eureka math lesson 3 homework 5.5 answer key

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5th grade (Eureka Math/EngageNY)

Unit 1: module 1: place value and decimal fractions, unit 2: module 2: multi-digit whole number and decimal fraction operations, unit 3: module 3: addition and subtractions of fractions, unit 4: module 4: multiplication and division of fractions and decimal fractions, unit 5: module 5: addition and multiplication with volume and area, unit 6: module 6: problem solving with the coordinate plane.

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• Grade 5 Eureka - Answer Keys Module 2

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Eureka Math Grade 5 Module 3 Lesson 15 Answer Key

Engage ny eureka math 5th grade module 3 lesson 15 answer key, eureka math grade 5 module 3 lesson 15 sprint answer key.

Eureka Math Grade 5 Module 3 Lesson 15 Problem Set Answer Key

Solve the word problems using the RDW strategy. Show all of your work. Question 1. In a race, the-second place finisher crossed the finish line 1\(\frac{1}{3}\) minutes after the winner. The third-place finisher was 1\(\frac{3}{4}\) minutes behind the second-place finisher. The third-place finisher took 34\(\frac{2}{3}\) minutes. How long did the winner take? Answer: Fraction of time of Second place finisher crossed the line after = 1\(\frac{1}{3}\) minutes = \(\frac{4}{3}\) Fraction of time of Third place finisher is behind the second place  = 1\(\frac{3}{4}\) minutes  = \(\frac{7}{4}\) Fraction of time the third place finisher took = 34\(\frac{2}{3}\) = \(\frac{105}{3}\) Fraction of time the second place runner took = \(\frac{105}{3}\) – \(\frac{7}{4}\) = \(\frac{420}{12}\) – \(\frac{21}{12}\) = \(\frac{399}{12}\) = \(\frac{133}{4}\) Fraction of time the First place runner took = \(\frac{133}{4}\) – \(\frac{4}{3}\) = \(\frac{399}{12}\) – \(\frac{16}{12}\) = \(\frac{383}{12}\) = 31 \(\frac{11}{12}\) . Therefore the First Runner took = 31 \(\frac{11}{12}\) .minutes.

Question 2. John used 1\(\frac{3}{4}\) kg of salt to melt the ice on his sidewalk. He then used another 3\(\frac{4}{5}\) kg on the driveway. If he originally bought 10 kg of salt, how much does he have left? Answer: Fraction of Salt used by John =1\(\frac{3}{4}\) kg = \(\frac{7}{4}\) kg Fraction of Salt used again =3\(\frac{4}{5}\) kg = \(\frac{24}{5}\) kg Fraction of salt used = \(\frac{7}{4}\)  + \(\frac{24}{5}\) = \(\frac{35}{20}\)  + \(\frac{96}{20}\) = \(\frac{131}{20}\)  = 6 \(\frac{11}{20}\) . Total Salt = 10 kg. Fraction of salt left = 10 – \(\frac{131}{20}\)  = \(\frac{200}{20}\)  – \(\frac{131}{20}\)  = \(\frac{69}{20}\)  = 3\(\frac{9}{20}\)  . Therefore Fraction of salt left = 3\(\frac{9}{20}\)  .

Question 3. Sinister Stan stole 3\(\frac{3}{4}\) oz of slime from Messy Molly, but his evil plans require 6\(\frac{3}{8}\) oz of slime. He stole another 2\(\frac{3}{5}\) oz of slime from Rude Ralph. How much more slime does Sinister Stan need for his evil plan? Answer: Fraction of slime stolen from Messy Molly = 3\(\frac{3}{4}\) = \(\frac{15}{4}\) oz Fraction of slime stolen from Messy Molly again = 2\(\frac{3}{5}\) = \(\frac{13}{5}\) oz Total Fraction Stolen = \(\frac{15}{4}\)  + \(\frac{13}{5}\) = \(\frac{75}{20}\) + \(\frac{52}{20}\) = \(\frac{127}{20}\) = 6\(\frac{7}{20}\) . Fraction of more slime required = 6\(\frac{3}{8}\) – \(\frac{127}{20}\) = \(\frac{51}{8}\) – \(\frac{127}{20}\) = \(\frac{255}{40}\) – \(\frac{254}{40}\) = \(\frac{1}{40}\) . Therefore, Fraction of more slime required = \(\frac{1}{40}\) oz.

