## Engage NY Eureka Math 5th Grade Module 4 Lesson 6 Answer Key

### Eureka Math Grade 5 Module 4 Lesson 6 Sprint Answer Key

A
Divide Whole Numbers

Question 1.
1 ÷ 2 =

Question 2.
1 ÷ 3 =

Question 3.
1 ÷ 8 =

Question 4.
2 ÷ 2 =

Question 5.
2 ÷ 3 =

Question 6.
3 ÷ 3 =

Question 7.
3 ÷ 4 =

Question 8.
3 ÷ 10 =

Question 9.
3 ÷ 5 =

Question 10.
5 ÷ 5 =

Question 11.
6 ÷ 5 =

Question 12.
7 ÷ 5 =

Question 13.
9 ÷ 5 =

Question 14.
2 ÷ 3 =

Question 15.
4 ÷ 4 =

Question 16.
5 ÷ 4 =

Question 17.
7 ÷ 4 =

Question 18.
4 ÷ 2 =

Question 19.
5 ÷ 2 =

Question 20.
10 ÷ 5 =

Question 21.
11 ÷ 5 =

Question 22.
13 ÷ 5 =

Question 23.
6 ÷ 2 =

Question 24.
7 ÷ 2 =

Question 25.
8 ÷ 8 =

Question 26.
9 ÷ 8 =

Question 27.
15 ÷ 8 =

Question 28.
8 ÷ 4 =

Question 29.
11 ÷ 4 =

Question 30.
15 ÷ 2 =

Question 31.
24 ÷ 5 =

Question 32.
17 ÷ 4 =

Question 33.
20 ÷ 3 =

Question 34.
13 ÷ 6 =

Question 35.
30 ÷ 7 =

Question 36.
27 ÷ 8 =

Question 37.
49 ÷ 9 =

Question 38.
29 ÷ 6 =

Question 39.
47 ÷ 7 =

Question 40.
53 ÷ 8 =

Question 41
67 ÷ 9 =

Question 42.
59 ÷ 6 =

Question 43.
63 ÷ 8 =

Question 44.
71 ÷ 9 =

B
Divide Whole Numbers

Question 1.
1 ÷ 3 =

Question 2.
1 ÷ 4 =

Question 3.
1 ÷ 10 =

Question 4.
5 ÷ 5 =

Question 5.
5 ÷ 6 =

Question 6.
3 ÷ 3 =

Question 7.
3 ÷ 7 =

Question 8.
3 ÷ 10 =

Question 9.
3 ÷ 4 =

Question 10.
4 ÷ 4 =

Question 11.
5 ÷ 4 =

Question 12.
2 ÷ 2 =

Question 13.
3 ÷ 2 =

Question 14.
4 ÷ 5 =

Question 15.
10 ÷ 10 =

Question 16.
11 ÷ 10 =

Question 17.
13 ÷ 10 =

Question 18.
10 ÷ 5 =

Question 19.
11 ÷ 5 =

Question 20.
13 ÷ 5 =

Question 21.
4 ÷ 2 =

Question 22.
5 ÷ 2 =

Question 23.
15 ÷ 5 =

Question 24.
16 ÷ 5 =

Question 25.
6 ÷ 6 =

Question 26.
7 ÷ 6 =

Question 27.
11 ÷ 6 =

Question 28.
6 ÷ 3 =

Question 29.
8 ÷ 3 =

Question 30.
13 ÷ 2 =

Question 31.
23 ÷ 5 =

Question 32.
15 ÷ 4 =

Question 33.
19 ÷ 4 =

Question 34.
19 ÷ 6 =

Question 35.
31 ÷ 7 =

Question 36.
37 ÷ 8 =

Question 37.
50 ÷ 9 =

Question 38.
17 ÷ 6 =

Question 39.
48 ÷ 7 =

Question 40.
51 ÷ 8 =

Question 41.
68 ÷ 9 =

Question 42.
53 ÷ 6 =

Question 43.
61 ÷ 8 =

Question 44.
70 ÷ 9 =

### Eureka Math Grade 5 Module 4 Lesson 6 Problem Set Answer Key

Question 1.
Find the value of each of the following.
a.
$$\frac{1}{3}$$ of 9 =
$$\frac{2}{3}$$ of 9 =
$$\frac{3}{3}$$ of 9 =

b.
$$\frac{1}{3}$$ of 15 =
$$\frac{2}{3}$$ of 15 =
$$\frac{3}{3}$$ of 15 =

c.
$$\frac{1}{5}$$ of 20 =
$$\frac{4}{5}$$ of 20 =
$$\frac{}{5}$$ of 20 = 20

d.
$$\frac{1}{8}$$ of 24 =

$$\frac{3}{8}$$ of 24 =

$$\frac{4}{8}$$ of 24 =

$$\frac{6}{8}$$ of 24 =

$$\frac{7}{8}$$ of 24 =

Question 2.
Find $$\frac{4}{7}$$ of 14. Draw a set, and shade to show your thinking.

Question 3.
How does knowing $$\frac{1}{8}$$ of 24 help you find three-eighths of 24? Draw a picture to explain your thinking.

Question 4.
There are 32 students in a class. Of the class, $$\frac{3}{8}$$ of the students bring their own lunches. How many students bring their lunches?

Question 5.
Jack collected 18 ten-dollar bills while selling tickets for a show. He gave $$\frac{1}{6}$$ of the bills to the theater and kept the rest. How much money did he keep?

### Eureka Math Grade 5 Module 4 Lesson 6 Exit Ticket Answer Key

Question 1.
Find the value of each of the following.

a. $$\frac{1}{4}$$ of 16 =

b. $$\frac{3}{4}$$ of 16 =

Question 2.
Out of 18 cookies, $$\frac{2}{3}$$ are chocolate chip. How many of the cookies are chocolate chip?

### Eureka Math Grade 5 Module 4 Lesson 6 Homework Answer Key

Question 1.
Find the value of each of the following.
a.
$$\frac{1}{3}$$ of 12 =

$$\frac{2}{3}$$ of 12 =

$$\frac{3}{3}$$ of 12 =

b.
$$\frac{1}{4}$$ of 20 =

$$\frac{2}{4}$$ of 20 =

$$\frac{3}{4}$$ of 20 =

$$\frac{4}{4}$$ of 20 =

c.
$$\frac{1}{5}$$ of 35 =
$$\frac{2}{5}$$ of 35 =

$$\frac{3}{5}$$ of 35 =
$$\frac{4}{5}$$ of 35 =

$$\frac{5}{5}$$ of 35 =
$$\frac{6}{5}$$ of 35 =

Question 2.
Find $$\frac{2}{3}$$ of 18. Draw a set and shade to show your thinking.

Question 3.
How does knowing $$\frac{1}{5}$$ of 10 help you find $$\frac{3}{5}$$ of 10? Draw a picture to explain your thinking.

Question 4.
Sara just turned 18 years old. She spent $$\frac{4}{9}$$ of her life living in Rochester, NY. How many years did Sara live in Rochester?

Question 5.
A farmer collected 12 dozen eggs from her chickens. She sold $$\frac{5}{6}$$ of the eggs at the farmers’ market and gave the rest to friends and neighbors.
a. How many dozen eggs did the farmer give away? How many eggs did she give away?

