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Adding Fractions

There are 3 Simple Steps to add fractions:

  • Step 1: Make sure the bottom numbers (the denominators) are the same
  • Step 2: Add the top numbers (the numerators). Put the answer over the the same denominator as in step 1
  • Step 3: Simplify the fraction (if needed).

Example 1:

1  +  1
4 4

Step 1. The bottom numbers are already the same. Go straight to step 2.

Step 2. Add the top numbers and put the answer over the same denominator:

 

1  +  1  =  1 + 1  =  2
4 4 4 4

 

Step 3. Simplify the fraction:

2  =  1
4 2

 

(If you are unsure of the last step see the equivalent fractions page)

 

Example 2:

1  +  1
3 6

Step 1: The bottom numbers are different. We can't add them like this:

  1/3 + 1/6 = ?      
  1/3   1/6   1   1  

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
1   =   2
3 6
× 2

And now our question looks like this:

  2/6 + 1/6          
  2/6   1/6   1   1  

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      
  2/6   1/6   3/6   1  



Step 3: Simplify the fraction:

3/6 is the same as 1/2:

  2/6 + 1/6 = 3/6 = 1/2  
  2/6   1/6   3/6   1/2  

And we have the answer!

Example 3:

1  +  1
3 5

Again, they are different sizes!

  1/3 + 1/5 = ?      
  1/3   1/5   1   1  

But let us try dividing them into smaller sizes that will be the same:

  5/15 + 3/15          
  5/15   3/15   1   1  

By multiplying the top and bottom of the first fraction by 5 we ended up with 5/15 :

× 5
1   =   5
3 15
× 5

And by multiplying the top and bottom of the second fraction by 3 we ended up with 3/15 :

× 3
1   =   3
5 15
× 3

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

  5/15 + 3/15 = 8/15      
  5/15   3/15   8/15   1  

 

Making the Denominators the Same

In the previous example how did I know to cut them into 1/15ths 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.