# Into Math Grade 5 Module 8 Lesson 3 Answer Key Represent Multiplication of Whole Numbers by Fractions

We included HMH Into Math Grade 5 Answer Key PDF Module 8 Lesson 3 Represent Multiplication of Whole Numbers by Fractions to make students experts in learning maths.

## HMH Into Math Grade 5 Module 8 Lesson 3 Answer Key Represent Multiplication of Whole Numbers by Fractions

I Can solve a problem by multiplying unit fractions using a visual model.

A chef uses $$\frac{1}{4}$$ of a package of dough. Before using this part of the package of dough, she cuts it into thirds. What fraction of a whole package is each of these smaller pieces?

The fraction of a whole package is each of these smaller pieces is $$\frac{1}{12}$$.

Explanation:
Given that a chef uses $$\frac{1}{4}$$ of a package of dough. So the fraction of a whole package is each of these smaller pieces is $$\frac{1}{4}$$ × $$\frac{1}{3}$$ which is $$\frac{1}{12}$$.
Draw a visual model to show the problem. Justify how your visual model represents the problem.

Turn and Talk How does the word “thirds” in the word problem help you set up your visual model?

Build Understanding

1. Only $$\frac{1}{3}$$ of a chef’s specialty pizza is left at closing time. The chef eats $$\frac{1}{2}$$ of the leftover pizza. How much of the whole pizza does the chef eat?

The chef eat is $$\frac{1}{6}$$ part.

Explanation:
Given that only $$\frac{1}{3}$$ of a chef’s specialty pizza is left at closing time and the chef eats $$\frac{1}{2}$$ of the leftover pizza. So the whole pizza does the chef eat is $$\frac{1}{3}$$ × $$\frac{1}{2}$$ which is $$\frac{1}{6}$$.
Draw a visual model to show the fraction of the whole pizza that the chef eats. Justify your reasoning.

A. How do you name the fraction of the whole pizza that the chef eats? How do you know?
__________________________
__________________________

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

Explanation:
The fraction of the whole pizza that the chef eats is $$\frac{1}{6}$$.

B. What part of a whole pizza does the chef eat? Write an equation to model the problem.
__________________________

$$\frac{1}{3}$$ × $$\frac{1}{2}$$ = $$\frac{1}{6}$$.

Explanation:
The equation is $$\frac{1}{3}$$ × $$\frac{1}{2}$$ which is $$\frac{1}{6}$$.

2. The chef also makes stromboli. One serving 1 serving is $$\frac{1}{2}$$ of a stromboli. What fraction of a meter is the length of one serving?

The length is $$\frac{1}{8}$$ meters.

Explanation:
Given that one serving 1 serving is $$\frac{1}{2}$$ of a stromboli as full serving is $$\frac{1}{4}$$. So the fraction of a meter is the length of one serving is $$\frac{1}{2}$$ × $$\frac{1}{4}$$ which is $$\frac{1}{8}$$ meters.
Use the number line to show how you can find the length of one serving.

A. What fraction of a meter is one serving of stromboli? How do you know?
________________________
________________________
________________________

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

Explanation:
The fraction of a meter in one serving of stromboli is $$\frac{1}{8}$$ meters.

B. Write an equation to model the problem. ________________________

$$\frac{1}{2}$$ × $$\frac{1}{4}$$ = $$\frac{1}{8}$$ meters.

Explanation:
The equation will be $$\frac{1}{2}$$ × $$\frac{1}{4}$$ which is $$\frac{1}{8}$$ meters.

Turn and Talk How would your number line change if the stromboli were cut into thirds instead of halves?

Check Understanding Math Board

Question 1.
The chef makes a rectangular pizza. At closing time, $$\frac{1}{6}$$ of the pizza is left. The chef $$\frac{1}{2}$$ eats of the leftover pizza. Draw a visual model to find the fraction of a whole pizza that the chef eats. Write an equation to model the problem.
The equation is $$\frac{1}{12}$$.

Explanation:
Given that the chef makes a rectangular pizza. At closing time, $$\frac{1}{6}$$ of the pizza is left. The chef $$\frac{1}{2}$$ eats of the leftover pizza. So the equation is $$\frac{1}{6}$$ × $$\frac{1}{2}$$ which is $$\frac{1}{12}$$.

Question 2.
Use the number line to show $$\frac{1}{5}$$ × $$\frac{1}{2}$$.

$$\frac{1}{5}$$ × $$\frac{1}{2}$$ = $$\frac{1}{10}$$.

Explanation:
Given the equation is $$\frac{1}{5}$$ × $$\frac{1}{2}$$ which is $$\frac{1}{10}$$.

Question 3.
Reason A costume designer cuts the section of ribbon shown into fourths. What fraction of a foot is each piece of ribbon? ____

The fraction is $$\frac{1}{16}$$ ft.

Explanation:
Given that a costume designer cuts the section of the ribbon shown into fourths. So the fraction of a foot in each piece of ribbon is $$\frac{1}{4}$$ × $$\frac{1}{4}$$ which is $$\frac{1}{16}$$ ft.

Question 4.
Use Tools Jackson runs $$\frac{1}{2}$$ mile on Monday. On Tuesday, he runs $$\frac{1}{2}$$ of the distance he ran on Monday. What fraction of a mile does Jackson run on Tuesday?

• Show your solution on the number line.
• How does the number line show the solution?
• What fraction of a mile does Jackson run on Tuesday?

The fraction is $$\frac{1}{4}$$ miles.

Explanation:
Given that Jackson runs $$\frac{1}{2}$$ mile on Monday and on Tuesday, he runs $$\frac{1}{2}$$ of the distance he ran on Monday. So the fraction is $$\frac{1}{2}$$ × $$\frac{1}{2}$$ which is $$\frac{1}{4}$$ miles.

Question 5.
Draw a visual model to show $$\frac{1}{3}$$ × $$\frac{1}{5}$$.
$$\frac{1}{3}$$ × $$\frac{1}{5}$$ = $$\frac{1}{15}$$.
Given the equation is $$\frac{1}{3}$$ × $$\frac{1}{5}$$ which is $$\frac{1}{15}$$.