Lesson 8

Evaluate mentally.

\(100 \boldcdot 100\)

\(\text{-}3 \boldcdot 3\)

\(\text{-}300 + 300\)

\(1,\!279 + \text{-}1,\!279\)

Here is a method for multiplying 97 and 103:

97 is \(100 - 3\)

103 is \(100 + 3\)

So \(97 \boldcdot 103 = (100-3)(100+3)\)

	100	-3
100	10,000	-300
3	300	-9

1. Explain how this diagram is used to compute \(97 \boldcdot 103 = 9,\!991\).
2. Draw a similar diagram that helps you mentally compute \((30+1)(30-1)\). What is the result? What multiplication problem did you just solve?
3. Use this method to compute:
   1. \(7 \boldcdot 13\)
   2. \(102 \boldcdot 98\)
   3. \(995 \boldcdot 1,\!005\)
4. Create a challenge problem for your partner, that could use this method. Create a diagram that shows the answer before giving the problem to your partner.

Complete each diagram. Write some equivalent expressions based on the diagram.

1. 	10	5
   10	100
   		45

2. 		7
   10
   -7	-70

3. 	\(x\)	8
   \(x\)
   -8

4. 	\(a\)	-9
   		\(\text{-}9a\)
   9

5. 	\(b\)	\(\frac12\)
   \(b\)	\(b^2\)
   		\(\text{-}\frac{1}{4}\)

6. 	7
   \(c\)		\(\text{-}c^2\)
   7	49