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You are HERE >> Mathematics > Algebra > Grade 9

Algebra Lesson 12: Multiplying Positives and Negatives

AMAZON PRODUCTS
Practical Algebra: A Self-Teaching Guide, 2nd Edition 
Algebra Unplugged by Kenn Amdahl, Jim Loats
Algebra to Go : A Mathematics Handbook
  by Elaine Ernst Schneider
  January 25, 2001 

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. 

Submitted by:  © Elaine Ernst Schneider  is a freelance writer and a teacher. She has been writing since high school and has published articles, songs, and children's work. Presently, Elaine is a curriculum author for Group Publishing and also writes the City Songs column for www.newcolonist.com ezine.  Send a note to Elaine.

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