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### Meanings of Properties

```
Date: 07/23/97 at 17:31:13
From: Colleen
Subject: Wording

I have no idea what these words mean, and I need help.  Can you help
me out?  It's appreciated.

What do Associative Property, Commutative Property, and Distributive
Property mean?
```

```
Date: 07/23/97 at 17:53:08
From: Doctor Wilkinson
Subject: Re: wording

The associative property and the commutative property apply to the
operations of addition and multiplication; the distributive property
applies to the two operations working together.

The associative property says that when you add or multiply three or
more numbers, it doesn't matter how you group them: that is, we have
the formulas

(a + b) + c = a + (b + c)

and

(a x b) x c = a x (b x c)

For example

(4 + 6) + 5 = 10 + 5 = 15, which is the same thing you get if you
4 + (6 + 5) = 4 + 11 = 15

The commutative property says it doesn't matter which order you add or
multiply two numbers in:  the formulas are

a + b = b + a
and
a x b = b x a

For example,

4 x 7 = 28 = 7 x 4

The distributive property tells you what happens if you add two
numbers and multiply the sum by another number.  This formula is

a x (b + c) = a x b + a x c

For example,

3 x (4 + 5) = 3 x 9 = 27

which is the same thing you get if you multiply 3 by 4 and 3 by 5 and

3 x 4 + 3 x 5 = 12 + 15 = 27

You use these properties without thinking much about them when you do
arithmetic, but when you do algebra you have to be aware of them.

-Doctor Wilkinson,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Definitions

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