by Elaine Ernst Schneider
As we learned last lesson: Additive Inverses are opposites. Two numbers are opposites if their sum equals zero. For example, -8 and 8 are additive inverses because their sums total zero. This makes them opposites. You can do the same thing with variables. For example, -(-x) = x.
When this principle is used in multiplication, these rules of thumb emerge:
1. A negative times a negative gives a positive answer.
2. A negative times a positive is negative.
3. A positive times a positive is a positive result.
Examples
(-6)(8) = -48
(-3)(-12) = 36
(12)(11) = 132
Now, what happens when there are three numbers to multiply? Simply work in sequence, following the rules you have learned.
Example: (-5) (-4) (-20)
(20) (-20) [multiply –5 times –4 to get positive 20]
-400 [multiply positive 20 from last step by –20 to get –400]
And what about exponents? Just write them out and follow the rules.
Example: -4
= (-4) (-4) (-4) (-4) (-4)
(16) (-4) (-4) (-4)
-64 (-4) (-4)
256 (-4)
-1024
Exercises:
1. (10) (-8)
2. (-5) (-26)
3. -5³
4. (-2) (-3)²
5. (-1.5) (4)
6. (-5) (22) (-2)
7. (-3) (-5) (-4)
8. (-1) (-3)
9. (-1)
10. (-2)² (-3)
Answer key:
1. –80
2. 130
3. –125
4. –18
5. –6
6. 220
7. –60
8. –81
9. –1 *
10. 324
*Note: Did you learn something about exponents? If the exponent is even, the answer is positive. If the exponent is odd, the answer is negative.
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