b. She sold each dozen for $4.50. How much did she earn from the eggs she sold? ## Eureka Math Grade 5 Module 4 Lesson 10 Answer Key ## Engage NY Eureka Math 5th Grade Module 4 Lesson 10 Answer Key ### Eureka Math Grade 5 Module 4 Lesson 10 Problem Set Answer Key Question 1. Write expressions to match the diagrams. Then, evaluate. Question 2. Write an expression to match, and then evaluate. a. $$\frac{1}{6}$$ the sum of 16 and 20 b. Subtract 5 from $$\frac{1}{3}$$ of 23. c. 3 times as much as the sum of $$\frac{3}{4}$$ and $$\frac{2}{6}$$ d. $$\frac{2}{5}$$ of the product of $$\frac{5}{6}$$ and 42 e. 8 copies of the sum of 4 thirds and 2 more f. 4 times as much as 1 third of 8 Question 3. Circle the expression(s) that give the same product as $$\frac{4}{5}$$ × 7. Explain how you know. Question 4. Use <, >, or = to make true number sentences without calculating. Explain your thinking. a. 4 × 2 + 4 × $$\frac{2}{3}$$ 3 × $$\frac{2}{3}$$ b. (5 × $$\frac{3}{4}$$ ) (5 × $$\frac{3}{4}$$) × $$\frac{2}{7}$$ c. 3 × (3 + $$\frac{15}{12}$$) (3 × 3) + $$\frac{15}{12}$$ Question 5. Collette bought milk for herself each month and recorded the amount in the table below. For (a)–(c), write an expression that records the calculation described. Then, solve to find the missing data in the table.  Month Amount (in pounds) January 3 February 2 March 1$$\frac{1}{4}$$ April May $$\frac{9}{8}$$ June July 1$$\frac{1}{4}$$ August September $$\frac{11}{4}$$ October $$\frac{3}{4}$$ a. She bought $$\frac{1}{4}$$ of July’s total in June. b. She bought $$\frac{3}{4}$$ as much in September as she did in January and July combined. c. In April, she bought $$\frac{1}{2}$$ gallon less than twice as much as she bought in August. d. Display the data from the table in a line plot. e. How many gallons of milk did Collette buy from January to October? ### Eureka Math Grade 5 Module 4 Lesson 10 Exit Ticket Answer Key Question 1. Rewrite these expressions using words. $$\frac{3}{4}$$ × (2$$\frac{2}{5}$$ – $$\frac{5}{6}$$) b. 2$$\frac{1}{4}$$ + $$\frac{8}{3}$$ Question 2. Write an expression, and then solve. Three less than one-fourth of the product of eight thirds and nine ### Eureka Math Grade 5 Module 4 Lesson 10 Homework Answer Key Question 1. Write expressions to match the diagrams. Then, evaluate. Question 2. Circle the expression(s) that give the same product as 6 × $$\frac{3}{8}$$. Explain how you know. Question 3. Write an expression to match, and then evaluate. a. $$\frac{1}{8}$$ the sum of 23 and 17 b. Subtract 4 from $$\frac{1}{6}$$ of 42. c. 7 times as much as the sum of $$\frac{1}{3}$$ and $$\frac{4}{5}$$ d. $$\frac{2}{3}$$ of the product of $$\frac{3}{8}$$ and 16 e. 7 copies of the sum of 8 fifths and 4 f. 15 times as much as 1 fifth of 12 Question 4. Use <, >, or = to make true number sentences without calculating. Explain your thinking. a. $$\frac{2}{3}$$ × (9 + 12) 15 × $$\frac{2}{3}$$ b. (3 × $$\frac{5}{4}$$) (3 × $$\frac{5}{4}$$) × $$\frac{3}{8}$$ c. 6 × (2 + $$\frac{32}{16}$$) (6 × 2) + $$\frac{32}{16}$$) Question 5. Fantine bought flour for her bakery each month and recorded the amount in the table to the right. For (a)–(c), write an expression that records the calculation described. Then, solve to find the missing data in the table.  Month Amount (in pounds) January 3 February 2 March 1$$\frac{1}{4}$$ April May $$\frac{9}{8}$$ June July 1$$\frac{1}{4}$$ August September $$\frac{11}{4}$$ October $$\frac{3}{4}$$ a. She bought $$\frac{3}{4}$$ of January’s total in August. b. She bought $$\frac{7}{8}$$ as much in April as she did in October and July combined. c. In June, she bought $$\frac{1}{8}$$ pound less than three times as much as she bought in May. d. Display the data from the table in a line plot. e. How many pounds of flour did Fantine buy from January to October? ## Eureka Math Grade 5 Module 4 Lesson 12 Answer Key ## Engage NY Eureka Math 5th Grade Module 4 Lesson 12 Answer Key ### Eureka Math Grade 5 Module 4 Lesson 12 Problem Set Answer Key Question 1. A baseball team played 32 games and lost 8. Katy was the catcher in $$\frac{5}{8}$$ of the winning games and $$\frac{1}{4}$$ of the losing games. a. What fraction of the games did the team win? b. In how many games did Katy play catcher? Question 2. In Mrs. Elliott’s garden, $$\frac{1}{8}$$ of the flowers are red, $$\frac{1}{4}$$ of them are purple, and $$\frac{1}{5}$$ of the remaining flowers are pink. If there are 128 flowers, how many flowers are pink? Question 3. Lillian and Darlene plan to get their homework finished within one hour. Darlene completes her math homework in $$\frac{3}{5}$$ hour. Lillian completes her math homework with $$\frac{5}{6}$$ hour remaining. Who completes her homework faster, and by how many minutes? Bonus: Give the answer as a fraction of an hour. Question 4. Create and solve a story problem about a baker and some flour whose solution is given by the expression $$\frac{1}{4}$$ × (3 + 5). Question 5. Create and solve a story problem about a baker and 36 kilograms of an ingredient that is modeled by the following tape diagram. Include at least one fraction in your story. Question 6. Of the students in Mr. Smith’s fifth-grade class, $$\frac{1}{3}$$ were absent on Monday. Of the students in Mrs. Jacobs’ class, $$\frac{2}{5}$$ were absent on Monday. If there were 4 students absent in each class on Monday, how many students are in each class? ### Eureka Math Grade 5 Module 4 Lesson 12 Exit Ticket Answer Key In a classroom, $$\frac{1}{6}$$ of the students are wearing blue shirts, and $$\frac{2}{3}$$ are wearing white shirts. There are 36 students in the class. How many students are wearing a shirt other than blue or white? ### Eureka Math Grade 5 Module 4 Lesson 12 Homework Answer Key Question 1. Terrence finished a word search in $$\frac{3}{4}$$ the time it took Frank. Charlotte finished the word search in $$\frac{2}{3}$$ the time it took Terrence. Frank finished the word search in 32 minutes. How long did it take Charlotte to finish the word search? Question 2. Ms. Phillips ordered 56 pizzas for a school fundraiser. Of the pizzas ordered, $$\frac{2}{7}$$ of them were pepperoni, 19 were cheese, and the rest were veggie pizzas. What