## Engage NY Eureka Math 5th Grade Module 4 Lesson 13 Answer Key

### Eureka Math Grade 5 Module 4 Lesson 13 Problem Set Answer Key

Solve. Draw a rectangular fraction model to show your thinking. Then, write a multiplication sentence. The first one has been done for you.

a. Half of $$\frac{1}{4}$$ pan of brownies = $$\frac{1}{4}$$ pan of brownies.
$$\frac{1}{2}$$ × $$\frac{1}{4}$$ = $$\frac{1}{8}$$

b. Half of $$\frac{1}{3}$$ pan of brownies = _____ pan of brownies.

$$\frac{1}{6}$$ pan of brownies.

Explanation:
Given that there is half of $$\frac{1}{3}$$ pan of brownies which is $$\frac{1}{2}$$ × $$\frac{1}{3}$$ = $$\frac{1}{6}$$ pan of brownies.

c. A fourth of $$\frac{1}{3}$$ pan of brownies = _____ pan of brownies.

$$\frac{1}{12}$$ pan of brownies.

Explanation:
Given that there is half of $$\frac{1}{3}$$ pan of brownies which is $$\frac{1}{4}$$ × $$\frac{1}{3}$$ = $$\frac{1}{12}$$ pan of brownies.

d. $$\frac{1}{4}$$ of $$\frac{1}{4}$$

$$\frac{1}{16}$$.

Explanation:
Given that $$\frac{1}{4}$$ of $$\frac{1}{4}$$ which is $$\frac{1}{4}$$ × $$\frac{1}{4}$$ = $$\frac{1}{16}$$.

e. $$\frac{1}{2}$$ of $$\frac{1}{6}$$

$$\frac{1}{12}$$.

Explanation:
Given that $$\frac{1}{2}$$ of $$\frac{1}{6}$$ which is $$\frac{1}{2}$$ × $$\frac{1}{6}$$ = $$\frac{1}{12}$$.

Question 2.
Draw rectangular fraction models of 3 × $$\frac{1}{4}$$ and $$\frac{1}{3}$$ × $$\frac{1}{4}$$. Compare multiplying a number by 3 and by 1 third.

$$\frac{3}{4}$$ > $$\frac{1}{12}$$.

Explanation:
Given the equations are 3 × $$\frac{1}{4}$$ which is $$\frac{3}{4}$$ and $$\frac{1}{3}$$ × $$\frac{1}{4}$$ which is $$\frac{1}{12}$$. And $$\frac{3}{4}$$ > $$\frac{1}{12}$$.

Question 3.
$$\frac{1}{2}$$ of Ila’s workspace is covered in paper. $$\frac{1}{3}$$ of the paper is covered in yellow sticky notes. What fraction of Ila’s workspace is covered in yellow sticky notes? Draw a picture to support your answer.

$$\frac{1}{6}$$

Explanation:
Given that $$\frac{1}{2}$$ of Ila’s workspace is covered in paper and $$\frac{1}{3}$$ of the paper is covered in yellow sticky notes, so the fraction of Ila’s workspace is covered in yellow sticky notes is $$\frac{1}{2}$$ × $$\frac{1}{3}$$ which is $$\frac{1}{6}$$.

Question 4.
A marching band is rehearsing in rectangular formation. $$\frac{1}{5}$$ of the marching band members play percussion instruments. $$\frac{1}{2}$$ of the percussionists play the snare drum. What fraction of all the band members play the snare drum?

The fraction of all the band members who play the snare drum is $$\frac{1}{10}$$.

Explanation:
Given that a $$\frac{1}{5}$$ of the marching band members play percussion instruments and $$\frac{1}{2}$$ of the percussionists play the snare drum, so the fraction of all the band members play the snare drum is $$\frac{1}{2}$$ of $$\frac{1}{5}$$ which is $$\frac{1}{2}$$ × $$\frac{1}{5}$$ = $$\frac{1}{10}$$.

Question 5.
Marie is designing a bedspread for her grandson’s new bedroom. $$\frac{2}{3}$$ of the bedspread is covered in race cars, and the rest is striped. $$\frac{1}{4}$$ of the stripes are red. What fraction of the bedspread is covered in red stripes?

The fraction of the bedspread is covered in red stripes is $$\frac{1}{12}$$.

Explanation:
Given that $$\frac{2}{3}$$ of the bedspread is covered in race cars, and the rest is stripped and $$\frac{1}{4}$$ of the stripes are red. The striped bedspread would be 1 – $$\frac{2}{3}$$ which is $$\frac{1}{3}$$.
So the fraction of the bedspread is covered in red stripes is $$\frac{1}{3}$$ × $$\frac{1}{4}$$ which is $$\frac{1}{12}$$.

### Eureka Math Grade 5 Module 4 Lesson 13 Exit Ticket Answer Key

Question 1.
Solve. Draw a rectangular fraction model, and write a number sentence to show your thinking.

$$\frac{1}{3}$$ × $$\frac{1}{3}$$ =

$$\frac{1}{9}$$.