Question 4. Gavin had 20 minutes to do a three-problem quiz. He spent 9\(\frac{3}{4}\) minutes on Problem 1 and 3\(\frac{4}{5}\) minutes on Problem 2. How much time did he have left for Problem 3? Write the answer in minutes and seconds. Answer: Time given for 3 problems = 20 minutes Fraction of time Spent on Problem 1 = 9\(\frac{3}{4}\) minutes = \(\frac{39}{4}\) . Fraction of Time spent on Problem 2 = 3\(\frac{4}{5}\) = \(\frac{19}{5}\) . Fraction of Time spent on Problem 3 = x 20 = \(\frac{39}{4}\) + \(\frac{19}{5}\) + x x = 20 – \(\frac{39}{4}\) – \(\frac{19}{5}\) x = \(\frac{400}{20}\) – \(\frac{195}{20}\) – \(\frac{76}{20}\) x = \(\frac{129}{20}\) = 6\(\frac{9}{20}\) . Therefore, Fraction of Time spent on Problem 3 = 6\(\frac{9}{20}\) .

Question 5. Matt wants to shave 2\(\frac{1}{2}\) minutes off his 5K race time. After a month of hard training, he managed to lower his overall time from 21\(\frac{1}{5}\) minutes to 19\(\frac{1}{4}\) minutes. By how many more minutes does Matt need to lower his race time? Answer: Fraction of Time lowered = 21\(\frac{1}{5}\) minutes to 19\(\frac{1}{4}\) minutes. = \(\frac{106}{5}\) – \(\frac{77}{4}\) = \(\frac{424}{20}\) – \(\frac{385}{20}\) = \(\frac{39}{20}\) =1\(\frac{19}{20}\) . Fraction of Time shaved = 2\(\frac{1}{2}\) =\(\frac{5}{2}\) . Fraction of More Time Matt need to lower his race time = \(\frac{5}{2}\) – \(\frac{39}{20}\) = \(\frac{50}{20}\) – \(\frac{39}{20}\) = \(\frac{11}{20}\) = \(\frac{33}{60}\) = 33 minutes .

Eureka Math Grade 5 Module 3 Lesson 15 Exit Ticket Answer Key

Solve the word problem using the RDW strategy. Show all of your work. Cheryl bought a sandwich for 5\(\frac{1}{2}\) dollars and a drink for $2.60. If she paid for her meal with a $10 bill, how much money did she have left? Write your answer as a fraction and in dollars and cents. Answer: Fraction of Cost of sandwich = 5\(\frac{1}{2}\) = \(\frac{11}{2}\) dollar = 5.5 dollar Fraction of Cost of Drink = $2.60. Total Cost = 5.5 +2.60 = 8.1 $. Amount paid = 10$. Money left = 10 – 8.1 = 1.9 $ .

Eureka Math Grade 5 Module 3 Lesson 15 Homework Answer Key

Solve the word problems using the RDW strategy. Show all of your work. Question 1. A baker buys a 5 lb bag of sugar. She uses 1\(\frac{2}{3}\) lb to make some muffins and 2\(\frac{3}{4}\) lb to make a cake. How much sugar does she have left? Answer: Total Quantity of Sugar = 5 lb Fraction of Quantity of Suagr used for muffins = 1\(\frac{2}{3}\) lb = \(\frac{5}{3}\) Fraction of Quantity of Suagr used cake = 2\(\frac{3}{4}\) lb = \(\frac{11}{4}\) Fraction of Quantity of Sugar used = \(\frac{5}{3}\) + \(\frac{11}{4}\) = \(\frac{20}{12}\) + \(\frac{33}{12}\) = \(\frac{53}{12}\) Fraction of Quantity of Sugar left = 5 – \(\frac{53}{12}\) = \(\frac{60}{12}\) – \(\frac{53}{12}\) =\(\frac{7}{12}\) . Therefore, Fraction of Quantity of sugar left = \(\frac{7}{12}\) .

Question 2. A boxer needs to lose 3\(\frac{1}{2}\) kg in a month to be able to compete as a flyweight. In three weeks, he lowers his weight from 55.5 kg to 53.8 kg. How many kilograms must the boxer lose in the final week to be able to compete as a flyweight? Answer: Fraction of weight need to lose in month = 3\(\frac{1}{2}\) = \(\frac{7}{2}\) = 3.5 kg Weight lost in 3 weeks = 55.5 –  53.8 = 1.7 kg Weight need to lose in final week = 3.5 – 1.7 = 1.8 kg.

