Why a Negative x Negative = Positive

Date: 4/11/96 at 16:57:21
From: Anonymous
Subject: proofs, multiplying integers

A teacher in a course I took last fall challenged us to come up 
with a way to demonstrate or prove how it is that a negative times 
a negative equals a positive (how to explain this).  The only 
thing I could come up with is that it is positive because one is 
negating a negative.  No one came up with a very satisfying 
explanation. Can you help?  Thanks.

Date: 4/18/96 at 13:26:36
From: Anonymous
Subject: Math equations

Hello. I am a student at The Colorado Institute of Art and have 
had a question/problem presented to me by our Gen ED math 
instructor.  The question is:

Are there any other forms of proof to show that (- + - = +)
Negative plus a negative equals a positive?

I have done more researching than one brain could handle, and I 
was hoping that with several brains together the answer could be 
completed.

I would greatly appreciate your help in any way.

Thank you very much.

Julia

Date: 5/3/96 at 14:42:2
From: Doctor Steven
Subject: Re: proofs, multiplying integers

Well, when we say -1 we mean the additive inverse of 1 so we have:

  1 + -1 = 0          (since they are inverses)

  1 + (1)*-1 = 0      (1 multiplied by anything is that thing)

  1 = -(1)*-1         (subtract (1)*-1 from both sides)

  1 = -1*-1           (the parenthesis don't mean anything)

So a negative times a negative means a positive. 

Hope this helps.

-Doctor Steven,  The Math Forum