fraction of the pizzas was veggie? Question 3. In an auditorium, $$\frac{1}{6}$$ of the students are fifth graders, $$\frac{1}{3}$$ are fourth graders, and $$\frac{1}{4}$$ of the remaining students are second graders. If there are 96 students in the auditorium, how many second graders are there? Question 4. At a track meet, Jacob and Daniel compete in the 220 m hurdles. Daniel finishes in $$\frac{3}{4}$$ of a minute. Jacob finishes with $$\frac{5}{12}$$ of a minute remaining. Who ran the race in the faster time? Bonus: Express the difference in their times as a fraction of a minute. Question 5. Create and solve a story problem about a runner who is training for a race. Include at least one fraction in your story. Question 6. Create and solve a story problem about two friends and their weekly allowance whose solution is given by the expression $$\frac{1}{5}$$ × (12 + 8). ## Eureka Math Grade 5 Module 4 Lesson 18 Answer Key ## Engage NY Eureka Math 5th Grade Module 4 Lesson 18 Answer Key ### Eureka Math Grade 5 Module 4 Lesson 18 Sprint Answer Key A Multiply Fractions Question 1. $$\frac{1}{2}$$ × $$\frac{1}{2}$$ = Question 2. $$\frac{1}{2}$$ × $$\frac{1}{3}$$ = Question 3. $$\frac{1}{2}$$ × $$\frac{1}{4}$$ = Question 4. $$\frac{1}{2}$$ × $$\frac{1}{7}$$ = Question 5. $$\frac{1}{7}$$ × $$\frac{1}{2}$$ = Question 6. $$\frac{1}{3}$$ × $$\frac{1}{2}$$ = Question 7. $$\frac{1}{3}$$ × $$\frac{1}{3}$$ = Question 8. $$\frac{1}{3}$$ × $$\frac{1}{6}$$ = Question 9. $$\frac{1}{3}$$ × $$\frac{1}{5}$$ = Question 10. $$\frac{1}{5}$$ × $$\frac{1}{3}$$ = Question 11. $$\frac{1}{5}$$ × $$\frac{2}{3}$$ = Question 12. $$\frac{2}{5}$$ × $$\frac{2}{3}$$ = Question 13. $$\frac{1}{4}$$ × $$\frac{1}{3}$$ = Question 14. $$\frac{1}{4}$$ × $$\frac{2}{3}$$ = Question 15. $$\frac{3}{4}$$ × $$\frac{2}{3}$$ = Question 16. $$\frac{1}{6}$$ × $$\frac{1}{3}$$ = Question 17. $$\frac{5}{6}$$ × $$\frac{1}{3}$$ = Question 18. $$\frac{5}{6}$$ × $$\frac{2}{3}$$ = Question 19. $$\frac{5}{4}$$ × $$\frac{2}{3}$$ = Question 20. $$\frac{1}{5}$$ × $$\frac{1}{5}$$ = Question 21. $$\frac{2}{5}$$ × $$\frac{2}{5}$$ = Question 22. $$\frac{2}{5}$$ × $$\frac{3}{5}$$ = Question 23. $$\frac{2}{5}$$ × $$\frac{5}{3}$$ = Question 24. $$\frac{3}{5}$$ × $$\frac{5}{2}$$ = Question 25. $$\frac{1}{3}$$ × $$\frac{1}{3}$$ = Question 26. $$\frac{1}{3}$$ × $$\frac{2}{3}$$ = Question 27. $$\frac{2}{3}$$ × $$\frac{2}{3}$$ = Question 28. $$\frac{2}{3}$$ × $$\frac{3}{2}$$ = Question 29. $$\frac{2}{3}$$ × 4 ⁄3 = Question 30. $$\frac{2}{3}$$ × $$\frac{5}{3}$$ = Question 31. $$\frac{3}{2}$$ × $$\frac{3}{5}$$ = Question 32. $$\frac{3}{4}$$ × $$\frac{1}{5}$$ = Question 33. $$\frac{3}{4}$$ × $$\frac{4}{5}$$ = Question 34. $$\frac{3}{4}$$ × $$\frac{5}{5}$$ = Question 35. $$\frac{3}{4}$$ × $$\frac{6}{5}$$ = Question 36. $$\frac{1}{4}$$ × $$\frac{6}{5}$$ = Question 37. $$\frac{1}{7}$$ × $$\frac{1}{7}$$ = Question 38. $$\frac{1}{8}$$ × $$\frac{3}{5}$$ = Question 39. $$\frac{5}{6}$$ × $$\frac{1}{4}$$ = Question 40. $$\frac{3}{4}$$ × $$\frac{3}{4}$$ = Question 41. $$\frac{2}{3}$$ × $$\frac{6}{6}$$ = Question 42. $$\frac{3}{4}$$ × $$\frac{6}{2}$$ = Question 43. $$\frac{7}{8}$$ × $$\frac{7}{9}$$ = Question 44. $$\frac{7}{12}$$ × $$\frac{9}{8}$$ = B Multiply Fractions Question 1. $$\frac{1}{2}$$ × $$\frac{1}{3}$$ = Question 2. $$\frac{1}{2}$$ × $$\frac{1}{4}$$ = Question 3. $$\frac{1}{2}$$ × $$\frac{1}{5}$$ = Question 4. $$\frac{1}{2}$$ × $$\frac{1}{9}$$ = Question 5. $$\frac{1}{9}$$ × $$\frac{1}{2}$$ = Question 6. $$\frac{1}{5}$$ × $$\frac{1}{2}$$ = Question 7. $$\frac{1}{5}$$ × $$\frac{1}{3}$$ = Question 8. $$\frac{1}{5}$$ × $$\frac{1}{7}$$ = Question 9. $$\frac{1}{5}$$ × $$\frac{1}{3}$$ = Question 10. $$\frac{1}{3}$$ × $$\frac{1}{5}$$ = Question 11. $$\frac{1}{3}$$ × $$\frac{2}{5}$$ = Question 12. $$\frac{2}{3}$$ × $$\frac{2}{5}$$ = Question 13. $$\frac{1}{3}$$ × $$\frac{1}{4}$$ = Question 14. $$\frac{1}{3}$$ × $$\frac{3}{4}$$ = Question 15. $$\frac{2}{3}$$ × $$\frac{3}{4}$$ = Question 16. $$\frac{1}{3}$$ × $$\frac{1}{6}$$ = Question 17. $$\frac{2}{3}$$ × $$\frac{1}{6}$$ = Question 18. $$\frac{2}{3}$$ × $$\frac{5}{6}$$ = Question 19. $$\frac{3}{2}$$ × $$\frac{3}{4}$$ = Question 20. $$\frac{1}{5}$$ × $$\frac{1}{5}$$ = Question 21. $$\frac{3}{5}$$ × $$\frac{3}{5}$$ = Question 22. $$\frac{3}{5}$$ × $$\frac{4}{5}$$ = Question 23. $$\frac{3}{5}$$ × $$\frac{5}{4}$$ = Question 24. $$\frac{1}{5}$$ × $$\frac{5}{3}$$ = Question 25. $$\frac{1}{4}$$ × $$\frac{1}{4}$$ = Question 26. $$\frac{1}{4}$$ × $$\frac{3}{4}$$ = Question 27. $$\frac{3}{4}$$ × $$\frac{3}{4}$$ = Question 28. $$\frac{3}{4}$$ × $$\frac{4}{3}$$ = Question 29. $$\frac{3}{4}$$ × $$\frac{5}{4}$$ = Question 30. $$\frac{3}{4}$$ × $$\frac{6}{4}$$ = Question 31. $$\frac{4}{3}$$ × $$\frac{4}{6}$$ = Question 32. $$\frac{2}{3}$$ × $$\frac{1}{5}$$ = Question 33. $$\frac{2}{3}$$ × $$\frac{4}{5}$$ = Question 34. $$\frac{2}{3}$$ × $$\frac{5}{5}$$ = Question 35. $$\frac{2}{3}$$ × $$\frac{6}{5}$$ = Question 36. $$\frac{1}{3}$$ × $$\frac{6}{5}$$ = Question 37. $$\frac{1}{9}$$ × $$\frac{1}{9}$$ = Question 38. $$\frac{1}{5}$$ × $$\frac{3}{8}$$ = Question 39. $$\frac{3}{4}$$ × $$\frac{1}{6}$$ = Question 40. $$\frac{2}{3}$$ × $$\frac{2}{3}$$ = Question 41. $$\frac{3}{4}$$ × $$\frac{8}{8}$$ = Question 42. $$\frac{2}{3}$$ × $$\frac{6}{3}$$ = Question 43. $$\frac{6}{7}$$ × $$\frac{8}{9}$$ = Question 44. $$\frac{7}{12}$$ × $$\frac{8}{7}$$ = ### Eureka Math Grade 5 Module 4 Lesson 18 Problem Set Answer Key Question 1. Multiply using both fraction form and unit form. Check your answer by counting the decimal places. The first one is done for you. a. b. 2.3 × 0.9 = c. 6.6 × 2.8 = d. 3.3 × 1.4 = Question 2. Multiply using fraction form and unit form. Check your answer by counting the decimal places. The first one is done for you. a. b. 2.37 × 0.9 = c. 6.06 × 2.8 = d. 3.3 × 0.14 = Question 3. Solve using the standard algorithm. Show your thinking about the units of your product. The first one is done for you. a. 3.2 × 0.6 = 1.92 b. 3.2 × 1.2 = __________ c. 8.31 × 2.4 = __________ d. 7.50 × 3.5 = __________ Question 4. Carolyn buys 1.2 pounds of chicken breast. If each pound of chicken breast costs$3.70, how much will she pay for the chicken breast?

