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math worksheets > > fractions > > adding fractions

How to Add Fractions

Adding fractions with COMMON denominators
Creating common denominators
Adding fractions with DIFFERENT denominators

Remember . . .
numerator/denominator

Here's a memory trick: the Denominator is the bottom, or Down number in a fraction -- and both Denominator and Down start with the letter D.

Adding Fractions with COMMON Denominators
Adding fractions with COMMON denominators is simple. Just add the top numbers (the numerators) together, and place the resulting answer in the top of a fraction using the existing denominator for the bottom number. Then reduce the fraction, if possible

Example 1: Simple fraction addition

1/5 + 2/5 = 3/5

No reduction is possible, so we have found the answer!

Example 2: Reducing the fraction answer

2/10 + 3/10 = 5/10

Then reduce:

5/10 = 1/2

Example 3: Converting the answer to a mixed number

2/4 + 3/4 = 5/4

Then convert the improper fraction to a mixed number:

5/4 = 1-1/4

Creating Common Denominators
How do we do that? Simple! Remember, if you multiply the top and bottom of a fraction by the same number, it doesn't affect the value of the fraction.
Example 1: If we have the fraction 2/3, we can multiply the top and bottom by 2, and not change its value: (2/2) x (2/3) = 4/6 Then if we reduce 4/6, we still get the original number, 2/3
Example 2: If we have the fraction 2/3, we could multiply top and bottom by 5, and not change its value: (5/5) x (2/3) = 10/15. Then if we reduce 10/15, we still get the original number, 2/3.
Why does this work? Because any number divided by itself equals one. 2/2 = 1, 5/5 = 1, etc. And any number multiplied by 1 equals itself! The point is, you don't change the value of a fraction if you multiply its top and bottom numbers by the same number!

Adding Fractions with DIFFERENT denominators
You can only add together fractions which have the same denominator, so you must first change one or both of the fractions so that you end up with two fractions having a common denominator. The easiest way to do this, is to simply select the opposite fraction's denominator to use as a top and bottom multiplier.

Example 1: Say you have the fractions 2/3 and 1/4
Select the denominator of the second fraction (4) and multiply the top and bottom of the first fraction (2/3) by that number:

4/4 x 2/3 = 8/12

Select the denominator of the first fraction (3) and multiply the top and bottom of the second fraction (1/4) by that number:

3/3 x 1/4 = 3/12

These two fractions (8/12 and 3/12) have common denominators - the number 12 on the bottom of the fraction.

Add these two new fractions together:

8/12 + 3/12 = 11/12

Example 2: Say you have the fractions 3/5 and 2/7
Select the denominator of the second fraction (7) and multiply the top and bottom of the first fraction (3/5) by that number

7/7 x 3/5 = 21/35

Select the denominator of the first fraction (5) and multiply the top and bottom of the second fraction (2/7) by that number

5/5 x 2/7 = 10/35

These two fractions (21/35 and 10/35) have common denominators -- the number 35 on the bottom of the fraction.

We can now add these two fractions together, because they have common denominators:

21/35 + 10/35 = 31/35

Got it? Great! Then go to the SuperKids Math Worksheet Creator for Basic Fractions, and give it a try!

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