From: Suzanne A. (for Teacher2Teacher Service)
Date: Sep 21, 2002 at 22:20:03
Subject: Re: Integers

Hi Ellie,

I'll see if I can explain subtracting a negative number using a number line.

Here's our number line with "|" representing 0 and each dash representing one
unit, some going to the left of "|" representing "negative" and others going
to the right representing "positive".

  - - - - - - - - - - -|- - - - - - - - - -

Let's just try 3 - 4 for starters.

                       |- - -
                            x

I start at zero and "positive" three means that I go 3 spaces to the right. I
mark the 3 by putting an x below it. Now I want to subtract 4. When I subtract
I go in the OPPOSITE direction. If I move 4 spaces to the left, I end up at
one space to the left of 0.


                      -|
                      x

My answer to 3 - 4 is -1 (1 space to the left of 0 on the number line.)

Now let's try -4 - 4 (similar to your original problem)

                - - - -|
                x

I start at 0 but because the first number is "negative" I go to the left four
spaces and I mark it with an x. I'm standing on -4 and when I subtract 4 I
have to move to the left 4 more spaces.

        - - - - - - - -|
        x

My answer this time is -8 (8 spaces to the left of 0 on the number line)

Now let's try your problem, -4 - -4

If you start at -4 on the number line, it would be here:

                - - - -|
                x

If I subtract it means I'm going to continue moving to the left BUT I have to
also think what -4 means. That second negative makes me change direction and
now I'm going to the right and I end up at 0!

                       |
                       x

Here's another way to think about it. What if I owe you 4 dollars? I can
represent that as -4 (4 dollars in the red). If I subtract that amount that I
owe you then it would be the same as paying you back. The amount I owe is 0
dollars. The only way that I could owe you a total of 8 dollars would be if I
added -4 and -4.

So,

   -4 + -4 = -8
   -4 +  4 =  0
    4 + -4 =  0
   -4 - -4 =  0
    4 - -4 =  8
    4 -  4 =  0

I hope that helps.

 -Suzanne A., for the T2T service


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