OOT: Negative number multiplication

[Chuck MATTSEN]

On Tue, 23 May 2006 22:03:01 -0500, Groundhog <linuxmurah at gmail.com> wrote:

> dear friends,
>
> few weeks ago I had a question, acctually really simple question, but
> until today nobody can give me answer. okay here is my question:
>
> "as we know since Elementary School:
> (+) x (+) = (+)
> (+) x (-) = (-)
> (-) x (+) = (-)
> (-) x (-) = (+)
>
> now when I change with numbers:
> 5 x 3 = 5 + 5 + 5 = 15 (everybody know this very well)
> 5 x (-3) = ....................... = -15 (everybody getting confused)
> (-5) x (3) = (-5) + (-5) + (-5) = -15 (no problem with it)
> (-5) x (-3) = ....................... = 15 (then, everybody get  
> frustated)
>
> could someone give answer about this 'elementary' question??

Interesting what crops up on this list.  I'm no mathemetician, but I think  
it's easier to look at it this way, using your four examples with the 5's  
and 3's:

5 x 3 = 3 + 3 + 3 + 3+ 3 = 15
5 x (-3) = (-3) +(-3) +(-3) +(-3) +(-3) = -15
            (or simply -3 -3 -3 -3 -3 = -15)
(-5) x 3 = -(3 + 3 + 3 + 3 + 3) = -15
(-5) x (-3) = -((-3) +(-3) +(-3) +(-3) +(-3)) = 15

There are probably more correct ways to express it -- certainly easier to  
understand at a glance, I'm sure.


-- 
Chuck Mattsen (Mahnomen, MN)
mattsen at arvig.net