How Do You Add Fractions With Unlike Denominators?


Quick Answer

Fractions cannot be added unless they have like denominators. Therefore, to add fractions with unlike denominators, you have to convert one of the fractions so that it's expressed in terms of the other fraction. This is easiest to do by rewriting lower fractions to match higher ones.

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Full Answer

  1. Determine which denominator you want to use, and find the least common multiple

    Assume you have fractions of 2/3, 9/10 and 4/5. It's easier to multiply than to divide, so you need to find the least common multiple of all the denominators. In this case, the least common multiple is 30.

  2. Convert the fractions

    Start with the fraction with the largest number in the denominator; 10 multiplied by 3 is 30. To make the fraction equal, both the numerator and denominator have to be converted; 9/10 converts to 27/30. 2/3 converts to 20/30, and 4/5 converts to 24/30.

  3. Add the numerators

    You should have numerators of 27, 24 and 20. Adding them yields 71/30. Converting this fraction to a mixed number yields 2 11/30. After adding the numerators, it's best to resimplify the fraction for easy reading. In this case, 11 and 30 don't have any common factors, so the fraction part of the number has to stay as is.

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