Properties of SubtractionDate: 04/08/97 at 17:22:35 From: kim Sebastian Subject: Properties of Subtraction 1) Is subtraction commutative? How can this be justified? 2) Is subtraction associative? and how can this be justified? Thanks, Mrs. Sebastian Date: 04/09/97 at 15:01:08 From: Doctor Mike Subject: Re: Properties of Subtraction Dear Mrs. Sebastian, This is an interesting question, and the answer is subtle, but there IS an answer. It's sort of a "yes and no" answer. Here goes. 1. Subtraction is NOT commutative. If you evaluate 3-2 and 2-3 you get +1 and -1, respectively. NOT the same thing. 2. Subtraction is NOT associative. If you evaluate (3-2)-1 and 3-(2-1) you get 0 and 2, respectively. NOT the same thing. 3. However, **addition** is commutative for all numbers, even including negative numbers. An example related to (1.) is: 3 + -2 = -2 + 3 = +1 4. Also, **addition** is associative for all numbers, even the negative numbers. An example related to (2.) above is: (3 + -2) + -1 = 3 + (-2 + -1) = 0 To see this better, evaluate what is inside parentheses, getting ( 1 ) + -1 = 3 + ( -3 ) = 0 I hope this helps. Feel free to write back if you're not yet completely comfortable with this. I'm glad you want to get it. -Doctor Mike, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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