# Illustrative Mathematics Unit 6.6, Lesson 9: The Distributive Property

Learning Targets:

• I can use a diagram of a rectangle split into two smaller rectangles to write different expressions representing its area. I can use the distributive property to help do computations in my head.

Related Pages
Illustrative Math

#### Lesson 9: The Distributive Property

Let’s use the distributive property to make calculating easier.

Illustrative Math Unit 6.6, Lesson 9 (printable worksheets)

#### Lesson 9 Summary

The following diagram shows how to use the distributive property to make calculating easier. #### Lesson 9.1 Number Talk: Ways to Multiply

Find each product mentally.
5 · 102
5 · 98
5 · 999

Scroll down the page for the solutions to the “Are you ready for more?” section.

#### Lesson 9.2 Ways to Represent Area of a Rectangle

Here is a diagram of x + 2 and 3x when x is 4. Notice that the two diagrams are lined up on their left sides.

1. Select all the expressions that represent the area of the large, outer rectangle in figure A. Explain your reasoning.
• 6 + 3 + 2
• 6 · 3 + 6 · 2
• 6 · 3 + 2
• 6 · 5
• 6(3 + 2)
• 6 · 3 · 2
1. Select all the expressions that represent the area of the shaded rectangle on the left side of figure B. Explain your reasoning.
• 4 · 7 + 4 · 2
• 4 · 7 · 2
• 4 · 5
• 4 · 7 - 4 · 2
• 4(7 - 2)
• 4(7 + 2)
• 4 · 2 - 4 · 7

#### Lesson 9.3 Distributive Practice

Complete the table. If you get stuck, skip an entry and come back to it, or consider drawing a diagram of two rectangles that share a side.

 column 1 column 2 column 3 column 4 value 5 · 98 5(100 - 2) 5 · 100 - 5 · 2 500 - 10 490 33 · 12 33(10 + 2) 3 · 10 = 3 · 4 30 - 12 100(0.04 + 0.06) 8 · 1/2 + 8 · 1/4 9 + 12 24 - 16

#### Are you ready for more?

1. Use the distributive property to write two expressions that equal 360. (There are many correct ways to do this.)
2. Is it possible to write an expression like a(b + c) that equals 360 where is a fraction? Either write such an expression, or explain why it is impossible.
3. Is it possible to write an expression like a(b - c) that equals 360? Either write such an expression, or explain why it is impossible.
4. How many ways do you think there are to make 360 using the distributive property? #### Lesson 9 Practice Problems

1. Select all the expressions that represent the area of the large, outer rectangle.
A. 5(2 + 4)
B. 5 · 2 + 4
C. 5 · 2 + 5 · 4
D. 5 · 2 · 4
E. 5 + 2 + 4
F. 5 · 6
2. Draw and label diagrams that show these two methods for calculating 19 - 50.
a. First find 10 · 50 and then add 9 · 50.
b. First find 20 · 50 and then take away 50.
3. Complete each calculation using the distributive property.
a. 98 · 24
(100 - 2) · 24
b. 21 · 15
(20 + 1) · 15
c. 0.51 · 40
(0.5 + 0.01) · 40
4. A group of 8 friends go to the movies. A bag of popcorn costs \$2.99. How much will it cost to get one bag of popcorn for each friend? Explain how you can calculate this amount mentally.
5. a. On graph paper, draw diagrams of a + a + a + a and 4a when a is 1, 2, and 3. What do you notice?
b. Do a + a + a + a and 4a have the same value for any value of a? Explain how you know.
6. 120% of x is equal to 78.
a. Write an equation that shows the relationship of 120%, x, and 78.
7. Kiran’s aunt is 17 years older than Kiran.
a. How old will Kiran’s aunt be when Kiran is:
15 years old?
30 years old?
x years old?
b. How old will Kiran be when his aunt is 60 years old?

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

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