## Engage NY Eureka Math 5th Grade Module 4 Lesson 14 Answer Key

### Eureka Math Grade 5 Module 4 Lesson 14 Sprint Answer Key

A

Multiply a Fraction and a Whole Number

Question 1.

\(\frac{1}{5}\) × 2 =

Answer:

\(\frac{2}{5}\)

Explanation:

The multiplication of \(\frac{1}{5}\) × 2 is \(\frac{2}{5}\).

Question 2.

\(\frac{1}{5}\) × 3 =

Answer:

\(\frac{3}{5}\)

Explanation:

The multiplication of \(\frac{1}{5}\) × 3 is \(\frac{3}{5}\).

Question 3.

\(\frac{1}{5}\) × 4 =

Answer:

\(\frac{4}{5}\)

Explanation:

The multiplication of \(\frac{1}{5}\) × 4 is \(\frac{4}{5}\).

Question 4.

4 × \(\frac{1}{5}\) =

Answer:

\(\frac{4}{5}\)

Explanation:

The multiplication of \(\frac{1}{5}\) × 4 is \(\frac{4}{5}\).

Question 5.

\(\frac{1}{8}\) × 3 =

Answer:

\(\frac{3}{8}\)

Explanation:

The multiplication of \(\frac{1}{8}\) × 3 is \(\frac{3}{8}\).

Question 6.

\(\frac{1}{8}\) × 5 =

Answer:

\(\frac{5}{8}\)

Explanation:

The multiplication of \(\frac{1}{8}\) × 5 is \(\frac{5}{8}\).

Question 7.

\(\frac{1}{8}\) × 7 =

Answer:

\(\frac{7}{8}\)

Explanation:

The multiplication of \(\frac{1}{8}\) × 7 is \(\frac{7}{8}\).

Question 8.

7 × \(\frac{1}{8}\) =

Answer:

\(\frac{7}{8}\)

Explanation:

The multiplication of \(\frac{1}{8}\) × 7 is \(\frac{7}{8}\).

Question 9.

3 × \(\frac{1}{10}\) =

Answer:

\(\frac{3}{10}\)

Explanation:

The multiplication of \(\frac{1}{10}\) × 3 is \(\frac{3}{10}\).

Question 10.

7 × \(\frac{1}{10}\) =

Answer:

\(\frac{7}{10}\)

Explanation:

The multiplication of \(\frac{1}{10}\) × 7 is \(\frac{7}{10}\).

Question 11.

\(\frac{1}{10}\) × 7 =

Answer:

\(\frac{7}{10}\)

Explanation:

The multiplication of \(\frac{1}{10}\) × 7 is \(\frac{7}{10}\).

Question 12.

4 ÷ 2 =

Answer:

4 ÷ 2 = 2

Explanation:

The division of 4 ÷ 2 is 2.

Question 13.

4 × \(\frac{1}{2}\) =

Answer:

4 × \(\frac{1}{2}\) = 2

Explanation:

The multiplication of 4 × \(\frac{1}{2}\) is 2.

Question 14.

6 ÷ 3 =

Answer:

6 ÷ 3 = 2

Explanation:

The division of 6 ÷ 3 is 2.

Question 15.

\(\frac{1}{3}\) × 6 =

Answer:

\(\frac{1}{3}\) × 6 = 2.

Explanation:

The multiplication of \(\frac{1}{3}\) × 6 is 2.

Question 16.

10 ÷ 5 =

Answer:

10 ÷ 5 = 2.

Explanation:

The division of 10 ÷ 5 is 2.

Question 17.

10 × \(\frac{1}{5}\) =

Answer:

10 × \(\frac{1}{5}\) = 2.

Explanation:

The multiplication of 10 × \(\frac{1}{5}\) is 2.

Question 18.

\(\frac{1}{3}\) × 9 =

Answer:

\(\frac{1}{3}\) × 9 = 3.

Explanation:

The multiplication of \(\frac{1}{3}\) × 9 is 3.

