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/