Question 5.
A kitchen measures 3.75 meters by 4.2 meters.
a. Find the area of the kitchen.

b. The area of the living room is one and a half times that of the kitchen. Find the total area of the living room and the kitchen.

### Eureka Math Grade 5 Module 4 Lesson 18 Exit Ticket Answer Key

Multiply. Do at least one problem using unit form and at least one problem using fraction form.
a. 3.2 × 1.4 =

b. 1.6 × 0.7 =

c. 2.02 × 4.2 =

d. 2.2 × 0.42 =

### Eureka Math Grade 5 Module 4 Lesson 18 Homework Answer Key

Question 1.
Multiply using fraction form and unit form. Check your answer by counting the decimal places.
The first one is done for you.
a.

b. 3.3 × 0.8 =

c. 4.4 × 3.2 =

d. 2.2 × 1.6 =

Question 2.
Multiply using fraction form and unit form. The first one is partially done for you.
a.

b. 3.35 × 0.7 =

c. 4.04 × 3.2 =

d. 4.4 × 0.16 =

Question 3.
Solve using the standard algorithm. Show your thinking about the units of your product. The first one is done for you.
a.

b. 2.3 × 2.1 = __________

c. 7.41 × 3.4 = __________

d. 6.50 × 4.5 = __________

Question 4.
Erik buys 2.5 pounds of cashews. If each pound of cashews costs $7.70, how much will he pay for the cashews? Question 5. A swimming pool at a park measures 9.75 meters by 7.2 meters. a. Find the area of the swimming pool. b. The area of the playground is one and a half times that of the swimming pool. Find the total area of the swimming pool and the playground. ## Eureka Math Grade 5 Module 4 Lesson 33 Answer Key ## Engage NY Eureka Math 5th Grade Module 4 Lesson 33 Answer Key ### Eureka Math Grade 5 Module 4 Lesson 33 Sprint Answer Key A Divide Decimals Question 1. 1 ÷ 1 = Answer: Question 2. 1 ÷ 0.1 = Answer: Question 3. 2 ÷ 0.1 = Answer: Question 4. 7 ÷ 0.1 = Answer: Question 5. 1 ÷ 0.1 = Answer: Question 6. 10 ÷ 0.1 = Answer: Question 7. 20 ÷ 0.1 = Answer: Question 8. 60 ÷ 0.1 = Answer: Question 9. 1 ÷ 1 = Answer: Question 10. 1 ÷ 0.1 = Answer: Question 11. 10 ÷ 0.1 = Answer: Question 12. 100 ÷ 0.1 = Answer: Question 13. 200 ÷ 0.1 = Answer: Question 14. 800 ÷ 0.1 = Answer: Question 15. 1 ÷ 0.1 = Answer: Question 16. 1 ÷ 0.01 = Answer: Question 17. 2 ÷ 0.01 = Answer: Question 18. 9 ÷ 0.01 = Answer: Question 19. 5 ÷ 0.01 = Answer: Question 20. 50 ÷ 0.01 = Answer: Question 21. 60 ÷ 0.01 = Answer: Question 22. 20 ÷ 0.01 = Answer: Question 23. 5 ÷ 0.1 = Answer: Question 24. 0.5 ÷ 0.1 = Answer: Question 25. 0.05 ÷ 0.1 = Answer: Question 26. 0.08 ÷ 0.1 = Answer: Question 27. 4 ÷ 0.01 = Answer: Question 28. 40 ÷ 0.01 = Answer: Question 29. 47 ÷ 0.01 = Answer: Question 30. 59 ÷ 0.01 = Answer: Question 31. 3 ÷ 0.1 = Answer: Question 32. 30 ÷ 0.1 = Answer: Question 33. 32 ÷ 0.1 = Answer: Question 34. 32.5 ÷ 0.1 = Answer: Question 35. 25 ÷ 5 = Answer: Question 36. 2.5 ÷ 0.5 = Answer: Question 37. 2.5 ÷ 0.05 = Answer: Question 38. 3.6 ÷ 0.04 = Answer: Question 39. 32 ÷ 0.08 = Answer: Question 40. 56 ÷ 0.7 = Answer: Question 41. 77 ÷ 1.1 = Answer: Question 42. 4.8 ÷ 0.12 = Answer: Question 43. 4.84 ÷ 0.4 = Answer: Question 44. 9.63 ÷ 0.03 = Answer: B Divide Decimals Question 1. 10 ÷ 1 = Answer: Question 2. 1 ÷ 0.1 = Answer: Question 3. 2 ÷ 0.1 = Answer: Question 4. 8 ÷ 0.1 = Answer: Question 5. 1 ÷ 0.1 = Answer: Question 6. 10 ÷ 0.1 = Answer: Question 7. 20 ÷ 0.1 = Answer: Question 8. 70 ÷ 0.1 = Answer: Question 9. 1 ÷ 1 = Answer: Question 10. 1 ÷ 0.1 = Answer: Question 11. 10 ÷ 0.1 = Answer: Question 12. 100 ÷ 0.1 = Answer: Question 13. 200 ÷ 0.1 = Answer: Question 14. 900 ÷ 0.1 = Answer: Question 15. 1 ÷ 0.1 = Answer: Question 16. 1 ÷ 0.01 = Answer: Question 17. 2 ÷ 0.01 = Answer: Question 18. 7 ÷ 0.01 = Answer: Question 19. 4 ÷ 0.01 = Answer: Question 20. 40 ÷ 0.01 = Answer: Question 21. 50 ÷ 0.01 = Answer: Question 22. 80 ÷ 0.01 = Answer: Question 23. 4 ÷ 0.1 = Answer: Question 24. 0.4 ÷ 0.1 = Answer: Question 25. 0.04 ÷ 0.1 = Answer: Question 26. 0.07 ÷ 0.1 = Answer: Question 27. 5 ÷ 0.01 = Answer: Question 28. 50 ÷ 0.01 = Answer: Question 29. 53 ÷ 0.01 = Answer: Question 30. 68 ÷ 0.01 = Answer: Question 31. 2 ÷ 0.1 = Answer: Question 32. 20 ÷ 0.1 = Answer: Question 33. 23 ÷ 0.1 = Answer: Question 34. 23.6 ÷ 0.1 = Answer: Question 35. 15 ÷ 5 = Answer: Question 36. 1.5 ÷ 0.5 = Answer: Question 37. 1.5 ÷ 0.05 = Answer: Question 38. 3.2 ÷ 0.04 = Answer: Question 39. 28 ÷ 0.07 = Answer: Question 40. 42 ÷ 0.6 = Answer: Question 41. 88 ÷ 1.1 = Answer: Question 42. 3.6 ÷ 0.12 = Answer: Question 43. 3.63 ÷ 0.3 = Answer: Question 44. 8.44 ÷ 0.04 = Answer: ### Eureka Math Grade 5 Module 4 Lesson 33 Problem Set Answer Key Question 1. Ms. Hayes has $$\frac{1}{2}$$ liter of juice. She distributes it equally to 6 students in her tutoring group. a. How many liters of juice does each student get? b. How many more liters of juice will Ms. Hayes need if she wants to give each of the 24 students in her class the same amount of juice found in Part (a)? Answer: Question 2. Lucia has 3.5 hours left in her workday as a car mechanic. Lucia needs $$\frac{1}{2}$$ of an hour to complete one oil change. a. How many oil changes can Lucia complete during the rest of her workday? b. Lucia can complete two car inspections in the same amount of time it takes her to complete one oil change. How long does it take her to complete one car inspection? c. How many inspections can she complete in the rest of her workday? Answer: Question 3. Carlo buys$14.40 worth of grapefruit. Each grapefruit costs $0.80. a. How many grapefruits does Carlo buy? b. At the same store, Kahri spends one-third as much money on grapefruits as Carlo. How many grapefruits does she buy? Answer: Question 4. Studies show that a typical giant hummingbird can flap its wings once in 0.08 of a second. a. While flying for 7.2 seconds, how many times will a typical giant hummingbird flap its wings? b. A ruby-throated hummingbird can flap its wings 4 times faster than a giant hummingbird. How many times will a ruby-throated hummingbird flap its wings in the same amount of time? Answer: Question 5. Create a story context for the following expression. $$\frac{1}{3}$$ × ($20 – $3.20) Answer: Question 6. Create a story context about painting a wall for the following tape diagram. Answer: ### Eureka Math Grade 5 Module 4 Lesson 33 Exit Ticket Answer Key An entire commercial break is 3.6 minutes. a. If each commercial takes 0.6 minutes, how many commercials will be played? b. A different commercial break of the same length plays commercials half as long. How many commercials will play during this break? Answer: ### Eureka Math Grade 5 Module 4 Lesson 33 Homework Answer Key Question 1. Chase volunteers at an animal shelter after school, feeding and playing with the cats. a. If he can make 5 servings of cat food from a third of a kilogram of food, how much does one serving weigh? b. If Chase wants to give this same serving size to each of 20 cats, how many kilograms of food will he need? Answer: Question 2. Anouk has 4.75 pounds of meat. She uses a quarter pound of meat to make one hamburger. a. How many hamburgers can Anouk make with the meat she has? b. Sometimes Anouk makes sliders. Each slider is half as much meat as is used for a regular hamburger. How many sliders could Anouk make with the 4.75 pounds? Answer: Question 3. Ms. Geronimo has a$10 gift certificate to her local bakery.
a. If she buys a slice of pie for $2.20 and uses the rest of the gift certificate to buy chocolate macaroons that cost$0.60 each, how many macaroons can Ms. Geronimo buy?
