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### Multiplying and Dividing Negatives

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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 = ?

Thanks a lot,
Brittany
```

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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

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

Example 1: (-2)(-3)(4)(-1). Note that there are 3 negatives, so the
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
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/
```
Associated Topics:
Elementary Division
Elementary Multiplication
Middle School Division
Middle School Negative Numbers

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