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### Simplifying Fractions by Factorizing

```
Date: 05/22/98 at 16:47:15
From: David Duranceau
Subject: Product of Primes

How do I get the product of primes for 144/360 and simplify it?
```

```
Date: 05/23/98 at 23:02:59
From: Doctor White
Subject: Re: Product of Primes

David:

Welcome to the exciting world of mathematics. One way to solve your
problem is to prime factor the numerator first, then prime factor the
denominator, and finally cancel. You can prime factor your numbers by
using a factor tree.

For example: simplify 188/240.

First, factor the numerator (188) into primes:

188
/ \
2 x 94
/ \
2 x 47

Then, factor the denominator (240) into primes:

240
/  \
2 x 120
/ \
2 x 60
/ \
2 x 30
/ \
2 x 15
/ \
3 x 5

We have:

188   2 x 2 x 47              47               47
--- = --------------------- = ------------- = ----
240   2 x 2 x 2 x 2 x 3 x 5   2 x 2 x 3 x 5    60

Two 2's from the numerator cancel out the two 2's in the denominator.
Hope this helps you to solve your problem. Come back to see us again
soon.

-Doctor White, The Math Forum
Check out our web site! http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Factoring Numbers
Middle School Fractions

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