b. If she changes her mind and instead buys a loaf of bread for $4.60 and uses the rest to buy cookies that cost 1$$\frac{1}{2}$$ times as much as the macaroons, how many cookies can she buy? Answer: Question 4. Create a story context for the following expressions. a. (5$$\frac{1}{4}$$ – 2$$\frac{1}{8}$$) ÷ 4 b. 4 × ($$\frac{4.8}{0.8}$$) Answer: Question 5. Create a story context for the following tape diagram. Answer: ## Eureka Math Grade 5 Module 4 Lesson 32 Answer Key ## Engage NY Eureka Math 5th Grade Module 4 Lesson 32 Answer Key ### Eureka Math Grade 5 Module 4 Lesson 32 Problem Set Answer Key Question 1. Circle the expression equivalent to the sum of 3 and 2 divided by $$\frac{1}{3}$$. $$\frac{1}{2}$$ 3 + (2 ÷ $$\frac{1}{3}$$) (3 + 2) ÷ $$\frac{1}{3}$$ $$\frac{1}{3}$$ ÷ (3 + 2) Answer: Question 2. Circle the expression(s) equivalent to 28 divided by the difference between $$\frac{4}{5}$$ and $$\frac{7}{10}$$. 28 ÷ ($$\frac{4}{5}$$ – $$\frac{7}{10}$$) $$\frac{28}{\frac{4}{5}-\frac{7}{10}}$$ ($$\frac{4}{5}$$ – $$\frac{7}{10}$$) ÷ 28 28 ÷ ($$\frac{7}{10}$$ – $$\frac{4}{5}$$) Answer: Question 3. Fill in the chart by writing an equivalent numerical expression.  a. Half as much as the difference between 2$$\frac{1}{4}$$ and $$\frac{3}{8}$$. b. The difference between 2$$\frac{1}{4}$$ and $$\frac{3}{8}$$ divided by 4. c. A third of the sum of $$\frac{7}{8}$$ and 22 tenths. d. Add 2.2 and $$\frac{7}{8}$$, and then triple the sum. Answer: Question 4. Compare expressions 3(a) and 3(b). Without evaluating, identify the expression that is greater. Explain how you know. Answer: Question 5. Fill in the chart by writing an equivalent expression in word form.  a. $$\frac{3}{4}$$ × (1.75 + $$\frac{3}{5}$$) b. $$\frac{1}{2}$$ – ($$\frac{1}{8}$$ × 0.2) c. (1.75 + $$\frac{3}{5}$$) × $$\frac{4}{3}$$ d. 2 ÷ ($$\frac{1}{2}$$ × $$\frac{4}{5}$$ ) Answer: Question 6. Compare the expressions in 5(a) and 5(c). Without evaluating, identify the expression that is less. Explain how you know. Answer: Question 7. Evaluate the following expressions. a. (9 – 5) ÷ $$\frac{1}{3}$$ b. $$\frac{5}{3}$$ × (2 × $$\frac{1}{4}$$) c. $$\frac{1}{3}$$ ÷ (1 ÷ $$\frac{1}{4}$$) d. $$\frac{1}{2}$$ × $$\frac{3}{5}$$ × $$\frac{5}{3}$$ e. Half as much as ($$\frac{3}{4}$$ × 0.2) f. 3 times as much as the quotient of 2.4 and 0.6 Answer: Question 8. Choose an expression below that matches the story problem, and write it in the blank. $$\frac{2}{3}$$ × (20 – 5) ($$\frac{2}{3}$$ × 20) – ($$\frac{2}{3}$$ × 5) $$\frac{2}{3}$$ × 20 – 5 (20 – $$\frac{2}{3}$$) – 5 a. Farmer Green picked 20 carrots. He cooked $$\frac{2}{3}$$ of them, and then gave 5 to his rabbits. Write the expression that tells how many carrots he had left. Expression: ___________________________ b. Farmer Green picked 20 carrots. He cooked 5 of them, and then gave $$\frac{2}{3}$$ of the remaining carrots to his rabbits. Write the expression that tells how many carrots the rabbits will get. Expression: ___________________________ Answer: ### Eureka Math Grade 5 Module 4 Lesson 32 Exit Ticket Answer Key Question 1. Write an equivalent expression in numerical form. A fourth as much as the product of two-thirds and 0.8 Answer: Question 2. Write an equivalent expression in word form. a. $$\frac{3}{8}$$ × (1 – $$\frac{1}{3}$$) b. (1 – $$\frac{1}{3}$$) ÷ 2 Answer: Question 3. Compare the expressions in 2(a) and 2(b). Without evaluating, determine which expression is greater, and explain how you know. Answer: ### Eureka Math Grade 5 Module 4 Lesson 32 Homework Answer Key Question 1. Circle the expression equivalent to the difference between 7 and 4, divided by a fifth. 7 + (4 ÷ $$\frac{1}{5}$$) $$\frac{7-4}{5}$$ (7 – 4) ÷ $$\frac{1}{5}$$ $$\frac{1}{5}$$ ÷ (7 – 4) Answer: Question 2. Circle the expression(s) equivalent to 42 divided by the sum of $$\frac{2}{3}$$ and $$\frac{3}{4}$$. ($$\frac{2}{3}$$ + $$\frac{3}{4}$$) ÷ 42 (42 ÷ $$\frac{2}{3}$$) + $$\frac{3}{4}$$ 42 ÷ ($$\frac{2}{3}$$ + $$\frac{3}{4}$$) $$\frac{42}{\frac{2}{8}+\frac{3}{4}}$$ Answer: Question 3. Fill in the chart by writing the equivalent numerical expression or expression in word form.  Expression in word form Numerical expression a. A fourth as much as the sum of 3 and 4.5 b. (3$$\frac{1}{8}$$ + 4.5) ÷ 5 c. Multiply by 5.8; then halve the product d. $$\frac{1}{6}$$ × (4.8 – $$\frac{1}{2}$$) e. 8 – ($$\frac{1}{2}$$ ÷ 9) Answer: Question 4. Compare the expressions in 3(a) and 3(b). Without evaluating, identify the expression that is greater. Explain how you know. Answer: Question 5. Evaluate the following expressions. a. (11 – 6) ÷ $$\frac{1}{6}$$ b. $$\frac{9}{5}$$ × (4 × $$\frac{1}{6}$$) c. $$\frac{1}{10}$$ ÷ (5 ÷ $$\frac{1}{2}$$) d. $$\frac{3}{4}$$ × $$\frac{2}{5}$$ × $$\frac{4}{3}$$ e. 50 divided by the difference between $$\frac{3}{4}$$ and $$\frac{5}{8}$$ Answer: Question 6. Lee is sending out 32 birthday party invitations. She gives 5 invitations to her mom to give to family members. Lee mails a third of the rest, and then she takes a break to walk her dog. a. Write a numerical expression to describe how many invitations Lee has already mailed. b. Which expression matches how many invitations still need to be sent out? 32 – 5 – $$\frac{1}{3}$$(32 – 5) $$\frac{2}{3}$$ × 32 – 5 (32 – 5) ÷ $$\frac{1}{3}$$ $$\frac{1}{3}$$ × (32 – 5) Answer: ## Eureka Math Grade 5 Module 4 Lesson 31 Answer Key ## Engage NY Eureka Math 5th Grade Module 4 Lesson 31 Answer Key ### Eureka Math Grade 5 Module 4 Lesson 31 Problem Set Answer Key Question 1. Estimate and then divide. An example has been done for you. a. 53.2 ÷ 0.4 ≈ b. 1.52 ÷ 0.8 ≈ Answer: Question 2. Estimate and then divide. The first one has been done for you. a. 9.42 ÷ 0.03 ≈ b. 39.36 ÷ 0.96 ≈ Answer: Question 3. Solve using the standard algorithm. Use the thought bubble to show your thinking as you rename the divisor as a whole number. a. 46.2 ÷ 0.3 = ______ b. 3.16 ÷ 0.04 = ______ c. 2.31 ÷ 0.3 = ______ d. 15.6 ÷ 0.24 = ______ Answer: Question 4. The total distance of a race is 18.9 km. a. If volunteers set up a water station every 0.7 km, including one at the finish line, how many stations will they have? b. If volunteers set up a first aid station every 0.9 km, including one at the finish line, how many stations will they have? Answer: Question 5. In a laboratory, a technician combines a salt solution contained in 27 test tubes. Each test tube contains 0.06 liter of the solution. If he divides the total amount into test tubes that hold 0.3 liter each, how many test tubes will he need? Answer: ### Eureka Math Grade 5 Module 4 Lesson 31 Exit Ticket Answer Key Estimate first, and then solve using the standard algorithm. Show how you rename the divisor as a whole number. Question 1. 6.39 ÷ 0.09 Answer: Question 2. 82.14 ÷ 0.6 Answer: ### Eureka Math Grade 5 Module 4 Lesson 31 Homework Answer Key Question 1. Estimate and then divide. An example has been done for you. a. 61.6 ÷ 0.8 ≈ b. 5.74 ÷ 0.7 ≈ Answer: Question 2. Estimate and then divide. An example has been done for you. a. 4.74 ÷ 0.06 ≈ b. 19.44 ÷ 0.54 ≈ Answer: Question 3. Solve using the standard algorithm. Use the thought bubble to show your thinking as you rename the divisor as a whole number. a. 38.4 ÷ 0.6 = ______ b. 7.52 ÷ 0.08 = ______ c. 12.45 ÷ 0.5 = ______ d. 5.6 ÷ 0.16 = ______ Answer: Question 4. Lucia is making a 21.6 centimeter beaded string to hang in the window. She decides to put a green bead every 0.4 centimeters and a purple bead every 0.6 centimeters. How many green beads and how many purple beads will she need? Answer: Question 5. A group of 14 friends collects 0.7 pound of blueberries and decides to make blueberry muffins. They put 0.05 pound of berries in each muffin. How many muffins can they make if they use all the blueberries they collected? Answer: ## Eureka Math Grade 5 Module 4 Lesson 30 Answer Key ## Engage NY Eureka Math 5th Grade Module 4 Lesson 30 Answer Key ### Eureka Math Grade 5 Module 4 Lesson 30 Sprint Answer Key A Divide Whole Numbers by Fractions and Fractions by Whole Numbers Question 1. $$\frac{1}{2}$$ ÷ 2 = Answer: Question 2. $$\frac{1}{2}$$ ÷ 3 = Answer: Question 3. $$\frac{1}{2}$$ ÷ 4 = Answer: Question 4. $$\frac{1}{2}$$ ÷ 7 = Answer: Question 5. 