Subtract Fractions with Unlike Denominators

Unlike denominators cannot be subtracted as they sit.

Rewrite both fractions with the same bottom, then subtract the tops.

Read it: Make one cut, then count

1/5 and 3/10 are cut differently: one bar in fifths, one in tenths. Cut each fifth into 2 and 1/5 is 2/10. Now the pieces line up: 2/10 + 3/10 = 5/10, which is 1/2.

1. Find a cut both bottom numbers go into: 5 and 10 both go into 10.
2. Write each fraction in that cut: 1/5 is 2/10, and 3/10 stays 3/10.
3. Add or take away the top numbers and keep the cut: 2/10 + 3/10 = 5/10, which is 1/2.

Pieces of different sizes cannot be counted together, so both bars are cut into the same pieces first.

Cutting a piece into smaller pieces does not change the amount: 1/5 and 2/10 shade the same part of a bar.

The least common denominator is the smallest cut both go into, so its pieces are the biggest that line up.

To add or subtract fractions with different denominators, write both in a common denominator, then add or subtract the numerators.

11/12 − 1/2 = ___ — 5/12. Cut both bars into 12: 11/12 stays 11/12 and 1/2 is 6/12. Take 6 twelfths from 11: 5/12.