Question 3. A construction company builds a new rail line from Town A to Town B. They complete 1\(\frac{1}{4}\) miles in their first week of work and 1\(\frac{2}{3}\) miles in the second week. If they still have 25\(\frac{3}{4}\) miles left to build, what is the distance from Town A to Town B? Answer: Fraction of work completed in first week = 1\(\frac{1}{4}\) miles = \(\frac{5}{4}\) Fraction of work completed in second week = 1\(\frac{2}{3}\) miles = \(\frac{5}{3}\) Fraction of work left to built = 25\(\frac{3}{4}\) miles = \(\frac{103}{4}\) Fraction of Distance from Town A to Town B = \(\frac{103}{4}\) + \(\frac{5}{4}\)  + \(\frac{5}{3}\) = \(\frac{108}{4}\) + \(\frac{5}{3}\) = \(\frac{324}{12}\) + \(\frac{20}{12}\) = \(\frac{344}{12}\)= 28\(\frac{2}{3}\) . Therefore, Fraction of Distance from Town A to Town B = 28\(\frac{2}{3}\) miles.

Question 4. A catering company needs 8.75 lb of shrimp for a small party. They buy 3\(\frac{2}{3}\) lb of jumbo shrimp, 2\(\frac{5}{8}\) lb of medium-sized shrimp, and some mini-shrimp. How many pounds of mini-shrimp do they buy? Answer: Quantity of shrimp needed = 8.75 lb =8\(\frac{3}{4}\) = \(\frac{27}{4}\) Quantity of jumbo shrimp = 3\(\frac{2}{3}\) lb = \(\frac{11}{3}\) Quantity of  medium – sized shrimp = 2\(\frac{5}{8}\) lb = \(\frac{21}{8}\) Quantity of mini shrimp = x \(\frac{35}{4}\)  = \(\frac{11}{3}\) + \(\frac{21}{8}\) + x x = \(\frac{210}{24}\)  – \(\frac{88}{24}\) – \(\frac{63}{24}\) x =  \(\frac{59}{24}\) = 2 \(\frac{11}{24}\) Therefore, Quantity of mini shrimp = x = 2 \(\frac{11}{24}\) lb .

Question 5. Mark breaks up a 9-hour drive into 3 segments. He drives 2\(\frac{1}{2}\) hours before stopping for lunch. After driving some more, he stops for gas. If the second segment of his drive was 1\(\frac{2}{3}\) hours longer than the first segment, how long did he drive after stopping for gas? Answer: Total time of the drive = 9 hours . Fraction of Time drived for first segment = 2\(\frac{1}{2}\) hours  = \(\frac{5}{2}\) Fraction of Time of second segment = 1\(\frac{2}{3}\) hours longer than the first segment = \(\frac{5}{3}\) + \(\frac{5}{2}\) = \(\frac{10}{6}\) + \(\frac{15}{6}\) = \(\frac{25}{6}\) =4 \(\frac{1}{6}\) Fraction of Time of first and second segment= \(\frac{5}{2}\) + \(\frac{25}{6}\) = \(\frac{15}{6}\) + \(\frac{25}{6}\) = \(\frac{40}{6}\) = 6\(\frac{4}{6}\) Fraction of Time he drive after stopping gas = 9 – \(\frac{40}{6}\) = \(\frac{54}{6}\) –  \(\frac{40}{6}\) = \(\frac{14}{6}\) = 2\(\frac{2}{6}\) . Therefore, Fraction of Time he drive after stopping gas = third segment = 2\(\frac{2}{6}\) hours .

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Eureka Math Grade 5 Module 5 Lesson 18 Answer Key

Engage ny eureka math 5th grade module 5 lesson 18 answer key, eureka math grade 5 module 5 lesson 18 sprint answer key.

