**Algebra Lesson 12: Multiplying Positives and Negatives**

*by Elaine Ernst Schneider*

**Algebra Lesson 11**

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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