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

Materials Needed: None

Why
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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.
 * $$\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} $$

Activity
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