Question 1. \(\frac{1}{2}\) ÷ 2 = Answer: 1/4

Question 2. \(\frac{1}{2}\) ÷ 3 = Answer: 1/6

Question 3. \(\frac{1}{2}\) ÷ 4 = Answer: 1/8

Question 4. \(\frac{1}{2}\) ÷ 7 = Answer: 1/14

Question 5. 7 ÷ \(\frac{1}{2}\) = Answer: 14

Question 6. 6 ÷ \(\frac{1}{2}\) = Answer: 12

Question 7. 5 ÷ \(\frac{1}{2}\) = Answer: 10

Question 8. 3 ÷ \(\frac{1}{2}\) = Answer: 6

Question 9. 2 ÷ \(\frac{1}{5}\) = Answer: 10

Question 10. 3 ÷ \(\frac{1}{5}\) = Answer: 15

Question 11. 4 ÷ \(\frac{1}{5}\) = Answer: 20

Question 12. 7 ÷ \(\frac{1}{5}\) = Answer: 35

Question 13. \(\frac{1}{5}\) ÷ 7 = Answer: 1//35

Question 14. \(\frac{1}{3}\) ÷ 2 = Answer: 1/6

Question 15. 2 ÷ \(\frac{1}{3}\) = Answer: 1/6

Question 16. \(\frac{1}{4}\) ÷ 2 = Answer: 1/8

Question 17. 2 ÷ \(\frac{1}{4}\) = Answer:  8

Question 18. \(\frac{1}{5}\) ÷ 2 = Answer: 1/10

Question 19. 2 ÷ \(\frac{1}{5}\) = Answer: 10

Question 20. 3 ÷ \(\frac{1}{4}\) = Answer: 12

Question 21. \(\frac{1}{4}\) ÷ 3 = Answer: 1/12

Question 22. \(\frac{1}{4}\) ÷ 4 = Answer: 1/16

Question 23. 4 ÷ \(\frac{1}{4}\) = Answer: 16

Question 24. \(\frac{1}{3}\) ÷ 3 = Answer: 1/9

Question 25. \(\frac{2}{3}\) ÷ 3 = Answer: 2/9

Question 26. \(\frac{1}{4}\) ÷ 2 = Answer: 1/8

Question 27. \(\frac{3}{4}\) ÷ 2 = Answer: 3/8

Question 28. \(\frac{1}{5}\) ÷ 2 = Answer: 1/10

Question 29. \(\frac{3}{5}\) ÷ 2 = Answer: 3/10

Question 30. \(\frac{1}{6}\) ÷ 2 = Answer: 1/12

Question 31. \(\frac{5}{6}\) ÷ 2 = Answer: 5/12

Question 32. \(\frac{5}{6}\) ÷ 3 = Answer: 5/18

Question 33. \(\frac{1}{6}\) ÷ 3 = Answer: 1/18

Question 34. 3 ÷ \(\frac{1}{6}\) = Answer: 18

Question 35. 6 ÷ \(\frac{1}{6}\) = Answer: 36

Question 36. 7 ÷ \(\frac{1}{7}\) = Answer: 49

Question 37. 8 ÷ \(\frac{1}{8}\) = Answer: 64

Question 38. 9 ÷ \(\frac{1}{9}\) = Answer: 81

Question 39. \(\frac{1}{8}\) ÷ 7 = Answer: 1/56

Question 40. 9 ÷ \(\frac{1}{8}\) = Answer: 72

Question 41. \(\frac{1}{8}\) ÷ 7 = Answer: 1/56

Question 42. 7 ÷ \(\frac{1}{6}\) = Answer: 42

Question 43. 9 ÷ \(\frac{1}{7}\) = Answer: 63

Question 44. \(\frac{1}{8}\) ÷ 9 = Answer: 1/72

Question 2. \(\frac{1}{5}\) ÷ 3 = Answer: 1/15

Question 3. \(\frac{1}{5}\) ÷ 4 = Answer: 1/20

Question 4. 7 ÷ \(\frac{1}{5}\) = Answer: 1/35

Question 5. 6 ÷ \(\frac{1}{5}\) = Answer: 30

Question 6. 6 ÷ \(\frac{1}{5}\) = Answer: 30

Question 7. 5 ÷ \(\frac{1}{5}\) = Answer: 25

Question 8. 3 ÷ \(\frac{1}{5}\) = Answer: 15

Question 9. 2 ÷ \(\frac{1}{2}\) = Answer: 4

Question 10. 3 ÷ \(\frac{1}{2}\) = Answer: 6

Question 11. 4 ÷ \(\frac{1}{2}\) = Answer: 8

Question 12. 7 ÷ \(\frac{1}{2}\) = Answer: 14

Question 13. \(\frac{1}{2}\) ÷ 7 = Answer: 1/14

Question 14. \(\frac{1}{4}\) ÷ 2 = Answer: 1/8

Question 15. 2 ÷ \(\frac{1}{4}\) = Answer: 8

Question 16. \(\frac{1}{3}\) ÷ 2 = Answer: 1/6

Question 17. 2 ÷ \(\frac{1}{3}\) = Answer: 6

Question 18. \(\frac{1}{2}\) ÷ 2 = Answer: 1/4

Question 19. 2 ÷ \(\frac{1}{2}\) = Answer: 4

Question 20. 4 ÷ \(\frac{1}{4}\) = Answer: 16

Question 21. \(\frac{1}{3}\) ÷ 4 = Answer: 1/12

Question 22. \(\frac{1}{3}\) ÷ 3 = Answer: 1/9

Question 23. 3 ÷ \(\frac{1}{3}\) = Answer: 9

Question 24. \(\frac{1}{4}\) ÷ 4 = Answer: 1/16

Question 25. \(\frac{3}{4}\) ÷ 4 = Answer: 3/16

Question 26. \(\frac{1}{3}\) ÷ 3 = Answer: 1/9

Question 27. \(\frac{2}{3}\) ÷ 3 = Answer: 2/9

Question 28. \(\frac{1}{6}\) ÷ 2 = Answer: 1/12

Question 29. \(\frac{5}{6}\) ÷ 2 = Answer: 5/12

Question 30. \(\frac{1}{5}\) ÷ 5 = Answer: 1/25

