# Prealgebra for Two-Year Colleges/Workbook AIE/Properties of multiplication

Materials Needed: None

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## Learning Objectives

1. Use the distributive property to estimate products, and then to correct your estimate.
2. Find and use patterns in the multiplication table.

## Warm-up

You have $80 in your wallet. You want to buy 3 DVD's for$19.95 each. (Fortunately, you are in Oregon where there is no sales tax.)

1

Approximate the price a DVD to the nearest whole dollar.

2

Estimate the cost of the three DVD's.

3

Estimate how much money you will have in your wallet after the purchase.

4

What do you need to add or subtract from your approximate price of a DVD to get the actual price?

5

What do you need to add or subtract from your estimate of the cost of the three DVD's to get the actual cost?

6

Exactly how much money you will have in your wallet after the purchase?

7

Explain how your estimation and calculation is related to the following application of the distributive property. Be specific about why you are adding or subtracting.

{\displaystyle {\begin{aligned}80-\underbrace {3(20-0.05)} &=80-\underbrace {3(20)} +\underbrace {3(0.05)} \\&=\underbrace {80-60} +0.15\\&=\underbrace {20+0.15} \\&=20.15\\\end{aligned}}}

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