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

Materials Needed: None

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## Learning ObjectivesEdit

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

## Warm-upEdit

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.
\begin{align} 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{align}

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