Positive and Negative Multiplication

Date: 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/