1 
+ 
1 
= 
1 + 1 
= 
2 




4 
4 
4 
4 
Step 3. Simplify the fraction:
(If you are unsure of the last step see the equivalent fractions page)
Example 2:
Step 1: The bottom numbers are different. We can't add them like this:

^{1}/_{3} 
+ 
^{1}/_{6} 
= 
? 












So we need to do something to make them have the same denominator.
In this case we can multiply the top and bottom of the first fraction (^{1}/_{3}) by 2, like this:
× 2 


× 2 
And now our question looks like this:
The bottom numbers (the denominators) are the same, so we can go to step 2.
Step 2: Add the top numbers (the numerators) and put them over the same denominator:

^{2}/_{6} 
+ 
^{1}/_{6} 
= 
^{3}/_{6} 












Step 3: Simplify the fraction:
^{3}/_{6} is the same as ^{1}/_{2}:

^{2}/_{6} 
+ 
^{1}/_{6} 
= 
^{3}/_{6} 
= 
^{1}/_{2} 










And we have the answer!
Example 3:
Again, they are different sizes!

^{1}/_{3} 
+ 
^{1}/_{5} 
= 
? 












But let us try dividing them into smaller sizes that will be the same:
By multiplying the top and bottom of the first fraction by 5 we ended up with ^{5}/_{15} :
× 5 


× 5 
And by multiplying the top and bottom of the second fraction by 3 we ended up with ^{3}/_{15} :
× 3 


× 3 
The denominators are now the same, so we can go ahead and add them:

^{5}/_{15} 
+ 
^{3}/_{15} 
= 
^{8}/_{15} 












Making the Denominators the Same
In the previous example how did I know to cut them into ^{1}/_{15}ths to make the denominators the same? You can read how to do this using either one of these methods:
They both work, use whichever you prefer!
Adding Mixed Fractions
I have a special page on Adding Mixed Fractions.