Explanation:
Given that $$\frac{1}{3}$$ × $$\frac{1}{3}$$ which is $$\frac{1}{9}$$.

Question 2.
Ms. Sheppard cuts $$\frac{1}{2}$$ of a piece of construction paper. She uses $$\frac{1}{6}$$ of the piece to make a flower. What fraction of the sheet of paper does she use to make the flower?

The fraction of the sheet of paper does she use to make the flower is $$\frac{1}{12}$$.

Explanation:
Given that Ms. Sheppard cuts $$\frac{1}{2}$$ of a piece of construction paper and she uses $$\frac{1}{6}$$ of the piece to make a flower, so the fraction of the sheet of paper does she use to make the flower is $$\frac{1}{2}$$ × $$\frac{1}{6}$$ which is $$\frac{1}{12}$$.

### Eureka Math Grade 5 Module 4 Lesson 13 Homework Answer Key

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

a. Half of $$\frac{1}{2}$$ cake = _____ cake.

$$\frac{1}{4}$$.

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

b. One-third of $$\frac{1}{2}$$ cake = _____ cake.

$$\frac{1}{6}$$.

Explanation:
Given that One-third of $$\frac{1}{2}$$ cake which is $$\frac{1}{3}$$ × $$\frac{1}{2}$$ = $$\frac{1}{6}$$.

c. $$\frac{1}{4}$$ of $$\frac{1}{2}$$

$$\frac{1}{8}$$.

Explanation:
Given that latex]\frac{1}{4}[/latex] of $$\frac{1}{2}$$ which is latex]\frac{1}{4}[/latex] × $$\frac{1}{2}$$ = $$\frac{1}{8}$$.

d. $$\frac{1}{2}$$ × $$\frac{1}{5}$$

$$\frac{1}{10}$$.

Explanation:
Given that latex]\frac{1}{2}[/latex] of $$\frac{1}{5}$$ which is latex]\frac{1}{2}[/latex] × $$\frac{1}{5}$$ = $$\frac{1}{10}$$.

e. $$\frac{1}{3}$$ × $$\frac{1}{3}$$

$$\frac{1}{9}$$.

Explanation:
Given that latex]\frac{1}{3}[/latex] of $$\frac{1}{3}$$ which is latex]\frac{1}{3}[/latex] × $$\frac{1}{3}$$ = $$\frac{1}{9}$$.

f. $$\frac{1}{4}$$ × $$\frac{1}{3}$$

$$\frac{1}{12}$$.

Explanation:
Given that latex]\frac{1}{4}[/latex] of $$\frac{1}{3}$$ which is latex]\frac{1}{4}[/latex] × $$\frac{1}{3}$$ = $$\frac{1}{12}$$.

Question 2.
Noah mows $$\frac{1}{2}$$ of his property and leaves the rest wild. He decides to use $$\frac{1}{5}$$ of the wild area for a vegetable garden. What fraction of the property is used for the garden? Draw a picture to support your answer.

The fraction of the property is used for the garden is $$\frac{1}{10}$$.

Explanation:
Given that Noah mows $$\frac{1}{2}$$ of his property and leaves the rest wild and he decides to use $$\frac{1}{5}$$ of the wild area for a vegetable garden, so the fraction of the property is used for the garden is $$\frac{1}{2}$$ × $$\frac{1}{5}$$ which is $$\frac{1}{2}$$ × $$\frac{1}{5}$$ = $$\frac{1}{10}$$.

Question 3.
Fawn plants $$\frac{2}{3}$$ of the garden with vegetables. Her son plants the remainder of the garden. He decides to use $$\frac{1}{2}$$ of his space to plant flowers, and in the rest, he plants herbs. What fraction of the entire garden is planted in flowers? Draw a picture to support your answer.

The fraction of the entire garden is planted in flowers is $$\frac{1}{6}$$.
Given that fawn plants $$\frac{2}{3}$$ of the garden with vegetables and her son plants the remainder of the garden and he decides to use $$\frac{1}{2}$$ of his space to plant flowers, and in the rest, he plants herbs. So her son gets $$\frac{2}{3}$$ × $$\frac{1}{2}$$ which is $$\frac{1}{3}$$. So the fraction of the entire garden is planted in flowers is $$\frac{1}{2}$$ × $$\frac{1}{3}$$ which is $$\frac{1}{6}$$.
Diego eats $$\frac{1}{5}$$ of a loaf of bread each day. On Tuesday, Diego eats $$\frac{1}{4}$$ of the day’s portion before lunch. What fraction of the whole loaf does Diego eat before lunch on Tuesday? Draw a rectangular fraction model to support your thinking.
The fraction of the whole loaf does Diego eat before lunch on Tuesday is $$\frac{1}{20}$$.
Given that Diego eats $$\frac{1}{5}$$ of a loaf of bread each day and on tuesday, Diego eats $$\frac{1}{4}$$ of the day’s portion before lunch. So the fraction of the whole loaf does Diego eat before lunch on Tuesday is $$\frac{1}{5}$$ × $$\frac{1}{4}$$ which is $$\frac{1}{20}$$.