## Engage NY Eureka Math 5th Grade Module 4 Lesson 15 Answer Key

### Eureka Math Grade 5 Module 4 Lesson 15 Problem Set Answer Key

Question 1.
Solve. Draw a rectangular fraction model to explain your thinking. Then, write a multiplication sentence. The first one is done for you.

a. $$\frac{2}{3}$$ of $$\frac{3}{5}$$
$$\frac{2}{3}$$ × $$\frac{3}{5}$$ = $$\frac{6}{15}$$ = $$\frac{2}{5}$$

b. $$\frac{3}{4}$$ of $$\frac{4}{5}$$ =

latex]\frac{3}{4}[/latex] of $$\frac{4}{5}$$ = $$\frac{3}{5}$$.

Explanation:
Given that $$\frac{3}{4}$$ of $$\frac{4}{5}$$ which is
$$\frac{3}{4}$$ × $$\frac{4}{5}$$ = $$\frac{3}{5}$$

c. $$\frac{2}{5}$$ of $$\frac{2}{3}$$=

latex]\frac{2}{5}[/latex] of $$\frac{2}{3}$$ = $$\frac{4}{15}$$.

Explanation:
Given that $$\frac{2}{5}$$ of $$\frac{2}{3}$$ which is
$$\frac{2}{5}$$ × $$\frac{2}{3}$$ = $$\frac{4}{15}$$

d. $$\frac{4}{5}$$ × $$\frac{2}{3}$$ =

latex]\frac{4}{5}[/latex] of $$\frac{2}{3}$$ = $$\frac{8}{15}$$.

Explanation:
Given that $$\frac{4}{5}$$ of $$\frac{2}{3}$$ which is
$$\frac{4}{5}$$ × $$\frac{2}{3}$$ = $$\frac{8}{15}$$

e. $$\frac{3}{4}$$ × $$\frac{2}{3}$$=

latex]\frac{3}{4}[/latex] of $$\frac{2}{3}$$ = $$\frac{1}{2}$$.

Explanation:
Given that $$\frac{3}{4}$$ of $$\frac{2}{3}$$ which is
$$\frac{3}{4}$$ × $$\frac{2}{3}$$ = $$\frac{1}{2}$$

Question 2.
Multiply. Draw a rectangular fraction model if it helps you, or use the method in the example.

a. $$\frac{3}{4}$$ × $$\frac{5}{6}$$

latex]\frac{3}{4}[/latex] of $$\frac{5}{6}$$ = $$\frac{5}{8}$$.

Explanation:
Given that $$\frac{3}{4}$$ of $$\frac{5}{6}$$ which is
$$\frac{3}{4}$$ × $$\frac{5}{6}$$ = $$\frac{5}{8}$$.

b. $$\frac{4}{5}$$ × $$\frac{5}{8}$$

latex]\frac{4}{5}[/latex] of $$\frac{5}{8}$$ = $$\frac{1}{2}$$.

Explanation:
Given that $$\frac{4}{5}$$ of $$\frac{5}{8}$$ which is
$$\frac{4}{5}$$ × $$\frac{5}{8}$$ = $$\frac{1}{2}$$

c. $$\frac{2}{3}$$ × $$\frac{6}{7}$$

latex]\frac{2}{3}[/latex] of $$\frac{6}{7}$$ = $$\frac{1}{7}$$.

Explanation:
Given that $$\frac{2}{3}$$ of $$\frac{6}{7}$$ which is
$$\frac{2}{3}$$ × $$\frac{6}{7}$$ = $$\frac{1}{7}$$

d. $$\frac{4}{9}$$ × $$\frac{3}{10}$$

latex]\frac{4}{9}[/latex] of $$\frac{3}{10}$$ = $$\frac{2}{15}$$.

Explanation:
Given that $$\frac{4}{9}$$ of $$\frac{3}{10}$$ which is
$$\frac{4}{9}$$ × $$\frac{3}{10}$$ = $$\frac{2}{15}$$.

Question 3.
Phillip’s family traveled $$\frac{3}{10}$$ of the distance to his grandmother’s house on Saturday. They traveled $$\frac{4}{7}$$ of the remaining distance on Sunday. What fraction of the total distance to his grandmother’s house was traveled on Sunday?

Philip’s family traveled on Sunday is $$\frac{2}{5}$$.

Explanation:
Given that Phillip’s family traveled $$\frac{3}{10}$$ of the distance to his grandmother’s house on Saturday, so the remaining is 1 – $$\frac{3}{10}$$ which is $$\frac{7}{10}$$. So Philip’s family traveled on Sunday is $$\frac{4}{7}$$ × $$\frac{7}{10}$$ which is $$\frac{2}{5}$$.

Question 4.
Santino bought a $$\frac{3}{4}$$-pound bag of chocolate chips. He used $$\frac{2}{3}$$ of the bag while baking. How many pounds of chocolate chips did he use while baking?

The number of pounds of chocolate chips did he use while baking is $$\frac{1}{2}$$ lb.

