Different denominators

You can't add 1/2 + 1/3 directly — the pieces are different sizes. First you have to make them match, with a common denominator.

Find a common denominator

You need a number both denominators divide into. For 2 and 3, the smallest is 6. Convert each fraction to sixths:

• 1/2 = 3/6 (multiply top and bottom by 3)
• 1/3 = 2/6 (multiply top and bottom by 2)

Now add

Same denominator at last, so add the tops:

3/6 + 2/6 = 5/6

The quick way to a common denominator

Stuck finding one? Multiply the two denominators. For 1/4 + 1/6 that gives 24 — it always works, though you may need to simplify at the end. (The smallest common denominator here is 12, but 24 gets you the right answer too.)