Algebraic Proof That Positive Times Negative Equals NegativeDate: 03/28/2004 at 15:30:58 From: Jamie Subject: Proof? Is there an algebraic proof that a positive times a negative equals a negative? Date: 03/29/2004 at 22:37:26 From: Doctor Justin Subject: Re: Proof? Hi Jamie, Thanks for writing to Dr. Math. Here's an algebraic proof that should convince you that a positive times a negative equals a negative: For a, b > 0: Consider: 0*b = 0 Because [a + (-a)] = 0, use the Transitive Property: [a + (-a)]*b = 0*b Distributive Property: ab + (-a)(b) = 0*b Again, use the Transitive Property: ab + (-a)(b) = 0 It is assumed that a positive multiplied by a positive equals a positive, so the quantity ab must be positive. If ab is positive and (-a)(b) is added to it to equal zero, then (-a)(b) must be the additive inverse of ab. In other words, (-a)(b) must be less than zero, or negative. If you have any more questions, please write back. - Doctor Justin, The Math Forum http://mathforum.org/dr.math/ |
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