Question 19.

\(\frac{2}{3}\) × 9 =

Answer:

\(\frac{2}{3}\) × 9 = 6.

Explanation:

The multiplication of \(\frac{2}{3}\) × 9 is 6.

Question 20.

\(\frac{1}{4}\) × 8 =

Answer:

\(\frac{1}{4}\) × 8 = 2.

Explanation:

The multiplication of \(\frac{1}{4}\) × 8 is 2.

Question 21.

\(\frac{3}{4}\) × 8 =

Answer:

\(\frac{3}{4}\) × 8 = 6.

Explanation:

The multiplication of \(\frac{3}{4}\) × 8 is 6.

Question 22.

\(\frac{1}{6}\) × 12 =

Answer:

\(\frac{1}{6}\) × 12 = 2.

Explanation:

The multiplication of \(\frac{1}{6}\) × 12 is 2.

Question 23.

\(\frac{5}{6}\) × 12 =

Answer:

\(\frac{5}{6}\) × 12 = 10.

Explanation:

The multiplication of \(\frac{5}{6}\) × 12 is 10.

Question 24.

\(\frac{1}{3}\) × 15 =

Answer:

\(\frac{1}{3}\) × 15 = 5.

Explanation:

The multiplication of \(\frac{1}{3}\) × 15 is 5.

Question 25.

\(\frac{2}{3}\) × 15 =

Answer:

\(\frac{2}{3}\) × 15 = 10.

Explanation:

The multiplication of \(\frac{2}{3}\) × 15 is 10.

Question 26.

15 × \(\frac{2}{3}\) =

Answer:

15 × \(\frac{2}{3}\) = 10.

Explanation:

The multiplication of 15 × \(\frac{2}{3}\) is 10.

Question 27.

\(\frac{1}{5}\) × 15 =

Answer:

\(\frac{1}{5}\) × 15 = 3.

Explanation:

The multiplication of \(\frac{1}{5}\) × 15 is 3.

Question 28.

\(\frac{2}{5}\) × 15 =

Answer:

\(\frac{2}{5}\) × 15 = 6.

Explanation:

The multiplication of \(\frac{2}{5}\) × 15 is 6.

Question 29.

\(\frac{4}{5}\) × 15 =

Answer:

\(\frac{1}{5}\) × 15 = 3.

Explanation:

The multiplication of \(\frac{1}{5}\) × 15 is 3.

Question 30.

\(\frac{3}{5}\) × 15 =

Answer:

\(\frac{3}{5}\) × 15 = 9.

Explanation:

The multiplication of \(\frac{3}{5}\) × 15 is 9.

Question 31.

15 × \(\frac{3}{5}\) =

Answer:

15 × \(\frac{3}{5}\) = 9.

Explanation:

The multiplication of 15 × \(\frac{3}{5}\) is 9.

Question 32.

18 × \(\frac{1}{6}\) =

Answer:

18 × \(\frac{1}{6}\) = 3.

Explanation:

The multiplication of 18 × \(\frac{1}{6}\) is 3.

Question 33.

18 × \(\frac{5}{6}\) =

Answer:

18 × \(\frac{5}{6}\) = 15.

Explanation:

The multiplication of 18 × \(\frac{5}{6}\) is 15.

Question 34.

\(\frac{5}{6}\) × 18 =

Answer:

\(\frac{5}{6}\) × 18 = 15.

Explanation:

The multiplication of \(\frac{5}{6}\) × 18 is 15.

Question 35.

24 × \(\frac{1}{4}\) =

Answer:

24 × \(\frac{1}{4}\) = 6.

Explanation:

The multiplication of 24 × \(\frac{1}{4}\) is 6.

Question 36.

\(\frac{3}{4}\) × 24 =

Answer:

\(\frac{3}{4}\) × 24 = 18.

Explanation:

The multiplication of \(\frac{3}{4}\) × 24 is 18.

Question 37.

32 × \(\frac{1}{8}\) =

Answer:

32 × \(\frac{1}{8}\) = 4.