Explanation:
Given that Santino bought a $$\frac{3}{4}$$-pound bag of chocolate chips and he used $$\frac{2}{3}$$ of the bag while baking. So the number of pounds of chocolate chips did he use while baking is $$\frac{3}{4}$$ × $$\frac{2}{3}$$ which is $$\frac{1}{2}$$ lb.

Question 5.
Farmer Dave harvested his corn. He stored $$\frac{5}{9}$$ of his corn in one large silo and $$\frac{3}{4}$$ of the remaining corn in a small silo. The rest was taken to market to be sold.
a. What fraction of the corn was stored in the small silo?

The fraction of the corn was stored in the small silo $$\frac{1}{3}$$.

Explanation:
Given that Dave has stored $$\frac{5}{9}$$ of his corn in one large silo. Let the total corn be ‘X’, and the amount of corn stored in the silo is $$\frac{5}{9}$$X. The amount of corn remaining is X – $$\frac{5}{9}$$X which is $$\frac{9X – 5X}{9}$$ = $$\frac{4X}{9}$$. Thus the amount of corn stored in the small silo is $$\frac{3}{4}$$ × $$\frac{4}{9}$$X which is $$\frac{1}{3}$$X. Thus the fraction of the corn was stored in the small silo $$\frac{1}{3}$$.

b. If he harvested 18 tons of corn, how many tons did he take to market?

The amount of corn taken to market is 9 tonnes.

Explanation:
The amount of corn solid in the market is $$\frac{4X}{9}$$ – $$\frac{X}{3}$$ which is $$\frac{X}{9}$$. Thus the amount of corn taken to market is 18 × $$\frac{1}{9}$$ which is 9 tonnes.

### Eureka Math Grade 5 Module 4 Lesson 15 Exit Ticket Answer Key

Question 1.
Solve. Draw a rectangular fraction model to explain your thinking. Then, write a multiplication sentence.

a. $$\frac{2}{3}$$ of $$\frac{3}{5}$$ =

latex]\frac{2}{3}[/latex] of $$\frac{3}{5}$$ = $$\frac{2}{5}$$.

Explanation:
Given that $$\frac{2}{3}$$ of $$\frac{3}{5}$$ which is
$$\frac{2}{3}$$ × $$\frac{3}{5}$$ = $$\frac{2}{5}$$.

b. $$\frac{4}{9}$$ × $$\frac{3}{8}$$ =

latex]\frac{4}{9}[/latex] of $$\frac{3}{8}$$ = $$\frac{1}{6}$$.

Explanation:
Given that $$\frac{4}{9}$$ of $$\frac{3}{8}$$ which is
$$\frac{4}{9}$$ × $$\frac{3}{8}$$ = $$\frac{1}{6}$$.

Question 2.
A newspaper’s cover page is $$\frac{3}{8}$$ text, and photographs fill the rest. If $$\frac{2}{5}$$ of the text is an article about endangered species, what fraction of the cover page is the article about endangered species?

The fraction of the cover page is the article about endangered species $$\frac{3}{20}$$.

Explanation:
Given that a newspaper’s cover page is $$\frac{3}{8}$$ text, and photographs fill the rest, and if $$\frac{2}{5}$$ of the text is an article about endangered species. So the fraction of the cover page is the article about endangered species $$\frac{3}{8}$$ × $$\frac{2}{5}$$ which is $$\frac{3}{20}$$.

### Eureka Math Grade 5 Module 4 Lesson 15 Homework Answer Key

Question 1.
Solve. Draw a rectangular fraction model to explain your thinking. Then, write a multiplication sentence.
a. $$\frac{2}{3}$$ of $$\frac{3}{4}$$ =

latex]\frac{2}{3}[/latex] of $$\frac{3}{4}$$ = $$\frac{1}{2}$$.

Explanation:
Given that $$\frac{2}{3}$$ of $$\frac{3}{4}$$ which is
$$\frac{2}{3}$$ × $$\frac{3}{4}$$ = $$\frac{1}{2}$$.

b. $$\frac{2}{5}$$ of $$\frac{3}{4}$$ =

latex]\frac{2}{5}[/latex] of $$\frac{3}{4}$$ = $$\frac{3}{10}$$.

Explanation:
Given that $$\frac{2}{5}$$ of $$\frac{3}{4}$$ which is
$$\frac{2}{5}$$ × $$\frac{3}{4}$$ = $$\frac{3}{10}$$.

c. $$\frac{2}{5}$$ of $$\frac{4}{5}$$ =

latex]\frac{2}{5}[/latex] of $$\frac{4}{5}$$ = $$\frac{8}{25}$$.

Explanation:
Given that $$\frac{2}{5}$$ of $$\frac{4}{5}$$ which is
$$\frac{2}{5}$$ × $$\frac{4}{5}$$ = $$\frac{8}{25}$$.

d. $$\frac{4}{5}$$ of $$\frac{3}{4}$$ =

latex]\frac{4}{5}[/latex] of $$\frac{3}{4}$$ = $$\frac{3}{5}$$.

