Adding Fractions With Different Denominators

Why you can't just add

Halves and thirds are different sizes, so “1 half + 1 third” is like adding 1 inch and 1 foot: you can't count them together until they're in the same unit. Sixths work for both, because a half is 3 sixths and a third is 2 sixths. Now you're counting the same thing.

The steps

1. List multiples of each bottom number until you find a match. For 3/4 + 1/6: 4, 8, 12 and 6, 12. 2. Rewrite each fraction. 3/4 = 9/12, since 3 × 3 = 9 and 4 × 3 = 12. 1/6 = 2/12, since 1 × 2 = 2 and 6 × 2 = 12. 3. Add the tops: 9/12 + 2/12 = 11/12. 4. Simplify if you can.

Worked examples

1/2 + 1/4: 4 is already a multiple of 2, so 2/4 + 1/4 = 3/4. 2/3 + 1/4: common denominator 12, so 8/12 + 3/12 = 11/12. 3/5 − 1/2: common denominator 10, so 6/10 − 5/10 = 1/10. The step that goes wrong most often is changing the bottom without changing the top. Whatever you multiply the bottom by, multiply the top by the same number.

How to do it with Fraction Bakery

1. Check that equivalent fractions feel solid. This whole method depends on them.
2. Practice rewriting with the equivalent fractions game and worksheets.
3. Make sure like denominators are easy.
4. Then work through the examples above on paper. Our game doesn't cover unlike denominators yet.

Questions people ask