Positive and Negative MultiplicationDate: 7/30/96 at 11:2:38 From: Mohd Nasir bin Mahmud Subject: Positive and Negative Multiplication Hello, I would like to know why: + times + = + + times - = - - times - = + - times + = - Thank you. Date: 7/30/96 at 16:0:53 From: Doctor Robert Subject: Re: Positive and Negative Multiplication The short, but probably unsatisfactory, answer is that the field axioms of algebra can be used to prove the above outcomes with signed numbers. But, perhaps, the easiest way to convince you of their truth is to show you some patterns. The positive times a positive really presents no problem. But why is a negative times a positive a negative? 2 x 4 = 8 2 x 3 = 6 2 x 2 = 4 2 x 1 = 2 2 x 0 = 0 2 x -1 = ? If the pattern is to continue (subtracting 2 each time) the logical answer is -2. And mathematicians like logic! 2 x -2 = -4 Now, using a negative number as the multiplier, -2 x 3 = -6 -2 x 2 = -4 -2 x 1 = -2 -2 x 0 = 0 -2 x -1 = ? Again, to make the pattern consistent (adding two each time) the answer has to be +2. -2 x -2 = 4 I hope that this explains to some extent. What I have done here in no way constitutes a proof. Good luck. -Doctor Robert, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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