Adding fractions

Last updated: 11 Nov 2008

Addition is easy when the denominators are the same. You add the numerators and keep the denominator the same.

Example of Addition (1)

Both fractions are expressed in fifths and so the denominator is 5 in both fractions. In this case, simply add the two numerators 1 and 3 to give you 4. The denominator stays the same, so the sum is .

Sadly, it is much more common to find that the denominators are different. In these cases you have to reorganize the fractions so that they have the same denominator. This is called a common denominator.

If the two denominators have no common factors or are variables, then you simply multiply them together to find the common denominator. You then have to multiply the numerators by the same value that you multiplied the denominator by so that the fractions still have the same value. Now you have two fractions with the same denominator you can add them up as before.

Example of Addition (2)

The denominators are 3 and 4, which are different. Therefore we need to find a common denominator. Since the denominators 3 and 4 have no common factors, multiply them together .

Then multiply the numerators to give us the same fractions but expressed in twelfths i.e. with the same denominator.

Now we can add them.

If the two denominators do have a common factor then it is usually best to find the lowest common denominator you can, which will be smaller than that given by multiplying the two denominators together.

Example of Addition (3)

First find a common denominator. We could multiply the denominators 8 and 12 together to give us a common denominator of 96. But, since they have a common factor of 4 we can work with the lowest common denominator which is 24 and will make our calculations a little simpler.

Then multiply the numerators.

Now we can add them.

Next page: Subtracting fractions