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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)


    (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
       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 
add the two answers together:

 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
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