How to Add and Subtract Fractions with Different Denominators

When the denominators in the fractions are different, you should expand or cancel the fractions to give them equal denominators. This does not change the value of the fraction. Expanding or canceling fractions to give them equal denominators is called finding the common denominator. There are several different methods for finding the common denominator:

Multiplying the denominators:

This will always work, but you can end up with very large numbers that make the calculation unnecessarily complicated.

Simplify one fraction:

If one fraction can be canceled so that the denominators are equal, you save a lot of work.

Expanding one fraction:

If one fraction can be expanded so that the denominators are equal, the calculation becomes easier.

Finding the lowest common denominator:

This way will always give you the easiest and nicest looking numbers to work with. I recommend that you focus on this one.

When adding fractions with different denominators to each other, you should begin with finding the common denominator. Then you need to expand or simplify all the fractions so that you end up with the common denominator in all of them. Finally, you can add the numerators together.

When subtracting fractions with different denominators from each other, you should begin with finding the common denominator. Then you need to expand or simplify all the fractions so that you end up with the common denominator in all of them. Finally, you can subtract the numerators from each other.

Although there is only one formula for addition and one for subtraction with different denominators, the common denominator can be found in several different ways. These next four entries will show most used methods.