Question 31. \(\frac{3}{5}\) ÷ 5 = Answer: 3/25

Question 32. \(\frac{3}{5}\) ÷ 4 = Answer: 3/20

Question 33. \(\frac{1}{5}\) ÷ 5 = Answer: 1/30

Question 34. 6 ÷ \(\frac{1}{5}\) = Answer: 30

Question 35. 6 ÷ \(\frac{1}{4}\) = Answer: 24

Question 36. 7 ÷ \(\frac{1}{6}\) = Answer: 42

Question 37. 8 ÷ \(\frac{1}{7}\) = Answer: 56

Question 38. 9 ÷ \(\frac{1}{8}\) = Answer: 7 2

Question 39. \(\frac{1}{8}\) ÷ 8 = Answer: 1/64

Question 40. 9 ÷ \(\frac{1}{9}\) = Answer: 81

Question 41. \(\frac{1}{9}\) ÷ 8 = Answer:  1/72

Question 42. 7 ÷ \(\frac{1}{7}\) = Answer: 49

Question 43. 9 ÷ \(\frac{1}{6}\) = Answer: 54

Question 44. \(\frac{1}{8}\) ÷ 6 = Answer: 1/48

Eureka Math Grade 5 Module 5 Lesson 18 Problem Set Answer Key

Question 1. Draw the figures in each box with the attributes listed. a. Rhombus with no right angles b. Rectangle with not all sides equal c. Rhombus with 1 right angle d. Rectangle with all sides equal Answer:

Question 2. Use the figures you drew to complete the tasks below. a. Measure the angles of the figures with your protractor, and record the measurements on the figures. b. Use a marker or crayon to circle pairs of angles inside each figure with a sum equal to 180°. Use a different color for each pair. Answer:

• 100 degrees + 80 degrees = 180 degrees
• 90 degrees + 90 degrees = 180 degrees

Question 3. Draw a rhombus and a rectangle below. a. Draw the diagonals, and measure their lengths. Record the measurements on the figure. b. Measure the length of each segment of the diagonals from the vertex to the intersection point of the diagonals. Using a marker or crayon, color segments that have the same length. Use a different color for each different length. Answer:

Question 4. a. List the properties that are shared by all of the rhombuses that you worked with today. b. List the properties that are shared by all of the rectangles that you worked with today. c. When can a trapezoid also be called a rhombus? d. When can a parallelogram also be called a rectangle? e. When can a quadrilateral also be called a rhombus? Answer:

Properties:

They have all the sides with equal length.

The pair of sides are parallel to each other

Their angles add up to 180 degress between to sides.

All the angles are 90 degrees and both the  pair of sides are parallel and equal

A treapezoid is also called a rhombus when all the 4 sides are equal

A parallelogram is also called a rectangle when all the angles measures 90 degrees

A quadrilateral is also called a rhombus when all 4 sides are equal and pair of sides are parallel to each other.

Eureka Math Grade 5 Module 5 Lesson 18 Exit Ticket Answer Key

Question 1. Draw a rhombus. Answer:

Question 2. Draw a rectangle. Answer:

Eureka Math Grade 5 Module 5 Lesson 18 Homework Answer Key

Question 2. A rhombus has a perimeter of 217 cm. What is the length of each side of the rhombus? Answer:

Given, the perimetre of rhombus = 217 cm

In rhombus, all sides are equal.

So, 217/4 = 51 1/4

Therefore, the length of each side = 54 1/4

Question 3. List the properties that all rhombuses share. Answer:

Properties of rhombus:

a. All sides are equal

b. Their bisect bisect each other

c. Rhombuses are parallelograms , trapezoids

Question 4. List the properties that all rectangles share. Answer:

Properties of rectangles:

a.All the angles are right angles

b. Their diagnols bisect with each other

c. Rectangles are parallelograms and trapezoid.

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