Associative, Distributive PropertiesDate: 9/5/96 at 17:26:3 From: Michael F. Biondi Subject: Associative, Distributive Properties We would like to know how to explain the differences between associative and distributive properties to our eighth grade algebra student. Date: 9/5/96 at 20:34:9 From: Doctor Robert Subject: Re: Associative, Distributive Properties The associative property is needed because addition and multiplication are really binary operations. By this I mean that you can only do addition or multiplication with two numbers at one time. So, how do you handle this question: 1+2+3=? You can either say (1+2)+3 or 1+(2+3) where the parentheses ( ) indicate which operation is to be done first. Luckily it turns out that you get the same answer both ways. This is the associative property. It doesn't make any difference which numbers you associate together. When you have multiplication and addition in the same problem, it's a bit different. The order of operations requires that when you simplify 3 x (4+5), you do the operation inside the parentheses first. However, you get the same answer if you distribute the 3 over the addition and write it as 3x4+3x5. This is the distributive property of multiplication over addition. It doesn't seems like such a big deal in straight arithmetic questions, but when variables are involved it can help one simplify an otherwise messy situation. For example: 3(x+5) + 2(x-4) can not be simplified since I don't know what x stands for and the parentheses must be done first. BUT, if I invoke the distributive property the expression becomes 3x+15+2x-8 = 5x +7 which is quite a bit simpler than the original quantity. I hope that this helps. -Doctor Robert, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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