Multiplying Negative Integers

Date: 11/07/2001 at 19:53:09
From: Angelica 
Subject: Multiplying Integers

My question is on the topic Multiplying Integers. 

I can't figure out (-3)2 = a. 

Please help me!

Date: 11/08/2001 at 12:25:44
From: Doctor Ian
Subject: Re: Multiplying Integers

Hi Angelica,

Until you get more comfortable with negative numbers, you might try 
breaking each negative number into a positive number multiplied by -1:

  (-3)2 = (-1*3)2 

       = (-1)(3*2)

       = (-1)(6)

       = -6

Let's look at a more complicated example:

  (-3)(2)(-4)(-2)(3) = (-1*3)(2)(-1*4)(-1*2)(3)

                     = (-1)(3)(2)(-1)(4)(-1)(2)(3)

                     = (-1)(-1)(-1)(3)(2)(4)(2)(3)

                     = (-1)(-1)(-1)(144)

Now, what about all those -1's?  Well, since (-1)(-1)=1, you can 
cancel them out in pairs:

                     = (-1)(-1)(-1)(144)
                           \_____/
                              1

                     = (-1)(144)

                     = -144

Eventually, you'll get so used to cancelling out signs that you'll 
start doing it directly:

       x          x
    ______     ______
   |      |   |      |
  (-3)(2)(-4)(-2)(3)(-5)(-7) = (3)(2)(4)(2)(3)(5)(-7)

                             = -(3 * 2 * 4 * 2 * 3 * 5 * 7)
    
Does this help?  Write back if you'd like to talk about this some 
more, or if you have any other questions. 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/