Explanation:

The multiplication of 32 × \(\frac{1}{8}\) is 4.

Question 38.

32 × \(\frac{3}{8}\) =

Answer:

32 × \(\frac{3}{8}\) = 12.

Explanation:

The multiplication of 32 × \(\frac{3}{8}\) is 12.

Question 39.

\(\frac{5}{8}\) × 32 =

Answer:

\(\frac{5}{8}\) × 32= 20.

Explanation:

The multiplication of \(\frac{5}{8}\) × 32 is 20.

Question 40.

32 × \(\frac{7}{8}\) =

Answer:

32 × \(\frac{7}{8}\)= 28.

Explanation:

The multiplication of 32 × \(\frac{7}{8}\) is 28.

Question 41.

\(\frac{5}{9}\) × 54 =

Answer:

\(\frac{5}{9}\) × 54= 30.

Explanation:

The multiplication of \(\frac{5}{9}\) × 54 is 30.

Question 42.

63 × \(\frac{7}{9}\) =

Answer:

63 × \(\frac{7}{9}\) = 49.

Explanation:

The multiplication of 63 × \(\frac{7}{9}\) is 49.

Question 43.

56 × \(\frac{3}{7}\) =

Answer:

56 × \(\frac{3}{7}\) = 24.

Explanation:

The multiplication of 56 × \(\frac{3}{7}\) is 24.

Question 44.

\(\frac{6}{7}\) × 49 =

Answer:

\(\frac{6}{7}\) × 49 = 42.

Explanation:

The multiplication of \(\frac{6}{7}\) × 49 is 42.

B

Multiply a Fraction and a Whole Number

Question 1.

\(\frac{1}{7}\) × 2 =

Answer:

\(\frac{1}{7}\) × 2 = \(\frac{2}{7}\).

Explanation:

The multiplication of \(\frac{1}{7}\) × 2 is \(\frac{2}{7}\).

Question 2.

\(\frac{1}{7}\) × 3 =

Answer:

\(\frac{1}{7}\) × 3 = \(\frac{3}{7}\).

Explanation:

The multiplication of \(\frac{1}{7}\) × 3 is \(\frac{3}{7}\).

Question 3.

\(\frac{1}{7}\) × 4 =

Answer:

\(\frac{1}{7}\) × 4 = \(\frac{4}{7}\).

Explanation:

The multiplication of \(\frac{1}{7}\) × 4 is \(\frac{4}{7}\).

Question 4.

4 × \(\frac{1}{7}\) =

Answer:

4 × \(\frac{1}{7}\) = \(\frac{4}{7}\).

Explanation:

The multiplication of 4 × \(\frac{1}{7}\) is \(\frac{4}{7}\).

Question 5.

\(\frac{1}{10}\) × 3 =

Answer:

\(\frac{1}{10}\) × 3 = \(\frac{3}{10}\).

Explanation:

The multiplication of \(\frac{1}{10}\) × 3 is \(\frac{3}{10}\).

Question 6.

\(\frac{1}{10}\) × 7 =

Answer:

\(\frac{1}{10}\) × 7 = \(\frac{7}{10}\).

Explanation:

The multiplication of \(\frac{1}{10}\) × 7 is \(\frac{7}{10}\).

Question 7.

\(\frac{1}{10}\) × 9 =

Answer:

\(\frac{1}{10}\) × 9 = \(\frac{9}{10}\).

Explanation:

The multiplication of \(\frac{1}{10}\) × 9 is \(\frac{9}{10}\).

Question 8.

9 × \(\frac{1}{10}\) =

Answer:

9 × \(\frac{1}{10}\) = \(\frac{9}{10}\).

Explanation:

The multiplication of 9 × \(\frac{1}{10}\) is \(\frac{9}{10}\).

Question 9.

3 × \(\frac{1}{8}\) =

Answer:

3 × \(\frac{1}{8}\) = \(\frac{3}{8}\).

