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### Associative and Commutative Properties

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Date: 08/20/2001 at 23:41:56
From: Deborah
Subject: Commutive and Associative Properties

Please tell me if this problem is associative or commutative and
explain the difference.  I think it is associative, but the book says
commutative.

6+(2+7) = 6+(7+2)

It has three or more numbers, so why is it not associative?
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```
Date: 08/21/2001 at 08:55:45
From: Doctor Peterson
Subject: Re: Commutive and Associative Properties

Hi, Deborah.

Look at the only difference between the two sides:

2+7       7+2

The order of the two addends has been changed, so the equation is true
because of the commutative property. The third number, 6, is not
involved in this change; essentially we have just added 6 to both
sides of an example of the commutative property.

If we applied the associative property to the left side, we would get

6+(2+7) = (6+2)+7

Here, we changed the order in which the two additions are done
(regrouping them using parentheses), rather than the order of the two
addends in one addition. The order of the numbers themselves is not
changed.

For Associative and Commutative properties, see the Dr. Math FAQ:

Glossary of Properties
http://mathforum.org/dr.math/faq/faq.property.glossary.html

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
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