



There
is one normal pizza that is cut into 8 slices. 











Another
pizza is cut into 6 slices: 











We
have one slice from each. 


How
much pizza do we have ? 











We
have a problem. 


To
add fractions, the numbers on the bottom of both fractions 


MUST
be the same as each other. 


Here
they're not. 





Swell! 


Is
there a way to make them the same. 





With
math, there's always a way. 


In
fact for this puppy, 


there's
a bunch of ways. 





Here's
one now: 





On
another page we looked at some fractions 


and
tried to make the numbers smaller. 


Here
we're going to do the opposite. 


We
start with fractions with kinda small numbers and make them
bigger. 


The
trick is to end up with both of the bottom numbers being the
same. 


We don't
really care what number they end up being,



just
so they're the same. 





You
can multiply something by 1 and it won't change the value. 


The
deal is, a 1 doesn't always look like a 1. 


Sometimes
it's a fraction where the number on top 


and
the number on the bottom are the same. 


Like
this: 











We
can multiply ANYTHING we like by this fraction. 


Since
it's equal to 1, it won't change the value. 


OK,
that's all we need to know. 


Now
here's the problem we're working on again 


so
you won't have to scroll to find it: 











Now
we're ready. 


Here's
the plan: 





STEP
1: 


Write
down a fraction where both the top part and bottom part 


are
the same as the bottom part of the first fraction we want to add: 











STEP
2: 


Multiply
the second fraction in the problem by this: 





Remember,
the second
fraction here is equal to one
so this doesn't change the value 

This
is our NEW second fraction
in the problem 






STEP
3: 


Write
down a fraction where both the top part and bottom part 


are
the same as the bottom part of the second fraction we want to add: 











STEP
4: 


Multiply
the first fraction in the problem by this: 





Remember,
the second
fraction here is equal to one
so this doesn't change the value 

This
is our NEW first fraction
in the problem 






STEP
5: 


The
new fractions have the same bottom number so we can now add! 





All
we did
was multiply the original fractions
by something equal to 1
so the values didn't change. 








STEP
6: 


Simplify
the answer if possible: 











This
works with subtraction too! 











STEP
1: 








STEP
2: 





This
goes where the 1/6 was. 








STEP
3: 








STEP
4: 





This
goes where the 3/5 was. 








STEP
5: 











STEP
6: 











copyright 2005 Bruce Kirkpatrick 