Explanation:

The multiplication of 3 × \(\frac{1}{8}\) is \(\frac{3}{8}\).

Question 10.

5 × \(\frac{1}{8}\) =

Answer:

5 × \(\frac{1}{8}\) = \(\frac{5}{8}\).

Explanation:

The multiplication of 5 × \(\frac{1}{8}\) is \(\frac{5}{8}\).

Question 11.

\(\frac{1}{8}\) × 5 =

Answer:

\(\frac{1}{8}\) × 5 = \(\frac{5}{8}\).

Explanation:

The multiplication of \(\frac{1}{8}\) × 5 is \(\frac{5}{8}\).

Question 12.

10 ÷ 5 =

Answer:

10 ÷ 5 = 2

Explanation:

The division of 10 ÷ 5 is 2.

Question 13.

10 × \(\frac{1}{5}\) =

Answer:

10 × \(\frac{1}{5}\) = 2.

Explanation:

The multiplication of 10 × \(\frac{1}{5}\) is 2.

Question 14.

9 ÷ 3 =

Answer:

9 ÷ 3 = 3.

Explanation:

The division of 9 ÷ 3 is 3.

Question 15.

\(\frac{1}{3}\) × 9 =

Answer:

10 × \(\frac{1}{5}\) = 2.

Explanation:

The multiplication of 10 × \(\frac{1}{5}\) is 2.

Question 16.

10 ÷ 2 =

Answer:

10 ÷ 2 = 5.

Explanation:

The division of 10 ÷ 2 is 5.

Question 17.

10 × \(\frac{1}{2}\) =

Answer:

10 × \(\frac{1}{2}\) = 5.

Explanation:

The multiplication of 10 × \(\frac{1}{2}\) is 5.

Question 18.

\(\frac{1}{3}\) × 6 =

Answer:

\(\frac{1}{3}\) × 6 = 2.

Explanation:

The multiplication of \(\frac{1}{3}\) × 6 is 2.

Question 19.

\(\frac{2}{3}\) × 6 =

Answer:

\(\frac{2}{3}\) × 6 = 4.

Explanation:

The multiplication of \(\frac{2}{3}\) × 6 is 4.

Question 20.

\(\frac{1}{6}\) × 12 =

Answer:

\(\frac{1}{6}\) × 12 = 2.

Explanation:

The multiplication of \(\frac{1}{6}\) × 12 is 2.

Question 21.

\(\frac{5}{6}\) × 12 =

Answer:

\(\frac{5}{6}\) × 12 = 10.

Explanation:

The multiplication of \(\frac{5}{6}\) × 12 is 10.

Question 22.

\(\frac{1}{4}\) × 8 =

Answer:

\(\frac{1}{4}\) × 8 = 2.

Explanation:

The multiplication of \(\frac{1}{4}\) × 8 is 2.

Question 23.

\(\frac{3}{4}\) × 8 =

Answer:

\(\frac{3}{4}\) × 8 = 6.

Explanation:

The multiplication of \(\frac{3}{4}\) × 8 is 6.

Question 24.

\(\frac{1}{5}\) × 15 =

Answer:

\(\frac{1}{5}\) × 15 = 3.

Explanation:

The multiplication of \(\frac{1}{5}\) × 15 is 3.

Question 25.

\(\frac{2}{5}\) × 15 =

Answer:

\(\frac{2}{5}\) × 15 = 6.

Explanation:

The multiplication of \(\frac{2}{5}\) × 15 is 6.

Question 26.

\(\frac{4}{5}\) × 15 =

Answer:

\(\frac{4}{5}\) × 15 = 12.

Explanation:

The multiplication of \(\frac{4}{5}\) × 15 is 12.

Question 27.

\(\frac{3}{5}\) × 15 =

Answer:

\(\frac{3}{5}\) × 15 = 9.

Explanation:

The multiplication of \(\frac{3}{5}\) × 15 is 9.

Question 28.

15 × \(\frac{3}{5}\) =

Answer:

15 × \(\frac{3}{5}\) = 9.

