Properties, Defined and IllustratedDate: 10/10/2001 at 11:25:54 From: rad2b 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: Commutative property of addition 3 4 ----- ------- * * * * * * * 3 + 4 = 4 + 3 ------- ----- 4 3 Commutative property of multiplication * * * * * * * * * * = * * * * 3 * 4 = 4 * 3 * * * * * * * * * * Associative property of addition (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 See also the Glossary of Properties from the Dr. Math FAQ: http://mathforum.org/dr.math/faq/faq.property.glossary.html I hope this helps. Write back if you'd like to talk about this some more, or if you have any other questions. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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