How to add fractions, step by step

Adding fractions is easy once you know one rule: the bottom numbers have to match first. Here's how to do it, with examples.

The parts of a fraction

In 3/4, the top number (3) is the numerator: how many pieces you have. The bottom number (4) is the denominator: how many equal pieces make one whole.

Case 1: same bottom numbers

When the denominators are the same, add the top numbers and keep the bottom number.

Case 2: different bottom numbers

You can't add 1/2 + 1/3 straight away, because halves and thirds are different-sized pieces. First make the bottom numbers the same.

1. Find a common denominator. Look for a number both 2 and 3 go into. 6 works, because 2 × 3 = 6.
2. Rewrite each fraction. Multiply the top and bottom by the same number: 1/2 = 1 × 3/2 × 3 = 3/6 and 1/3 = 1 × 2/3 × 2 = 2/6
3. Add the tops. 3/6 + 2/6 = 5/6
4. Simplify if you can. 5 and 6 share no common factor, so 5/6 is already simplest.

Try one yourself

Mixed numbers

For mixed numbers like 1 1/2 + 2 1/4, add the whole numbers (1 + 2 = 3), then add the fractions (1/2 + 1/4 = 3/4), and put them together: 3 3/4.

Common mistakes

• Adding the bottom numbers: 1/2 + 1/2 is not 2/4. It's 2/2, which is 1 whole.
• Changing only the top or only the bottom when rewriting. Always multiply both by the same number.
• Forgetting to simplify the answer at the end.