Explanation:

The multiplication of 15 × \(\frac{3}{5}\) is 9.

Question 29.

\(\frac{1}{3}\) × 15 =

Answer:

15 × \(\frac{3}{5}\) = 9.

Explanation:

The multiplication of 15 × \(\frac{3}{5}\) is 9.

Question 30.

\(\frac{2}{3}\) × 15 =

Answer:

\(\frac{2}{3}\) × 15 = 10.

Explanation:

The multiplication of \(\frac{3}{5}\) × 15 is 10.

Question 31.

15 × \(\frac{2}{3}\) =

Answer:

15 × \(\frac{2}{3}\) = 10.

Explanation:

The multiplication of 15 × \(\frac{2}{3}\) is 10.

Question 32.

24 × \(\frac{1}{6}\) =

Answer:

24 × \(\frac{1}{6}\) = 4.

Explanation:

The multiplication of 24 × \(\frac{1}{6}\) is 4.

Question 33.

24 × \(\frac{5}{6}\) =

Answer:

24 × \(\frac{5}{6}\) = 20.

Explanation:

The multiplication of 24 × \(\frac{5}{6}\) is 20.

Question 34.

\(\frac{5}{6}\) × 24 =

Answer:

\(\frac{5}{6}\) × 24 = 20.

Explanation:

The multiplication of \(\frac{5}{6}\) × 24 is 20.

Question 35.

20 × \(\frac{1}{4}\) =

Answer:

20 × \(\frac{1}{4}\) = 5.

Explanation:

The multiplication of 20 × \(\frac{1}{4}\) is 5.

Question 36.

\(\frac{3}{4}\) × 20 =

Answer:

\(\frac{3}{4}\) × 20 = 15.

Explanation:

The multiplication of \(\frac{3}{4}\) × 20 is 15.

Question 37.

24 × \(\frac{1}{8}\) =

Answer:

24 × \(\frac{1}{8}\) = 3.

Explanation:

The multiplication of 24 × \(\frac{1}{8}\) is 3.

Question 38.

24 × \(\frac{3}{8}\) =

Answer:

24 × \(\frac{3}{8}\) = 9.

Explanation:

The multiplication of 24 × \(\frac{3}{8}\) is 9.

Question 39.

\(\frac{5}{8}\) × 24 =

Answer:

\(\frac{5}{8}\) × 24 = 15.

Explanation:

The multiplication of \(\frac{5}{8}\) is 24.

Question 40.

24 × \(\frac{7}{8}\) =

Answer:

24 × \(\frac{7}{8}\) = 21.

Explanation:

The multiplication of 24 × \(\frac{7}{8}\) is 21.

Question 41.

\(\frac{5}{9}\) × 63 =

Answer:

\(\frac{5}{9}\) × 63 = 35.

Explanation:

The multiplication of \(\frac{5}{9}\) × 63 is 35.

Question 42.

54 × \(\frac{7}{9}\) =

Answer:

54 × \(\frac{7}{9}\) = 42.

Explanation:

The multiplication of 54 × \(\frac{7}{9}\) is 42.

Question 43.

49 × \(\frac{3}{7}\) =

Answer:

49 × \(\frac{3}{7}\) = 21.

Explanation:

The multiplication of 49 × \(\frac{3}{7}\) is 21.

Question 44.

\(\frac{6}{7}\) × 56 =

Answer:

\(\frac{6}{7}\) × 56 = 48.

Explanation:

The multiplication of \(\frac{6}{7}\) × 56 is 48.

### Eureka Math Grade 5 Module 4 Lesson 14 Problem Set Answer Key

Question 1.

Solve. Draw a rectangular fraction model to explain your thinking. Then, write a number sentence. An example has been done for you.

Example:

a. \(\frac{1}{3}\) of \(\frac{3}{4}\) = \(\frac{1}{3}\) of ____ fourth(s) = ____ fourth(s)

Answer:

3, 1.

