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Algebra Lesson 12: Multiplying Positives and Negatives

AMAZON PRODUCTS
 Practical Algebra: A Self-Teaching Guide, 2nd Edition
 Algebra Unplugged by Kenn Amdahl, Jim Loats
 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.