7 ÷ $$\frac{1}{2}$$ = Answer: Question 6. 6 ÷ $$\frac{1}{2}$$ = Answer: Question 7. 5 ÷ $$\frac{1}{2}$$ = Answer: Question 8. 3 ÷ $$\frac{1}{2}$$ = Answer: Question 9. 2 ÷ $$\frac{1}{5}$$ = Answer: Question 10. 3 ÷ $$\frac{1}{5}$$= Answer: Question 11. 4 ÷ $$\frac{1}{5}$$ = Answer: Question 12. 7 ÷ $$\frac{1}{5}$$ = Answer: Question 13. $$\frac{1}{5}$$ ÷ 7 = Answer: Question 14. $$\frac{1}{3}$$ ÷ 2 = Answer: Question 15. 2 ÷ $$\frac{1}{3}$$ = Answer: Question 16. $$\frac{1}{4}$$ ÷ 2 = Answer: Question 17. 2 ÷ $$\frac{1}{4}$$ = Answer: Question 18. $$\frac{1}{5}$$ ÷ 2 = Answer: Question 19. 2 ÷ $$\frac{1}{5}$$ = Answer: Question 20. 3 ÷ $$\frac{1}{4}$$ = Answer: Question 21. $$\frac{1}{4}$$ ÷ 3 = Answer: Question 22. $$\frac{1}{4}$$ ÷ 4 = Answer: Question 23. 4 ÷ $$\frac{1}{4}$$ = Answer: Question 24. $$\frac{1}{3}$$ ÷ 3 = Answer: Question 25. $$\frac{2}{3}$$ ÷ 3 = Answer: Question 26. $$\frac{1}{4}$$ ÷ 2 = Answer: Question 27. $$\frac{3}{4}$$ ÷ 2 = Answer: Question 28. $$\frac{1}{5}$$ ÷ 2 = Answer: Question 29. $$\frac{3}{5}$$ ÷ 2 = Answer: Question 30. $$\frac{1}{6}$$ ÷ 2 = Answer: Question 31. $$\frac{5}{6}$$ ÷ 2 = Answer: Question 32. $$\frac{5}{6}$$ ÷ 3 = Answer: Question 33. $$\frac{1}{6}$$ ÷ 3 = Answer: Question 34. 3 ÷ $$\frac{1}{6}$$ = Answer: Question 35. 6 ÷ $$\frac{1}{6}$$ = Answer: Question 36. 7 ÷ $$\frac{1}{7}$$ = Answer: Question 37. 8 ÷ $$\frac{1}{8}$$ = Answer: Question 38. 9 ÷ $$\frac{1}{9}$$ = Answer: Question 39. $$\frac{1}{8}$$ ÷ 7 = Answer: Question 40. 9 ÷ $$\frac{1}{8}$$ = Answer: Question 41. $$\frac{1}{8}$$ ÷ 7 = Answer: Question 42. 7 ÷ $$\frac{1}{6}$$ = Answer: Question 43. 9 ÷ $$\frac{1}{7}$$ = Answer: Question 44. $$\frac{1}{8}$$ ÷ 9 = Answer: B Divide Whole Numbers by Fractions and Fractions by Whole Numbers Question 1. $$\frac{1}{2}$$ ÷ 2 = Answer: Question 2. $$\frac{1}{5}$$ ÷ 3 = Answer: Question 3. $$\frac{1}{5}$$ ÷ 4 = Answer: Question 4. $$\frac{1}{5}$$ ÷ 7 = Answer: Question 5. 7 ÷ $$\frac{1}{5}$$ = Answer: Question 6. 6 ÷ $$\frac{1}{5}$$ = Answer: Question 7. 5 ÷ $$\frac{1}{5}$$ = Answer: Question 8. 3 ÷ $$\frac{1}{5}$$ = Answer: Question 9. 2 ÷ $$\frac{1}{2}$$ = Answer: Question 10. 3 ÷ $$\frac{1}{2}$$ = Answer: Question 11. 4 ÷ $$\frac{1}{2}$$ = Answer: Question 12. 7 ÷ $$\frac{1}{2}$$ = Answer: Question 13. $$\frac{1}{2}$$ ÷ 7 = Answer: Question 14. $$\frac{1}{4}$$ ÷ 2 = Answer: Question 15. 2 ÷ $$\frac{1}{4}$$ = Answer: Question 16. $$\frac{1}{3}$$ ÷ 2 = Answer: Question 17. 2 ÷ $$\frac{1}{3}$$ = Answer: Question 18. $$\frac{1}{2}$$ ÷ 2 = Answer: Question 19. 2 ÷ $$\frac{1}{2}$$ = Answer: Question 20. 4 ÷ $$\frac{1}{3}$$ = Answer: Question 21. $$\frac{1}{3}$$ ÷ 4 = Answer: Question 22. $$\frac{1}{3}$$ ÷ 3 = Answer: Question 23. 3 ÷ $$\frac{1}{3}$$ = Answer: Question 24. $$\frac{1}{4}$$ ÷ 4 = Answer: Question 25. $$\frac{3}{4}$$ ÷ 4 = Answer: Question 26. $$\frac{1}{3}$$ ÷ 3 = Answer: Question 27. $$\frac{2}{3}$$ ÷ 3 = Answer: Question 28. $$\frac{1}{6}$$ ÷ 2 = Answer: Question 29. $$\frac{5}{6}$$ ÷ 2 = Answer: Question 30. $$\frac{1}{5}$$ ÷ 5 = Answer: Question 31. $$\frac{3}{5}$$ ÷ 5 = Answer: Question 32. $$\frac{3}{5}$$ ÷ 4 = Answer: Question 33. $$\frac{1}{5}$$ ÷ 6 = Answer: Question 34. 6 ÷ $$\frac{1}{5}$$ = Answer: Question 35. 6 ÷ $$\frac{1}{4}$$ = Answer: Question 36. 7 ÷ $$\frac{1}{6}$$ = Answer: Question 37. 8 ÷ $$\frac{1}{7}$$ = Answer: Question 38. 9 ÷ $$\frac{1}{8}$$ = Answer: Question 39. $$\frac{1}{8}$$ ÷ 8 = Answer: Question 40. 9 ÷ $$\frac{1}{9}$$ = Answer: Question 41. $$\frac{1}{9}$$ ÷ 8 = Answer: Question 42. 7 ÷ $$\frac{1}{7}$$ = Answer: Question 43. 9 ÷ $$\frac{1}{6}$$ = Answer: Question 44. $$\frac{1}{8}$$ ÷ 6 = Answer: ### Eureka Math Grade 5 Module 4 Lesson 30 Problem Set Answer Key Question 1. Rewrite the division expression as a fraction and divide. The first two have been started for you. a. 2.7 ÷ 0.3 = b. 2.7 ÷ 0.03 = c. 3.5 ÷ 0.5 d. 3.5 ÷ 0.05 e. 4.2 ÷ 0.7 f. 0.42 ÷ 0.07 g. 10.8 ÷ 0.9 h. 1.08 ÷ 0.09 i. 3.6 ÷ 1.2 j. 0.36 ÷ 0.12 k. 17.5 ÷ 2.5 l. 1.75 ÷ 0.25 Answer: Question 2. 15 ÷ 3 = 5. Explain why it is true that 1.5 ÷ 0.3 and 0.15 ÷ 0.03 have the same quotient. Answer: Question 3. Mr. Volok buys 2.4 kg of sugar for his bakery. a. If he pours 0.2 kg of sugar into separate bags, how many bags of sugar can he make? b. If he pours 0.4 kg of sugar into separate bags, how many bags of sugar can he make? Answer: Question 4. Two wires, one 17.4 meters long and one 7.5 meters long, were cut into pieces 0.3 meters long. How many such pieces can be made from both wires? Answer: Question 5. Mr. Smith has 15.6 pounds of oranges to pack for shipment. He can ship 2.4 pounds of oranges in a large box and 1.2 pounds in a small box. If he ships 5 large boxes, what is the minimum number of small boxes required to ship the rest of the oranges? Answer: ### Eureka Math Grade 5 Module 4 Lesson 30 Exit Ticket Answer Key Rewrite the division expression as a fraction and divide. a. 3.2 ÷ 0.8 b. 3.2 ÷ 0.08 c. 7.2 ÷ 0.9 d. 0.72 ÷ 0.09 Answer: ### Eureka Math Grade 5 Module 4 Lesson 30 Homework Answer Key Question 1. Rewrite the division expression as a fraction and divide. The first two have been started for you. a. 2.4 ÷ 0.8 = b. 2.4 ÷ 0.08 = c. 4.8 ÷ 0.6 d. 0.48 ÷ 0.06 e. 8.4 ÷ 0.7 f. 0.84 ÷ 0.07 g. 4.5 ÷ 1.5 h. 0.45 ÷ 0.15 i. 14.4 ÷ 1.2 j. 1.44 ÷ 0.12 Answer: Question 2. Leann says 18 ÷ 6 = 3, so 1.8 ÷ 0.6 = 0.3 and 0.18 ÷ 0.06 = 0.03. Is Leann correct? Explain how to solve these division problems. Answer: Question 3. Denise is making bean bags. She has 6.4 pounds of beans. a. If she makes each bean bag 0.8 pounds, how many bean bags will she be able to make? b. If she decides instead to make mini bean bags that are half as heavy, how many can she make? Answer: Question 4. A restaurant’s small salt shakers contain 0.6 ounces of salt. Its large shakers hold twice as much. The shakers are filled from a container that has 18.6 ounces of salt. If 8 large shakers are filled, how many small shakers can be filled with the remaining salt? Answer: ## Eureka Math Grade 5 Module 4 Lesson 1 Answer Key ## Engage NY Eureka Math 5th Grade Module 4 Lesson 1 Answer Key ### Eureka Math Grade 5 Module 4 Lesson 1 Problem Set Answer Key Question 1. Estimate the length of your pencil to the nearest inch. ______________ Answer: 6 inch Explanation: The length of the pencil to the nearest inch is 6. Question 2. Using a ruler, measure your pencil strip to the nearest $$\frac{1}{2}$$ inch, and mark the measurement with an X above the ruler below. Construct a line plot of your classmates’ pencil measurements. Answer: Explanation: By using a ruler, I have measured the pencil strip to the nearest inch and marked the measurement with an X above the ruler. Question 3. Using a ruler, measure your pencil strip to the nearest $$\frac{1}{4}$$ inch, and mark the measurement with an X above the ruler below. Construct a line plot of your classmates’ pencil measurements. Answer: Explanation: By using a ruler, I have measured the pencil strip to the nearest inch and marked the measurement with an X above the ruler. Question 4. Using a ruler, measure your pencil