50 In order to solve this inequality, we need to multiply both sides by 0.50 and get: 0.50(\(\frac{x}{0.50}\)) ≤ 5.5 ∙ 0.50 x ≤ 2.75 So, conclusion is that Gary has at most 2.75.

Question 21. Florence wants to spend no more than $3 on onions. Will she be able to buy 2.5 pounds of onions? Explain. Answer: Let x represent the amount of onions Florence can buy. According to the table and informations, we get following inequality: 1.25x ≤ 3 In order to soLve this inequality, we need to divide both sides by 1.25 and get: \(\frac{1.25 x}{1.25} \leq \frac{3}{1.25}\) x ≤ 2.4 So, she can buy at most 2.4 pounds of onions. Conclusion is she can not buy 2.5 pounds of onions.

Question 22. The produce buyer for a local restaurant wants to buy more than 30 lb of onions. The produce buyer at a local hotel buys exactly 12 pounds of spinach. Who spends more at the produce stand? Explain. Answer: Let x represent the sum of money the produce buyer for a local restaurant will spend for buying onions. So, we have the following inequality : \(\frac{x}{1.25}\) > 30 In order to solve this inequality, we need to multiply both sides by 1.25 and get: 1.25(\(\frac{x}{1.25}\)) > 30 ∙ 1.25 x > 37.5 So, the produce buyer will spend more that $ 37.5 to by more than 30 lb of onions. Now, let y represent sum of money the produce buyer for a local hotel will spend for buying exactly 12 pounds of spinach. We have the following equation we need to solve: y ÷ 3 = 12 y = 12.3 y = 36 So, we can notice that the produce buyer will spend exactly $36 to buy 12 pounds of spinach. Conclusion is that the produce buyer for a local restaurant will spend more money than the produce buyer for a local hotel.

H.O.T. Focus on Higher Order Thinking

Question 23. Critique Reasoning A student solves \(\frac{r}{5}\) ≤ \(\frac{2}{5}\) and gets r ≤ \(\frac{2}{25}\) What is the correct solution? What mistake might the student have made? Answer: The mistake which student might made is that he divided by 5, not multiplied by 5 So, the right way to solve this inequality is to multiply by 5 and get: 5(\(\frac{r}{5}\)) ≤ \(\frac{2}{5}\) ∙ 5 r ≤ 2 So, the solution is r ≤ 2.

Question 24. Represent Real-World Problems Write and solve a word problem that can be represented with 240 ≤ 2x. Answer: Mary want’s to spend $240 or more on buying chocolate as presents for guests at lier party. One pack costs $2, so, how many packs of chocolate she can buy? Let x represent the number of packs of chocolate Mary can buy. According to all informations. we get the following inequality: 2x ≥ 240 We need to divide both sides by 2 and get: \(\frac{2 x}{2} \geq \frac{240}{2}\) x ≥ 120 So, she can at least buy 120 packs of chocolate or more.

Question 25. Persevere in Problem Solving A rectangular prism has a length of 13 inches and a width of \(\frac{1}{2}\) inch. The volume of the prism is at most 65 cubic inches. Find all possible heights of the prism. Show your work. Answer: First, we will calculate the area of basis of this rectangular prism multiplying the length by the width and get: B = 13 ∙ \(\frac{1}{2}\) = \(\frac{13}{2}\) So, the area of bassis of rectangular prism is \(\frac{13}{2}\) square inches. Formula for calculating the volume is: V = B ∙ H Where V is the volume, B is the area of basis and H is its height. According to all informations in the task, we have the following inequality we need to solve to find all possible heights of prism, where x represent height: \(\frac{13}{2}\)x ≤ 65 We need to multiply both sides by \(\frac{2}{13}\) and get: \(\frac{2}{13} \cdot \frac{13}{2} x \leq \frac{65}{1} \cdot \frac{2}{13}\) x ≤ 10 So, the height of the prism can be at most 10 inches.

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