



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 