strip to the nearest $$\frac{1}{8}$$ inch, and mark the measurement with an X above the ruler below. Construct a line plot of your classmates’ pencil measurements. Answer: Explanation: By using a ruler, I have measured the pencil strip to the nearest inch and marked the measurement with an X above the ruler. Question 5. Use all three of your line plots to complete the following: a. Compare the three plots, and write one sentence that describes how the plots are alike and one sentence that describes how they are different. Answer: All the 3 line plots are similar because they all show that the majority of the pencil lengths were between 4 and 5 1/2 inches. The 3rd line plot looks different from the others because there’s usually only 1 pencil per measurement, except for 4 5/8 and 4 3/4 in. b. What is the difference between the measurements of the longest and shortest pencils on each of the three-line plots? Answer: Line Plot 1: 7 in – 2 1/2 in = 4 1/2 in. Line Plot 2: 7 in – 2 1/4 in = 4 3/4 in. Line Plot 3: 7 in – 2 3/8 in = 4 5/8 in. Explanation: The difference between the measurements of the longest and shortest pencils on each of the three-line plots are Line Plot 1: 7 in – 2 1/2 in = 4 1/2 in, Line Plot 2: 7 in – 2 1/4 in = 4 3/4 in, Line Plot 3: 7 in – 2 3/8 in = 4 5/8 in. c. Write a sentence describing how you could create a more precise ruler to measure your pencil strip. Answer: The most precise ruler we’ve used so far had us measure to the nearest 1/8 inch. We could divide each 1/8 into 2 equal parts as a measure to the nearest 1/16 inch. Explanation: I have written a sentence describing how we could create a more precise ruler for measuring the pencil strip. ### Eureka Math Grade 5 Module 4 Lesson 1 Exit Ticket Answer Key Question 1. Draw a line plot for the following data measured in inches: 1$$\frac{1}{2}$$, 2$$\frac{3}{4}$$, 3, 2$$\frac{3}{4}$$, 3$$\frac{3}{4}$$, 3, 3$$\frac{1}{2}$$, 2$$\frac{1}{2}$$, 3$$\frac{1}{2}$$ Answer: Explanation: I have drawn a line plot with the following data given which are measured in inches. Question 2. Explain how you decided to divide your wholes into fractional parts and how you decided where your number scale should begin and end. ### Eureka Math Grade 5 Module 4 Lesson 1 Homework Answer Key A meteorologist set up rain gauges at various locations around a city and recorded the rainfall amounts in the table below. Use the data in the table to create a line plot using $$\frac{1}{8}$$ inches.  Location Rainfall Amount (inches) 1 $$\frac{1}{8}$$ 2 $$\frac{3}{8}$$ 3 $$\frac{3}{4}$$ 4 $$\frac{3}{4}$$ 5 $$\frac{1}{4}$$ 6 1$$\frac{1}{4}$$ 7 $$\frac{1}{8}$$ 8 $$\frac{1}{4}$$ 9 1 10 $$\frac{1}{8}$$ a. Which location received the most rainfall? Answer: Location 6 Explanation: Location 6 has received the most rainfall. b. Which location received the least rainfall? Answer: Location 1, 7, 10 Explanation: Location 1,7,10 has received the least rainfall. c. Which rainfall measurement was the most frequent? Answer: 1/8 inch Explanation: The most frequent rainfall measurement was 1/8 inch. d. What is the total rainfall in inches? Answer: 5 Inches. Explanation: 5 inches is the total rainfall and I have given the explanation below. 1/8 + 3/8 + 3/4 + 3/4 + 1/4 + 1 1/4 + 1/8 + 1/4 + 1 + 1/8 4/8 + 6/4 + 1 2/4 + 1/4 + 1 2/8 1 6/8 + 1 9/4 2 3/4 + 9/4 2 12/4 5 inches. ## Eureka Math Grade 5 Module 4 Lesson 29 Answer Key ## Engage NY Eureka Math 5th Grade Module 4 Lesson 29 Answer Key ### Eureka Math Grade 5 Module 4 Lesson 29 Problem Set Answer Key Question 1. Divide. Rewrite each expression as a division sentence with a fraction divisor, and fill in the blanks. The first one is done for you. Example: 2 ÷ 0.1 = 2 ÷ $$\frac{1}{10}$$ = 20 There are 10 tenths in 1 whole. There are 20 tenths in 2 wholes. a. 5 ÷ 0.1 There are ____ tenths in 1 whole. There are ____ tenths in 5 wholes. Answer: There are 10 tenths in 1 whole. There are 50 tenths in 5 wholes. Explanation: Given that 5 ÷ 0.1 which is 50. In that, there are 10 tenths in 1 whole and there are 50 tenths in 5 wholes. b. 8 ÷ 0.1 There are ____ tenths in 1 whole. There are ____ tenths in 8 wholes. Answer: There are 10 tenths in 1 whole. There are 8 tenths in 5 wholes. Explanation: Given that 8 ÷ 0.1 which is 80. In that, there are 10 tenths in 1 whole and there are 80 tenths in 8 wholes. c. 5.2 ÷ 0.1 There are tenths in 5 wholes. There are ____ tenths in 2 tenths. There are ____ tenths in 5.2. Answer: There are 2 tenths in 2 tenths. There are 52 tenths in 5.2. Explanation: Given that 5 ÷ 0.1 which is 50. In that, there are 10 tenths in 1 whole and there are 50 tenths in 5 wholes. d. 8.7 ÷ 0.1 There are ____ tenths in 8 wholes. There are ____ tenths in 7 tenths. There are ____ tenths in 8.7. Answer: There are 80 tenths in 8 wholes. There are 7 tenths in 7 tenths. There are 87 tenths in 8.7. Explanation: Given that 8.7 ÷ 0.1 which is 87. In that, there are 80 tenths in 8 whole and there are 7 tenths in 7 tenths and there are 87 tenths in 8.7. e. 5 ÷ 0.01 There are 100 hundredths in 1 whole. There are 500 hundredths in 5 wholes. Answer: There are ____ hundredths in 1 whole. There are ____ hundredths in 5 wholes. Explanation: Given that 5 ÷ 0.01 which is 500. In that, there are 100 hundredths in 1 whole and there are 500 hundredths in 5 wholes. f. 8 ÷ 0.01 There are ____ hundredths in 1 whole. There are ____ hundredths in 8 wholes. Answer: There are 100 hundredths in 1 whole. There are 800 hundredths in 8 wholes. Explanation: Given that 8 ÷ 0.01 which is 800. In that, there are 100 hundredths in 1 whole and there are 800 hundredths in 8 wholes. g. 5.2 ÷ 0.01 There are ____ hundredths in 5 wholes. There are ____ hundredths in 2 tenths. There are ____ hundredths in 5.2. Answer: There are 500 hundredths in 1 whole. There are 20 hundredths in 5 tenths. There are 520 hundredths in 5.2. Explanation: Given that 5.2 ÷ 0.01 which is 520. In that, there are 500 hundredths in 1 whole and there are 20 hundredths in 5 tenths and there are 520 hundredths in 5.2. h. 8.7 ÷ 0.01 There are ____ hundredths in 8 wholes. There are ____ hundredths in 7 tenths. There are ____ hundredths in 8.7. Answer: There are 800 hundredths in 8 whole. There are 70 hundredths in 7 tenths. There are 870 hundredths in 8.7. Explanation: Given that 8.7 ÷ 0.01 which is 870. In that, there are 800 hundredths in 8 whole and there are 70 hundredths in 7 tenths and there are 870 hundredths in 8.7. Question 2. Divide. a. 6 ÷ 0.1 Answer: 6 ÷ 0.1 = 60. Explanation: The division of 6 ÷ 0.1 is 60. b. 18 ÷ 0.1 Answer: 18 ÷ 0.1 = 180. Explanation: The division of 18 ÷ 0.1 is 180. c. 6 ÷ 0.01 Answer: 6 ÷ 0.01 = 600. Explanation: The division of 6 ÷ 0.01 is 600. d. 1.7 ÷ 0.1 Answer: 1.7 ÷ 0.1 = 17. Explanation: The division of 1.7 ÷ 0.1 is 17. e. 31 ÷ 0.01 Answer: 31 ÷ 0.01 = 3,100. Explanation: The division of 31 ÷ 0.01 is 3,100. f. 11 ÷ 0.01 Answer: 11 ÷ 0.01 = 1,100. Explanation: The division of 11 ÷ 0.01 is 1,100. g. 125 ÷ 0.1 Answer: 125 ÷ 0.1 = 1,250. Explanation: The division of 125 ÷ 0.1 is 1,250. h. 3.74 ÷ 0.01 Answer: 3.74 ÷ 0.01 = 374. Explanation: The division of 3.74 ÷ 0.01 is 374. i. 12.5 ÷ 0.01 Answer: 12.5 ÷ 0.01 = 1,250. Explanation: The division of 12.5 ÷ 0.01 is 1,250. Question 3. Yung bought$4.60 worth of bubble gum. Each piece of gum cost $0.10. How many pieces of bubble gum did Yung buy? Answer: Yung bought 46 pieces of gum. Explanation: Here, Yung bought$4.60 worth of bubble gum, and each piece of gum cost $0.10. So the number of pieces of bubble gum did Yung bought is$4.60 ÷ $0.10 =$46. So Yung bought 46 pieces of gum.

