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Date: 12/31/97 at 20:07:08
From: Tracey
Subject: How to add and subtract integers

I need help on how to add and subtract integers. An example of a
problem would be 12 + (-4) = ?. What I do is just add the problem, but
the answer turns out to be 16. Then I would check it on my calculator
and the answers is 8. I need help on the steps, and if you could
explain how you did each step it would be very helpful.

Thank you.

Date: 01/09/98 at 14:33:21
From: Doctor Sonya
Subject: Re: How to add and subtract integers

Tracey,

I can understand your frustrations in dealing with positive and
negative numbers.  It is a very difficult topic, but I know that you
will get it with practice.

When I think of adding and subtracting negative numbers, I always
imagine a number line, like this:

<---------------0-------------->

where each little dash stands for a number. The negative numbers are
on the left of 0 and the positive ones are on the right. If I want to
find 2 on the number line, I just go 2 spaces to the right. If I want
to find -3, I go 3 spaces to the left.

When you want to add two numbers together, think about moving on the
number line. For example, if I wanted to find the answer to:

3 + 5 = ?

I would first move three spaces, and them move 5 more spaces. This
would put me 8 spaces over, and the answer to 3 + 5 is 8:

<---------------0---3-----8------>
3  +  5

The same principle works with negative numbers, except that you move
to the left instead of to the right. Say you have the question:

(-3) + (-2) = ?

To find the answer I'm going to move three spaces to the left, and
then 2 more spaces to the left:

<-----------(-5)---(-2)--0---------------->
-3  +  -2

If the two numbers are of different signs, you just have to move
different directions along the number line. Let's say I have:

(-3) + 4 = ?

Now, the -3 means that you move three spaces to the left, and the 4
means that you move 4 spaces to the right. Where is this going to put
you on the number line?

<--(-5)-(-4)-(-3)-(-2)-(-1)-0-1-2-3-4-5-6-7-8-9-10-11-12->

Still thinking...

.

.

.

Hmmmmmm.

.
.
.

You say that the answer is 1?  Right!  Good job.

Here are some more examples for you to practice with.

2 + 4 =
(-3) + 8 =
3 + (-5) =
(-5) + (-6) =
8 + (-5) =
5 + 2 =
(-4) + (-3) =

Write us back if you have more questions.

-Doctor Sonya,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/

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