When adding and subtracting fractions, the first thing to check is if the denominators are the same.

## Adding and Subtracting Fractions with Like Denominators

If the denominators are the same, then it's pretty easy: just add or subtract the numerators, and write the result over the same denominator.

You may get an answer which is not in lowest terms, even if the fractions you were adding and subtracting both were. In this case, you have to reduce the fraction.

## Adding and Subtracting Fractions with Unlike Denominators

If the denominators are not the same, then you have to use equivalent fractions which do have a common denominator. To do this, you need to find the least common multiple (LCM) of the two denominators.

For example, suppose you want to add:

The LCM of 3 and 11 is 33. So, we need to find fractions equivalent to 1/11 and 2/3 which have 33 in the denominator. Multiply the numerator and denominator of 1/11 by 3, and multiply the numerator and denominator of 2/3 by 11.

Now we have like denominators, and we can add as described above.