Question 4.
Cheryl solved a problem: 84 ÷ 0.01 = 8,400.
Jane said, “Your answer is wrong because when you divide, the quotient is always smaller than the whole amount you start with, for example, 6 ÷ 2 = 3 and 100 ÷ 4 = 25.” Who is correct? Explain your thinking.

Some examples are,
84 ÷ 1 = 84, 84 ÷ 10 = 8.4, 84 ÷ 0.1 = 840.

Explanation:
Cheryl is correct and Jane is correct only some of the time and Cheryl can help Jane understand by showing some examples like,
84 ÷ 1 = 84, 84 ÷ 10 = 8.4, 84 ÷ 0.1 = 840.

Question 5.
The U.S. Mint sells 2 ounces of American Eagle gold coins to a collector. Each coin weighs one-tenth of an ounce. How many gold coins were sold to the collector?
The number of gold coins was sold to the collector is 20 gold coins.

Explanation:
Here, U.S. Mint sells 2 ounces of American Eagle gold coins to a collector and each coin weighs one-tenth of an ounce, so the number of gold coins were sold to the collector is 2 ÷ 1/10 which is 2 ÷ 0.1 = 20 gold coins.

### Eureka Math Grade 5 Module 4 Lesson 29 Exit Ticket Answer Key

Question 1.
8.3 is equal to
_______ tenths
_______ hundredths
83 tenths
830 hundredths.

Explanation:
Given that the number is 8.3 which is equal to 83 tenths and 830 hundred.

Question 2.
28 is equal to
_______ hundredths
_______ tenths
2800 tenths
830 hundredths.

Explanation:
Given that the number is 8.3 which is equal to 83 tenths and 830 hundred.

Question 3.
15.09 ÷ 0.01 = _______
15.09 ÷ 0.01 = 1,509.

Explanation:
Given that the equation is 15.09 ÷ 0.01 which is equal to 1,509.

Question 4.
267.4 ÷ $$\frac{1}{10}$$ = _______
267.4 ÷ $$\frac{1}{10}$$ = 2,674

Explanation:
Given that the equation is 267.4 ÷ $$\frac{1}{10}$$ which is equal to 2,674.

Question 5.
632.98 ÷ $$\frac{1}{100}$$ = _______
632.98 ÷ $$\frac{1}{100}$$ = 63,298

Explanation:
Given that the equation is 632.98 ÷ $$\frac{1}{100}$$ which is equal to 63,298.

### Eureka Math Grade 5 Module 4 Lesson 29 Homework Answer Key

Question 1.
Divide. Rewrite each expression as a division sentence with a fraction divisor, and fill in the blanks. The first one is done for you.
a. 9 ÷ 0.1
There are ______ tenths in 1 whole.
There are ______ tenths in 9 wholes.

There are 10 tenths in 1 whole.
There are 90 tenths in 9 wholes.

Explanation:
Given that 9 ÷ 0.1 which is 90. In that, there are 10 tenths in 1 whole and there are 90 tenths in 9 wholes.

b. 6 ÷ 0.1
There are ______ tenths in 1 whole.
There are ______ tenths in 6 wholes.

There are 10 tenths in 1 whole.
There are 60 tenths in 6 wholes.

Explanation:
Given that 6 ÷ 0.1 which is 60. In that, there are 10 tenths in 1 whole and there are 60 tenths in 6 wholes.

c. 3.6 ÷ 0.1
There are ______ tenths in 3 wholes.
There are ______ tenths in 6 tenths.
There are ______ tenths in 3.6.

There are 30 tenths in 3 wholes.
There are 6 tenths in 6 tenths.
There are 36 tenths in 3.6.

Explanation:
Given that 3.6 ÷ 0.1 which is 36. In that, there are 30 tenths in 3 wholes and there are 6 tenths in 6 tenths and there are 36 tenths in 3.6.

d. 12.8 ÷ 0.1
There are ______ tenths in 12 wholes.
There are ______ tenths in 8 tenths.
There are ______ tenths in 12.8.

There are 120 tenths in 12 wholes.
There are 8 tenths in 8 tenths.
There are 128 tenths in 12.8.

Explanation:
Given that 12.8 ÷ 0.1 which is 128. In that, there are 120 tenths in 12 wholes and there are 8 tenths in 8 tenths and there are 128 tenths in 12.8.

e. 3 ÷ 0.1
There are ______ tenths in 1 whole.
There are ______ tenths in 3 wholes.

There are 100 tenths in 1 whole.
There are 300 tenths in 3 wholes.

Explanation:
Given that 3 ÷ 0.1 which is 30. In that, there are 100 tenths in 1 whole and there are 300 tenths in 3 wholes.

f. 7 ÷ 0.1
There are ______ tenths in 1 whole.
There are ______ tenths in 7 wholes.

There are 100 tenths in 1 whole.
There are 700 tenths in 7 wholes.

Explanation:
Given that 7 ÷ 0.1 which is 70. In that, there are 100 tenths in 1 whole and there are 700 tenths in 7 wholes.

g. 4.7 ÷ 0.01
There are ______ tenths in 4 wholes.
There are ______ tenths in 7 tenths.
There are ______ tenths in 4.7.

There are 400 tenths in 4 wholes.
There are 70 tenths in 7 tenths.
There are 470 tenths in 4.7.

Explanation:
Given that 4.7 ÷ 0.01 which is 470. In that, there are 400 tenths in 4 wholes and there are 70 tenths in 7 tenths and there are 470 tenths in 4.7.

h. 11.3 ÷ 0.01
There are ______ tenths in 11 wholes.
There are ______ tenths in 3 tenths.
There are ______ tenths in 11.3.

There are 1100 tenths in 11 wholes.
There are 30 tenths in 3 tenths.
There are 1130 tenths in 11.3.

Explanation:
Given that 11.3 ÷ 0.01 which is 1,130. In that, there are 1100 tenths in 11 wholes and there are 30 tenths in 3 tenths and there are 1130 tenths in 11.3.

Question 2.
Divide.
a. 2 ÷ 0.1

2 ÷ 0.1 = 20.

Explanation:
The division of 2 ÷ 0.1 is 20.

b. 23 ÷ 0.1

23 ÷ 0.1 = 230.

Explanation:
The division of 23 ÷ 0.1 is 230.

c. 5 ÷ 0.01

5 ÷ 0.01 = 500.

Explanation:
The division of 5 ÷ 0.01 is 500.

d. 7.2 ÷ 0.1

7.2 ÷ 0.1 = 72.

Explanation:
The division of 7.2 ÷ 0.1 is 72.

e. 51 ÷ 0.01

51 ÷ 0.01 = 5,100.

Explanation:
The division of 51 ÷ 0.01 is 5,100.

f. 31 ÷ 0.1

31 ÷ 0.1 = 310.

Explanation:
The division of 31 ÷ 0.1 is 310.

g. 231 ÷ 0.1

231 ÷ 0.1 = 2,310.

Explanation:
The division of 231 ÷ 0.1 is 2,310.

h. 4.37 ÷ 0.01

4.37 ÷ 0.01 = 437.

Explanation:
The division of 4.37 ÷ 0.01 is 437.

i. 24.5 ÷ 0.01

24.5 ÷ 0.01 = 2,450.

Explanation:
The division of 24.5 ÷ 0.01 is 2,450.

Question 3.
Giovanna is charged $0.01 for each text message she sends. Last month, her cell phone bill included a$12.60 charge for text messages. How many text messages did Giovanna send?
The number of text messages did Giovanna send is 1,260.

Explanation:
Here, Giovanna is charged $0.01 for each text message she sends, and in last month, her cell phone bill included a$12.60 charge for text messages. So the number of text messages did Giovanna send is $12.60 ÷$0.01 which is 1,260.

Question 4.
Geraldine solved a problem: 68.5 ÷ 0.01 = 6,850.
Ralph said, “This is wrong because a quotient can’t be greater than the whole you start with. For example, 8 ÷ 2 = 4 and 250 ÷ 5 = 50.” Who is correct? Explain your thinking.
The price for an ounce of gold on September 23, 2013, was $1,326.40. A group of 10 friends decide to equally share the cost of 1 ounce of gold. How much money will each friend pay? Answer: Each friend pays$1326.40 ÷ 10 which is $132.64. Explanation: Here, the price for an ounce of gold on September 23, 2013, was$1,326.40 and a group of 10 friends decide to equally share the cost of 1 ounce of gold. So each friend pays $1326.40 ÷ 10 which is$132.64.