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Subtracting Fractions with Unlike Denominators

If the denominators are not the same, then you have to use equivalent fractions which do have a common denominator . To do this, you need to find the least common multiple (LCM) of the two denominators.

To subtract fractions with unlike denominators, rename the fractions with a common denominator. Then subtract and simplify.

For example, suppose you want to add:

6 7 2 3

The LCM of 3 and 11 is 33 . So, we need to find fractions equivalent to 6 7 and 2 3 which have 21 in the denominator. Multiply the numerator and denominator of 6 7 by 3 , and multiply the numerator and denominator of 2 3 by 7 .

6 × 3 7 × 3 2 × 7 3 × 7 = 18 21 14 21

Now we have like denominators, and we can subtract as described above.

= 4 21