Explanation:

Given that \(\frac{1}{3}\) of \(\frac{3}{4}\) = \(\frac{1}{4}\), so \(\frac{1}{3}\) of 3 fourth(s) = 1 fourth(s)

b. \(\frac{1}{2}\) of \(\frac{4}{5}\) = \(\frac{1}{2}\) of ____ fifth(s) = ____ fifth(s)

c. \(\frac{1}{2}\) of \(\frac{2}{2}\) =

d. \(\frac{2}{3}\) of \(\frac{1}{2}\) =

e. \(\frac{1}{2}\) × \(\frac{3}{5}\) =

f. \(\frac{2}{3}\) × \(\frac{1}{4}\) =

Question 2.

\(\frac{5}{8}\) of the songs on Harrison’s music player are hip-hop. \(\frac{1}{3}\) of the remaining songs are rhythm and blues. What fraction of all the songs are rhythm and blues? Use a tape diagram to solve.

Question 3.

Three-fifths of the students in a room are girls. One-third of the girls have blond hair. One-half of the boys have brown hair.

a. What fraction of all the students are girls with blond hair?

b. What fraction of all the students are boys without brown hair?

Question 4.

Cody and Sam mowed the yard on Saturday. Dad told Cody to mow \(\frac{1}{4}\) of the yard. He told Sam to mow \(\frac{1}{3}\) of the remainder of the yard. Dad paid each of the boys an equal amount. Sam said, “Dad, that’s not fair! I had to mow one-third, and Cody only mowed one-fourth!” Explain to Sam the error in his thinking. Draw a picture to support your reasoning.

### Eureka Math Grade 5 Module 4 Lesson 14 Exit Ticket Answer Key

Question 1.

Solve. Draw a rectangular fraction model to explain your thinking. Then, write a number sentence.

\(\frac{1}{3}\) of \(\frac{3}{7}\) =

Question 2.

In a cookie jar, \(\frac{1}{4}\) of the cookies are chocolate chip, and \(\frac{1}{2}\) of the rest are peanut butter. What fraction of all the cookies is peanut butter?

### Eureka Math Grade 5 Module 4 Lesson 14 Homework Answer Key

Question 1.

Solve. Draw a rectangular fraction model to explain your thinking.

a. \(\frac{1}{2}\) of \(\frac{2}{3}\) = \(\frac{1}{2}\) of ____ third(s) = ____ third(s)

b. \(\frac{1}{2}\) of \(\frac{4}{3}\) = \(\frac{1}{2}\) of ____ third(s) = ____ third(s)

c. \(\frac{1}{3}\) of \(\frac{3}{5}\) =

d. \(\frac{1}{2}\) of \(\frac{6}{8}\) =

e. \(\frac{1}{3}\) × \(\frac{4}{5}\) =

f. \(\frac{4}{5}\) × \(\frac{1}{3}\) =

Question 2.

Sarah has a photography blog. \(\frac{3}{7}\) of her photos are of nature. \(\frac{1}{4}\) of the rest are of her friends. What fraction of all of Sarah’s photos is of her friends? Support your answer with a model.

Question 3.

At Laurita’s Bakery, \(\frac{3}{5}\) of the baked goods are pies, and the rest are cakes. \(\frac{1}{3}\) of the pies are coconut. 1/6 of the cakes are angel food.

a. What fraction of all of the baked goods at Laurita’s Bakery are coconut pies?

b. What fraction of all of the baked goods at Laurita’s Bakery are angel food cakes?

Question 4.

Grandpa Mick opened a pint of ice cream. He gave his youngest grandchild \(\frac{1}{5}\) of the ice cream and his middle grandchild \(\frac{1}{4}\) of the remaining ice cream. Then, he gave his oldest grandchild \(\frac{1}{3}\) of the ice cream that was left after serving the others.

a. Who got the most ice cream? How do you know? Draw a picture to support your reasoning.

b. What fraction of the pint of ice cream will be left if Grandpa Mick serves himself the same amount as the second grandchild?