# Lesson 9: The Distributive Property, Part 1

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

## 9.1: Number Talk: Ways to Multiply

Find each product mentally.

$5 \boldcdot 102$

$5 \boldcdot 98$

$5 \boldcdot 999$

## 9.2: Ways to Represent Area of a Rectangle 1. Select all the expressions that represent the area of the large, outer rectangle in figure A. Explain your reasoning.

• $6 + 3 + 2$
• $6 \boldcdot 3 + 6 \boldcdot 2$
• $6 \boldcdot 3 + 2$
• $6 \boldcdot 5$
• $6 (3+2)$
• $6 \boldcdot 3 \boldcdot 2$
2. Select all the expressions that represent the area of the shaded rectangle on the left side of figure B. Explain your reasoning.

• $4 \boldcdot 7 + 4 \boldcdot 2$
• $4 \boldcdot 7 \boldcdot 2$
• $4 \boldcdot 5$
• $4 \boldcdot 7 - 4 \boldcdot 2$
• $4(7-2)$
• $4(7+2)$
• $4 \boldcdot 2 - 4 \boldcdot 7$

## 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
row 1 $5 \boldcdot 98$ $5 (100-2)$ $5 \boldcdot 100 - 5 \boldcdot 2$ $500 - 10$ 490
row 2 $33 \boldcdot 12$ $33 (10 + 2)$
row 3     $3 \boldcdot 10 - 3 \boldcdot 4$ $30-12$
row 4   $100 (0.04 + 0.06)$
row 5     $8 \boldcdot \frac 1 2 + 8 \boldcdot \frac 1 4$
row 6       $9 + 12$
row 7       $24 - 16$

## Summary

When we need to do mental calculations, we often come up with ways to make the calculation easier to do mentally.

Suppose we are grocery shopping and need to know how much it will cost to buy 5 cans of beans at 79 cents a can. We may calculate mentally in this way: $$5\boldcdot {79}$$ $$5\boldcdot {70}+5\boldcdot {9}$$ $$350+45$$ $$395$$

In general, when we multiply two numbers (or factors), we can break up one of the factors into parts, multiply each part by the other factor, and then add the products. The result will be the same as the product of the two original factors.

When we break up one of the factors and multiply the parts we are using the distributive property.

The distributive property also works with subtraction. Here is another way to find $5\boldcdot 79$: $$5\boldcdot 79$$ $$5\boldcdot {(80-1)}$$ $$400-5$$ $$395$$