We included **H****MH Into Math Grade 5 Answer Key**** PDF** **Module 8 Lesson 2 Represent Multiplication of Whole Numbers by Fractions** to make students experts in learning maths.

## HMH Into Math Grade 5 Module 8 Lesson 2 Answer Key Represent Multiplication of Whole Numbers by Fractions

I Can find the product of a whole number and a fraction using a visual model.

**Spark Your Learning**

Earl bakes 3 loaves of bread. He keeps \(\frac{1}{4}\) of the bread for himself and gives the rest to his neighbors. How many loaves of bread does Earl give to his neighbors?

Answer:

The number of loaves of bread does Earl give to his neighbors is 2 \(\frac{1}{4}\) loaves.

Explanation:

Given that Earl bakes 3 loaves of bread and he keeps \(\frac{1}{4}\) of the bread for himself and gives the rest to his neighbors. So the number of loaves of bread does Earl give to his neighbors is \(\frac{3}{4}\)×3 which is \(\frac{9}{4}\) = 2 \(\frac{1}{4}\) loaves.

**Draw a visual model to show how you can find how many loaves he gives away. Justify your reasoning.**

**Turn and Talk** How would your visual model change if Earl decides to keep \(\frac{1}{8}\) of the bread instead of \(\frac{1}{4}\)?

**Build Understanding**

1. Mrs. Fan bakes 2 cakes, each in the shape of a hexagon. She takes \(\frac{3}{4}\) of the cakes to a party.

Answer:

She takes 1\(\frac{1}{2}\) cake.

Explanation:

Given that Mrs. Fan bakes 2 cakes, each in the shape of a hexagon and she takes \(\frac{3}{4}\) of the cakes to a party. So \(\frac{3}{4}\) × 2 which is \(\frac{3}{2}\) = 1\(\frac{1}{2}\) cake she takes to the party.

**Determine how much cake she takes to the party using pattern blocks and then draw a visual model to show your work.**

A. How did you use pattern blocks to find the amount of cake Mrs. Fan takes to the party?

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B. What amount of the two cakes does Mrs. Fan take to the party?

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Answer:

1\(\frac{1}{2}\) cake.

Explanation:

The amount of cakes Mrs. Fan takes to the party is 1\(\frac{1}{2}\).

C. Write a multiplication equation to model the problem.

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Answer:

1\(\frac{1}{2}\).

Explanation:

The multiplication equation to model the problem is \(\frac{3}{4}\) × 2 which is \(\frac{3}{2}\) = 1\(\frac{1}{2}\).

**Turn and Talk** Why is it not appropriate to model this situation with the expression 2 × \(\frac{3}{4}\)?

2. Rashad bakes 4 equal-sized granola bars. He serves \(\frac{2}{3}\) of the bars to his friends.

Answer:

Rashad serves 2\(\frac{2}{3}\) granola bars.

Explanation:

Given that Rashad bakes 4 equal-sized granola bars and he serves \(\frac{2}{3}\) of the bars to his friends. So he serves 4 × \(\frac{2}{3}\) which is \(\frac{8}{3}\) = 1\(\frac{5}{3}\) granola bars.

**Draw a visual model to show how you can find how many granola bars he serves. **

A. How did you make equal-sized parts from 4 wholes? What does each part represent?

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Answer:

To make equal-sized parts from 4 wholes we will divide them equally.

B. What does the 2 in the fraction \(\frac{2}{3}\) represent? How did you show this in your visual model?

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Answer:

The 2 in the fraction \(\frac{2}{3}\) represent as 2 times of 3.

C. How many \(\frac{1}{3}\)-size pieces does he serve?

D. How many granola bars does he serve? Write a multiplication equation to model the problem.

Answer:

4 × \(\frac{2}{3}\).

Explanation:

The multiplication equation of the problem is 4 × \(\frac{2}{3}\) which is \(\frac{8}{3}\) = 2\(\frac{2}{3}\).

**Turn and Talk** How could you rearrange your visual model to find the number of whole bars Rashad serves? Explain.

3. Isa has 2 boxes of pizza. Each box has \(\frac{5}{8}\) of a pizza left. Jack says that this story context can be modeied with the equation \(\frac{5}{8}\) × 2 = 1\(\frac{1}{4}\).

A. Explain why Jack’s equation does not model the story context.

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B. Rewrite the story context so that it can be modeled with the equation \(\frac{5}{8}\) × 2 = 1\(\frac{1}{4}\). Then draw a visual model to represent the problem.

**Check Understanding Math Board**

Question 1.

Al bakes 4 round cakes that are decorated like baseballs for a team party. The party guests eat \(\frac{7}{8}\) of the cakes. How many cakes do they eat in all? Draw a visual model to find the answer. Then write an equation to model the problem.

Answer:

3\(\frac{1}{2}\) cakes do they eat in all.

