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Simplify Simplify
Simplification of Fractions

 
 On another page, you may have seen how to multiply fractions. 
 If you didn't see that page, here's a quick review.
 When you multiply two fractions together, 
 you multiply both the number on the top 
 and the number on the bottom. 
 Like this:
 

 Look at that fraction we got for an answer. 
 The number on top (6) is exactly half as big 
 as the number on the bottom (12). 
 If this was a pizza, the whole pizza would have 12 slices 
 and we would have 6. 
 Half of them. 
 Most of the time the way you write one half as a fraction 
 is with a 1 on the top and a 2 on the bottom. 
 Since the fraction with 6 on the top and 12 on the bottom 
 is worth the same, 
 we can write:
 

 
 That's OK, 
 But it would be great if we had a math way to do this kind of stuff.
 WE DO!
 Here's how it works.
 Start with:
 

 
 Now break up the 6 and the 12 into prime factors:
 

 
 
 Now write the fraction as prime factors:
 

 
 Now we get to use a new trick. 
 To use this trick, everything on top (in the numerator) 
 MUST be multiplied together. 
 Also, everything on the bottom (in the denominator) 
 MUST be multiplied together.
 It is. 
 OK, now what?
 Now if the same number shows up on the top and on the bottom, 
 you can turn them both into 1's
 
 You're kidding! 
 
 Nope! Works every time. 
 So:
 

Change a 3 on top
and a 3 on the bottom 
to 1's
 

Change a 2 on top
and a 2 on the bottom 
to 1's
 

And multiply
 
 Remember, 
 we can only do this trick if everything is multiplied together. 
 If we have stuff like:
 

OR

 
 We can't change anything to 1's because of the + and the -.
 
 Example:
 
 Simplify:
 

 
 Example:
 
 Simplify:
 

 
 Example:
 
 Simplify:
 

 

   copyright 2005 Bruce Kirkpatrick
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