Negative Times Negative
Date: 10/17/98 at 13:54:25 From: Julia Alaniz Subject: Negative values Could you provide an example for comprehending how a negative times a negative is a positive? - maybe on the number line. I would like to understand it rather than just take it as fact.
Date: 10/23/98 at 20:45:57 From: Doctor Gail Subject: Re: Negative values Dear Julia, Here are a couple of examples for you: If you are convinced that a positive times a negative is negative, then one way to look at negative times negative is to observe a pattern. Consider the following: 3x(-3) = -9 2x(-3) = -6 1x(-3) = -3 0x(-3) = 0 so what comes next in the pattern? Notice that in each case we are multiplying 3 by a number 1 smaller than the previous number. Also observe the pattern that is being created with the products. So the next logical multiplication sentence is (-1)x(-3) = 3 Note that negative times negative was positive. One of the best realistic interpretations that I have found concerns videotaping. Consider videotaping two students, Julia who is walking forward in the tape and holds a sign saying "I am walking forward." Also consider her friend who is walking backward in the tape and holds a sign saying "I am walking backward." Now playing the tapes in the normal fashion would be forward times forward or positive times positive and Julia looks like she is walking forward (the result is positive). Similarly, the meaning of negative times negative might be interpreted as viewing "rewind" times "the friend" or backward times backward. What would it look like the friend was actually doing? Walking forward! So one can visualize backward times backward is forward or negative times negative equals positive. I hope this explanations begin to convince you that negative times negative equals positive. Doctor Gail, The Math Forum http://mathforum.org/dr.math/
Date: 10/23/98 at 21:52:48 From: Julia Alaniz Subject: Thanks to Docter Gail What a most unusual example for visualizing a negative times a negative - the videotaped example. I am actually going to try it since I do video training tapes. Thanks ever so much. Julia Alaniz
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