When adding fractions, the first thing to check is if the denominators are the same.
Adding Fractions with Like Denominators
Fractions with the same denominators are called like fractions.
To add fractions with like denominators, add the numerators , and write the sum over the denominator.
Since the denominators are the same, add the numerators.
Adding 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 and is . So, we need to find fractions equivalent to and which have in the denominator. Multiply the numerator and denominator of by , and multiply the numerator and denominator of by .
Now we have like denominators, and we can add as described above.