We included **H****MH Into Math Grade 5 Answer Key**** PDF** **Module 2 Lesson 1 Relate Multiplication to Division** to make students experts in learning maths.

## HMH Into Math Grade 5 Module 2 Lesson 1 Answer Key Relate Multiplication to Division

I Can use an array or an area model to solve a division problem.

**Spark Your Learning**

A community center has 7 digital music players. Each music player has the same number of songs. If there is a total of 112 songs, how many songs are on each music player?

**Show your thinking.**

How many songs are on each music player? ____

Answer:

Given,

A community center has 7 digital music players.

Each music player has the same number of songs.

Number of songs = 112

112 ÷ 7 = 16

Therefore, there are 16 songs on each music player.

**Turn and Talk** How does your answer change if the number of digital music players is 8?

**Build Understanding**

1. A local theater group is performing a musical. The members arrange 105 chairs in 5 equal rows for the audience. How many chairs are in each row?

**Draw a rectangular array to represent the situation.**

A. How does your rectangular array represent the situation?

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B. How many groups of 5 can you make? ___________________

C. What multiplication equation and related division equation can you write to model the situation?

D. How are the factors and the product of the multiplication equation related to the dividend, divisor, and quotient in the division equation?

E. How many chairs are in each row?

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Answer:

The members arrange 105 chairs in 5 equal rows for the audience

105 ÷ 5 = 21

So, you can make 21 chairs in each row.

**Connect to Vocabulary** Opposite operations, or operations that undo each other, such as addition and subtraction or multiplication and division, are inverse operations.

**Turn and Talk** Why can you use the relationship between multiplication and division to solve a division problem?

2. Simone wants 6 of her friends to share 84 photos equally. How many photos will each friend get?

A. What division and multiplication equations model the situation? ____

You can use an area model or the Distributive Property.

B. What are two multiples of 6 that have a sum of 84? Use your multiples to complete the area model.

C. In Part B, how does each smaller rectangle show a quotient and a product?

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D. How can you use the quotients of the smaller rectangles to find the quotient 84 ÷ 6? ___________

E. Use the Distributive Property to show the partial products shown in your area model.

6 × = 84

___ + ___ = 84

(6 × __) + (6 × ___) = 84

___ × (___ + ___) = ___

____ × ____ = ____

F. What related division equation can you write to model the number of photos each friend will get?

________________

Answer:

Given,

Simone wants 6 of her friends to share 84 photos equally.

84 ÷ 6 = 14

Let the unknown factor be x.

6 × x = 84

x = 14

(6 × 7) + (6 × 7) = 84

6(7 + 7) = 84

6 × 14 = 84

Thus each friend will get 14 photos.

**Check Understanding Math Board**

Question 1.

Priya and her friends are decorating picture frames. Priya shares 96 beads equally between herself and her 3 friends. How many beads does each of them receive?

Show your work. ___________

Answer:

Given,

Priya and her friends are decorating picture frames.

Priya shares 96 beads equally between herself and her 3 friends.

96 ÷ 3 = 32

Thus each will receive 32 beads.

**On Your Own**

Question 2.

**Model with Mathematics** Four people make a playlist of 76 songs for a party. Each person provides the same number of songs for the playlist. How many songs does each person provide?

- Draw to represent the situation. ____________
- Write a multiplication equation and a division equation to model the situation. ____
- How many songs does each person provide? _____

Answer:

Given,

Four people make a playlist of 76 songs for a party.

Each person provides the same number of songs for the playlist.

4 × x = 76

x = 76/4

x = 19

Thus each person provides 19 songs.

Question 3.

**Attend to Precision** Nine friends collect 1,260 leaves at the forest preserve. They each collect the same number of leaves. Explain how to use an equation to find the number of leaves each friend collects.

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Answer:

Given,

Nine friends collect 1,260 leaves at the forest preserve.

They each collect the same number of leaves.

9 × x = 1260

x = 1260/9

x = 140

9 × 70 + 9 × 70 = 1260

9 (70 + 70) = 1260

630 +630 = 1260

Thus each friend will collect 140 leaves.

Question 4.

**Open Ended** Write a division word problem that relates to the multiplication equation 9 × 13 = 117.

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Answer:

9 × 13 = 117

117 ÷ 9 = 13

117 ÷ 13 = 9

**I’m in a Learning Mindset!**

How did I collaborate with a partner when relating multiplication to division?

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