Why Cancel?Date: 02/25/2003 at 21:28:25 From: Malinda Subject: Why you have to cancel Why do you have to cancel numbers? Like say 2/10 X 5/10 = Why do you cancel when you can have the answer when you just multiply it out and then reduce? Date: 02/25/2003 at 23:14:32 From: Doctor Peterson Subject: Re: Why you have to cancel Hi, Malinda. You don't _have_ to cancel, any more than you have to take the short route when you walk somewhere, or walk when you can ride. Canceling just saves effort, so it's good to know how to do it. And sometimes when you forget to cancel first, you feel really stupid afterward when you realize how much time you wasted! When you multiply first and then cancel, you are doing a lot of work only to undo it. In a simple problem, that's not hard; but suppose you have to multiply 155/346 by 346/754. Why would you bother to multiply 155*346 and 346*754 when you know you'll be dividing both numbers by 346 afterward? And you might not even notice that you can simplify in that case; simplifying is a much harder task than just dividing, because you have to look for common factors to divide by, and when they are large like this, you may miss them. It's much easier to spot opportunities to simplify when the numbers are still small. And that's a general rule for life: fix problems as early as possible, before they have a chance to grow bigger! Here are some discussions of canceling in more complex situations: Multiplying Fractions by Cancellation http://mathforum.org/library/drmath/view/58151.html Multiplying Fractions http://mathforum.org/library/drmath/view/58079.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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