Subtracting works just like adding unlike fractions: first make the pieces the same size, then take some away.
Key idea
Rename the fractions with a common denominator, then subtract the numerators. Keep the denominator. Check by adding your answer back.
Why it works
You can take 2 twelfths from 9 twelfths because they are the same kind of piece. You cannot take a third straight out of three fourths, since thirds do not line up with fourths. Renamed as twelfths, $\frac{3}{4} - \frac{1}{3}$ is $\frac{9}{12} - \frac{4}{12}$, and the answer is the 5 twelfths left over.
Worked examples
Worked example: Fourths and thirds
Find $\frac{3}{4} - \frac{1}{3}$.
- Use 12: $\frac{3}{4} = \frac{9}{12}$ and $\frac{1}{3} = \frac{4}{12}$.
- $\frac{9}{12} - \frac{4}{12} = \frac{5}{12}$.
- Check: $\frac{5}{12} + \frac{4}{12} = \frac{9}{12} = \frac{3}{4}$.
Answer: $\frac{5}{12}$
Worked example: Simplify at the end
Find $\frac{5}{6} - \frac{1}{2}$.
- 6 already works: $\frac{1}{2} = \frac{3}{6}$.
- $\frac{5}{6} - \frac{3}{6} = \frac{2}{6}$.
- Simplify: $\frac{2}{6} = \frac{1}{3}$.
Answer: $\frac{1}{3}$
Common mistake
Subtracting tops and bottoms: $\frac{3}{4} - \frac{1}{3} = \frac{2}{1} = 2$. Taking something away from less than 1 cannot give 2. Always rename first, and check by adding back.