How do you subtract two fractions with unlike denominators?

Answer 1

Make them into equivalent fractions with the same denominator, then the numerators can be subtracted and the resultant fraction simplified (if possible).

The first choice is the denominator for the equivalent fractions. Ideally this should be the lowest common multiple (LCM) of the given denominators, but just multiplying the two given denominators together will do.

The fractions can then be made into equivalent fractions with this chosen denominator.

If finding the LCM is too difficult, a simple "butterfly" (or "cross multiply") method can be used:

1. multiply the numerator of the first fraction by the denominator of the second fraction as the numerator of the equivalent first fraction;
2. multiply the denominator of the first fraction by the numerator of the second fraction as the numerator of the equivalent second fraction;
3. multiply the denominators together as the denominator of both of the equivalent fractions;
4. subtract the new numerators, keeping the new denominator;
5. simplify the result if possible.

eg 3/5 - 1/2 = 3x2/5x2 - 5x1/5x2

= 6/10 - 5/10

= 1/10

eg 5/6 - 1/2 = 5x2/6x2 - 6x1/6x2

= 10/12 - 6/12

= 4/12

= 1x4/3x4

= 1/3

The same method is used for addition of fractions with different denominators: add instead of subtract the numerators of the equivalent fractions.