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Lesson Tutor : Algebra Lesson 12 : Multiplying Positives and Negatives

  /  Lesson Tutor : Algebra Lesson 12 : Multiplying Positives and Negatives

Algebra Lesson 12: Multiplying Positives and Negatives
by Elaine Ernst Schneider
Before starting: Review/ complete 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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