Associative Property of Multiplication and Grouping Symbols
Date: 10/22/2006 at 15:50:37 From: Erika Subject: Associative Property of Multiplication Grouping Symbols Will the associative property of multiplication delete grouping symbols? Ex: (a x b) x c (b x c) x a a x b x c My algebra teacher says that each algebraic "tool" has certain things it can do. While you may be able to find a simple answer he always wants to know which tools you used to teach us to synthesize. I want to make sure I know what each property can do and what it can't. I would think that it could delete grouping symbols and not affect the answer because 2 x (3 x 4) = 24, (2 x 3) x 4 = 24, 2 x 3 x 4 = 24.
Date: 10/22/2006 at 23:08:39 From: Doctor Peterson Subject: Re: Associative Property of Multiplication Grouping Symbols Hi, Erika. Note that the associative property says (ab)c = a(bc) which does not EXPLICITLY drop the parentheses, just moves them around. But also note that when we write it without parentheses, as abc, the order of operations tells us to work left to right, so abc = (ab)c by definition. We multiply ab first, then multiply that by c. So to drop the parentheses in (ab)c, we can just use the order of operations; those parentheses are not really needed! But to drop the parentheses in a(bc), we have to first apply the associative property to change it to (ab)c, and THEN use the order of operations. The examples you give don't all have the same order for a, b, and c, so you would have to use the commutative property too for the middle one to be equal to the others. The first two have their parentheses on the left, so they don't require associativity. The net effect of associativity and the order of operations is that we can ignore parentheses where only multiplication (or only addition) is involved; we don't normally pay much attention to which we are actually doing, but it's good to notice the details once in a while! If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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