Explanation:
Given that $$\frac{4}{5}$$ of $$\frac{3}{4}$$ which is
$$\frac{4}{5}$$ × $$\frac{3}{4}$$ = $$\frac{3}{5}$$.

Question 2.
Multiply. Draw a rectangular fraction model if it helps you.
a. $$\frac{5}{6}$$ × $$\frac{3}{10}$$

latex]\frac{5}{6}[/latex] of $$\frac{3}{10}$$ = $$\frac{1}{4}$$.

Explanation:
Given that $$\frac{5}{6}$$ of $$\frac{3}{10}$$ which is
$$\frac{5}{6}$$ × $$\frac{3}{10}$$ = $$\frac{1}{4}$$.

b. $$\frac{3}{4}$$ × $$\frac{4}{5}$$

latex]\frac{3}{4}[/latex] of $$\frac{4}{5}$$ = $$\frac{3}{5}$$.

Explanation:
Given that $$\frac{3}{4}$$ of $$\frac{4}{5}$$ which is
$$\frac{3}{4}$$ × $$\frac{4}{5}$$ = $$\frac{3}{5}$$.

c. $$\frac{5}{6}$$ × $$\frac{5}{8}$$

latex]\frac{4}{9}[/latex] of $$\frac{3}{8}$$ = $$\frac{1}{6}$$.

Explanation:
Given that $$\frac{4}{9}$$ of $$\frac{3}{8}$$ which is
$$\frac{4}{9}$$ × $$\frac{3}{8}$$ = $$\frac{1}{6}$$.

d. $$\frac{3}{4}$$ × $$\frac{5}{12}$$

latex]\frac{4}{9}[/latex] of $$\frac{3}{8}$$ = $$\frac{1}{6}$$.

Explanation:
Given that $$\frac{4}{9}$$ of $$\frac{3}{8}$$ which is
$$\frac{4}{9}$$ × $$\frac{3}{8}$$ = $$\frac{1}{6}$$.

e. $$\frac{8}{9}$$ × $$\frac{2}{3}$$

latex]\frac{8}{9}[/latex] of $$\frac{2}{3}$$ = $$\frac{16}{27}$$.

Explanation:
Given that $$\frac{8}{9}$$ of $$\frac{2}{3}$$ which is
$$\frac{8}{9}$$ × $$\frac{2}{3}$$ = $$\frac{16}{27}$$.

f. $$\frac{3}{7}$$ × $$\frac{2}{9}$$

latex]\frac{3}{7}[/latex] of $$\frac{2}{9}$$ = $$\frac{2}{21}$$.

Explanation:
Given that $$\frac{3}{7}$$ of $$\frac{2}{9}$$ which is
$$\frac{3}{7}$$ × $$\frac{2}{9}$$ = $$\frac{2}{21}$$.

Question 3.
Every morning, Halle goes to school with a 1-liter bottle of water. She drinks $$\frac{1}{4}$$ of the bottle before school starts and $$\frac{2}{3}$$ of the rest before lunch.
a. What fraction of the bottle does Halle drink after school starts but before lunch?

The fraction of the bottle does Halle drinks after school starts but before lunch is $$\frac{1}{2}$$.

Explanation:
Given that Halle goes to school with a 1-liter bottle of water and she drinks $$\frac{1}{4}$$ of the bottle before school starts and $$\frac{2}{3}$$ of the rest before lunch and the amount left after drinking before school starts are 1 – $$\frac{1}{4}$$ which is $$\frac{3}{4}$$ and the fraction of the bottle does Halle drinks after school starts but before lunch is $$\frac{2}{3}$$ of Amount left
= $$\frac{2}{3}$$ × $$\frac{3}{4}$$
= $$\frac{1}{2}$$.

b. How many milliliters are left in the bottle at lunch?

The amount that left in the bottle at lunch is 250 milliliters.

Explanation:
The amount that left in the bottle at lunch is 1 – ($$\frac{3}{4}$$ + $$\frac{1}{2}$$)
= $$\frac{1}{4}$$, as we know that 1 litre is 1000 milliliters, so $$\frac{1}{4}$$ litre is $$\frac{1}{4}$$ × 1000 which is 250 milliliters.

Question 4.
Moussa delivered $$\frac{3}{8}$$ of the newspapers on his route in the first hour and $$\frac{4}{5}$$ of the rest in the second hour. What fraction of the newspapers did Moussa deliver in the second hour?

Question 5.
Rose bought some spinach. She used $$\frac{3}{5}$$ of the spinach on a pan of spinach pie for a party and $$\frac{3}{4}$$ of the remaining spinach for a pan for her family. She used the rest of the spinach to make a salad.
a. What fraction of the spinach did she use to make the salad?

b. If Rose used 3 pounds of spinach to make the pan of spinach pie for the party, how many pounds of spinach did Rose use to make the salad?