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### 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/
```
Associated Topics:
Elementary Fractions
Elementary Multiplication
Middle School Fractions

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