Order of Operations vs. Distributive Property
Date: 02/04/2005 at 20:39:08 From: Jeremy Subject: order of operations vs factoring Doesn't the distributive law contradict the rules of order of operations? We should do parentheses before multiplication or division, but the distributive law tells us it's ok to solve x(a + b) by a*x + b*x, in spite of the parentheses. Is this just an exceptional case?
Date: 02/04/2005 at 22:50:28 From: Doctor Peterson Subject: Re: order of operations vs factoring Hi, Jeremy. The roles of the order of operations and the distributive property are complementary, rather than contradictory. That is, each applies to a different aspect of algebra. The order of operations tells us what an expression MEANS: if we follow the rules, we will correctly evaluate the expression. Properties like the distributive property tell us how we can REWRITE an expression without changing its value. So if we are faced with an expression like a(b + c) which (taken at face value) MEANS that we add b and c, then multiply the result by a, we know that we will get the same value if we rearrange it and INSTEAD evaluate ab + ac So properties allow us to safely manipulate an expression to make it easier to evaluate, or to solve a problem, knowing that it still has the same value. That doesn't change its meaning, only how we actually calculate it. The following page discusses a similar issue: Order of Operations vs. Associative Property http://mathforum.org/library/drmath/view/61447.html 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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