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### Properties, Defined and Illustrated

```
Date: 10/10/2001 at 11:25:54
Subject: Property help

I need a page of information on the commutative, associative, and
F.O.I.L. properties, to be used as a study sheet for a quiz.
```

```
Date: 10/10/2001 at 12:45:22
From: Doctor Ian
Subject: Re: Property help

Hi,

If you understand the distributive property, you can ignore FOIL:

When FOIL Fails
http://mathforum.org/dr.math/problems/ryan.03.22.01.html

For that matter, if you _understand_ the commutative and associative
properties, then you don't need a study sheet to help you 'remember'
them. (To put that another way, if you have to 'remember' these
properties, then you probably don't _understand_ them.)

Take a look at the following diagrams, and construct enough other
examples to be sure that you would be able to explain to someone else
why the properties hold for _any_ numbers:

3      4
----- -------
* * * * * * *                   3 + 4 = 4 + 3
------- -----
4      3

Commutative property of multiplication

* * *       * * * *
* * *    =  * * * *             3 * 4 = 4 * 3
* * *       * * * *
* * *

(2+3)+4
-----------------
2+3
---------
* * * * * * * * *              (2 + 3) + 4 = 2 + (3 + 4)
-------------
3+4
-----------------
2+(3+4)

Associative property of multiplication

+--+--+--+--+
/  /  /  /  /|
+--+--+--+--+ +
/  /  /  /  /|/|
+--+--+--+--+ + +        (2 * 3) * 4 = 2 * (3 * 4)
|  |  |  |  |/|/|
+--+--+--+--+ + +
|  |  |  |  |/|/
+--+--+--+--+ +
|  |  |  |  |/
+--+--+--+--+

Distributive property of multiplication over addition:

2    3
--- -----
@ @ * * * |
@ @ * * * | 4             (2 * 4) + (3 * 4) = (2 + 3) * 4
@ @ * * * |
@ @ * * * |
---------
2 + 3

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

more, or if you have any other questions.

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