# Lesson 9

The Distributive Property, Part 1

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

### Problem 1

Select all the expressions that represent the area of the large, outer rectangle.

A:

$$5(2+4)$$

B:

$$5 \boldcdot 2 + 4$$

C:

$$5 \boldcdot 2 + 5 \boldcdot 4$$

D:

$$5 \boldcdot 2 \boldcdot 4$$

E:

$$5 + 2+ 4$$

F:

$$5 \boldcdot 6$$

### Problem 2

Draw and label diagrams that show these two methods for calculating $$19 \boldcdot 50$$.

• First find $$10\boldcdot 50$$ and then add $$9 \boldcdot 50$$.
• First find $$20 \boldcdot 50$$ and then take away 50.

### Problem 3

Complete each calculation using the distributive property.

$$\displaystyle 98 \boldcdot 24$$ $$\displaystyle (100-2) \boldcdot 24$$ $$\displaystyle \ldots$$

$$\displaystyle 21 \boldcdot 15$$ $$\displaystyle (20 + 1) \boldcdot 15$$ $$\displaystyle \ldots$$

$$\displaystyle 0.51 \boldcdot 40$$ $$\displaystyle (0.5 + 0.01) \boldcdot 40$$ $$\displaystyle \ldots$$

### Problem 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.

### Problem 5

1. On graph paper, draw diagrams of $$a+a+a+a$$ and $$4a$$ when $$a$$ is 1, 2, and 3. What do you notice?
2. Do $$a+a+a+a$$ and $$4a$$ have the same value for any value of $$a$$? Explain how you know.
(From Unit 6, Lesson 8.)

### Problem 6

120% of $$x$$ is equal to 78.

1. Write an equation that shows the relationship of 120%, $$x$$, and 78.
2. Use your equation to find $$x$$. Show your reasoning.

(From Unit 6, Lesson 7.)

### Problem 7

Kiran’s aunt is 17 years older than Kiran.

1. How old will Kiran’s aunt be when Kiran is:

15 years old?

30 years old?

$$x$$ years old?

2. How old will Kiran be when his aunt is 60 years old?
(From Unit 6, Lesson 6.)