Multiplying and Dividing Negatives

Date: 07/20/98 at 15:51:13
From: Brittany
Subject: Multiplying and dividing integers

Dear Dr. Math,

I need to figure out how to multiply and divide integers. We learned it 
last year, but I never got it. The negative sign always confuses me, 
and when integers are in fractions, I get lost. 

For example: -1/2 times +2/3 = ? 

Please help me.

Thanks a lot,
Brittany

Date: 07/20/98 at 19:12:57
From: Doctor White
Subject: Re: Multiplying and dividing integers

Brittany:

Let's talk about a few things before we get started:

   1) Integers are positive and negative whole numbers 
      (... -3, -2, -1, 0, 1, 2, 3, ...)

   2) Other numbers like fractions and decimals can have a positive 
      value or a negative value and are called positive or negative 
      numbers, but they are not considered integers.

   3) Regardless of whether they are integers or not, there is a quick 
      way to find the correct sign for your answer.

First, if the problem contains just multiplication, just division, or 
just multiplication and division, then the correct sign can be 
determined rather simply. Just count up how many negative (-) signs 
there are in the problem. If there is an even number of negative signs 
then the answer will be positive. If there is an odd number of negative 
signs then the answer will be negative. Then work the problem as if it 
had no signs and put the correct sign on the answer.

Example 1: (-2)(-3)(4)(-1). Note that there are 3 negatives, so the 
answer is negative. Then 
     2 x 3 x 4 x 1 = 24     so 
   (-2)(-3)(4)(-1) = -24

Example 2: (-1/3)(1/2)(-1/5). Note that there 2 negatives, so the 
answer is positive. Then 
     1/3 x 1/2 x 1/5 = 1/30  so 
   (-1/3)(1/2)(-1/5) = 1/30

Example 3: [(-2)(1/2)(-.4)]/[(-1)(-4)(-.5)]. Note that there are 5 
negatives, so the answer is negative. Then 

   [2 x 1/2 x .4]/[1 x 4 x .5] = .4/2 = .2
 
Since there is an odd number of negatives (5), the final answer is -.2.

This works only if the problem contains just multiplication and 
division. If it has addition or subtraction in it, then we have 
another situation to deal with.

You might want to look at the Dr. Math Archives and search for 
integers. You will find some neat discussions on signed numbers.

  http://mathforum.org/mathgrepform.html   

Hope this has helped. Let me know if you need more info. Come back 
soon, and good luck with Algebra next year.
             
- Doctor White, The Math Forum
Check out our web site! http://mathforum.org/dr.math/