Associative and Commutative Properties

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?

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/