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### 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.

```

```
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)

more, or if you have any other questions.

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Multiplication
Middle School Negative Numbers

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