Explanation:

Given that Al bakes 4 round cakes that are decorated like baseballs for a team party and the party guests eat \(\frac{7}{8}\) of the cakes. So 4×\(\frac{7}{8}\) which is \(\frac{7}{2}\) = 3\(\frac{1}{2}\) cakes do they eat in all.

Question 2.

A carpenter has 10 equal-sized pieces of wood. She uses \(\frac{3}{5}\) of the wood to make a box. Use a visual model to find the number of pieces of wood that the carpenter uses. Then write an equation to model the problem.

Answer:

The number of pieces of wood that the carpenter uses is 6 pieces.

Explanation:

Given that a carpenter has 10 equal-sized pieces of wood and she uses \(\frac{3}{5}\) of the wood to make a box. So the number of pieces of wood that the carpenter uses is \(\frac{3}{5}\) × 10 which is 3×2 = 6 pieces.

**On Your Own**

Question 3.

**Use Structure** Megan makes four giant oatmeal cookies and cuts them into equal-sized pieces. She puts \(\frac{11}{12}\) of the cookies into a cookie jar. In a visual model for this situation:

- How many wholes do you need? ____
- What is the fewest number of equal-sized pieces you should cut each cookie into if you want to put \(\frac{11}{12}\) of the cookies in the jar?

__________________ - How many cookies go into the jar?

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Answer:

The number of cookies will be 3\(\frac{2}{3}\).

Explanation:

Given that Megan makes four giant oatmeal cookies and cuts them into equal-sized pieces and she puts \(\frac{11}{12}\) of the cookies into a cookie jar. So the number of cookies will be \(\frac{11}{12}\) ×4 which is \(\frac{11}{3}\) = 3\(\frac{2}{3}\).

**Draw a visual model to find the product.**

Question 4.

\(\frac{3}{8}\) × 4 =

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Answer:

\(\frac{3}{8}\) × 4 = 1\(\frac{1}{2}\).

Explanation:

Given the equation is \(\frac{3}{8}\) × 4 which is \(\frac{3}{2}\) = 1\(\frac{1}{2}\).

Question 5.

\(\frac{2}{9}\) × 3 =

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Answer:

\(\frac{2}{9}\) × 3 = \(\frac{2}{3}\).

Explanation:

Given the equation is \(\frac{2}{9}\) × 3 which is \(\frac{2}{3}\).

Question 6.

**Attend to Precision** How could you use a visual model to show the product \(\frac{14}{15}\) × 3 ? Explain.

Answer:

\(\frac{14}{15}\) = 2\(\frac{4}{5}\).

Explanation:

The product of \(\frac{14}{15}\) × 3 which \(\frac{14}{5}\) = 2\(\frac{4}{5}\).

Question 7.

**Open Ended** Write a story problem for the given equation.

\(\frac{2}{3}\) × 12 =

Question 8.

**Use Tools** Use the number line to find \(\frac{7}{8}\) of 16.

Answer:

\(\frac{7}{8}\) × 16 = 14.

Explanation:

Given that the equation is \(\frac{7}{8}\) × 16 which is 7×2 = 14.

**Use a visual model to find the product.**

Question 9.

\(\frac{5}{6}\) × 3

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Answer:

\(\frac{5}{6}\) × 3 = 2\(\frac{1}{2}\).

Explanation:

Given the equation is \(\frac{5}{6}\) × 3 which is \(\frac{5}{2}\) = 2\(\frac{1}{2}\).

Question 10.

\(\frac{7}{8}\) × 4

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Answer:

\(\frac{7}{8}\) × 4 = 3\(\frac{1}{2}\).

Explanation:

Given the equation is \(\frac{7}{8}\) × 4 which is \(\frac{7}{2}\) = 3\(\frac{1}{2}\).

Question 11.

Write the equation that is represented by the visual model.

Answer:

\(\frac{8}{9}\) × 3 = 2\(\frac{2}{3}\).

Explanation:

The equation for the represented visual model is \(\frac{8}{9}\) × 3 which is \(\frac{8}{3}\) = 2\(\frac{2}{3}\).

Question 12.

**Use Structure** A chunk of honeycomb is made up of 8 hexagons. A beekeeper cuts out \(\frac{13}{16}\) of the honeycomb. In a visual model for this situation:

- How many wholes do you need?

_________________ - Into how many sections do you have to divide each whole?

_________________ - How many hexagons does the beekeeper cut out?

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Answer:

The number of hexagons does the beekeeper cut out is 6\(\frac{1}{2}\).

Explanation:

Given that a chunk of honeycomb is made up of 8 hexagons and a beekeeper cuts out \(\frac{13}{16}\) of the honeycomb. So the number of hexagons does the beekeeper cut out is \(\frac{13}{16}\)×8 which is \(\frac{13}{2}\) = 6\(\frac{1}{2}\).

**I’m in a Learning Mindset!**

What type of feedback can I provide about strategies for multiplying whole numbers by fractions?

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