How to Add Fractions with Unlike Denominators

You can only add fractions that are cut into the same size pieces. When the bottom numbers (denominators) differ, first rewrite both fractions with a common denominator, then add the tops.

Try it with your own problem ↓

The steps

Find a common denominator: the least common multiple (LCM) of the two denominators is the neatest choice.
Rewrite each fraction with that denominator by multiplying its top and bottom by the same number.
Add the numerators. Keep the denominator the same.
Simplify the result, and turn an improper fraction into a mixed number if you like.

A worked example

Work out 3/4 + 5/6.

Multiples of 4: 4, 8, 12. Multiples of 6: 6, 12. The common denominator is 12.
3/4 = (3 × 3)/(4 × 3) = 9/12.
5/6 = (5 × 2)/(6 × 2) = 10/12.
Add the tops: 9/12 + 10/12 = 19/12.
19/12 is improper. 19 ÷ 12 = 1 remainder 7, so it is 1 7/12. It can't be simplified because 7 and 12 share no factor.

3/4 + 5/6 = 19/12 = 1 7/12. Check with decimals: 0.75 + 0.8333… = 1.5833…, and 1 7/12 = 1.5833…. ✓

Try it with your own problem

Open the free The Carry Column with this example already filled in. It shows every step, and you can type over it with your own numbers.

Work it out: 3/4 + 5/6Opens The Carry Column with this example

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Common mistakes

Adding the tops and the bottoms. 3/4 + 5/6 is not 8/10. The bottom number names the size of the pieces, and it doesn't add.
Changing only the denominator. If you multiply the bottom by 3, multiply the top by 3 too.
Forgetting to simplify. Check whether the answer reduces.
Using a common denominator that isn't common. Make sure both denominators divide into it.

Questions people ask

Do I have to use the least common denominator?

No. Multiplying the two denominators (4 × 6 = 24) always works, but you will have bigger numbers to simplify at the end.

How do I add mixed numbers?

Add the whole numbers and the fractions separately, then combine. Or turn each into an improper fraction first.

Does subtraction work the same way?

Yes. Get a common denominator, then subtract the numerators instead.

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