Subtracting Fractions

Subtracting works exactly like adding: make the denominators match, then subtract the tops and keep the bottom. $\frac{4}{5}-\frac{1}{3}$: 15 is a multiple of 5 and of 3. $\frac{4}{5}$ is $\frac{12}{15}$ and $\frac{1}{3}$ is $\frac{5}{15}$, so the line becomes $\frac{12}{15}-\frac{5}{15}$, and 12 minus 5 is 7: $\frac{7}{15}$.

The bottom stays 15 for the same reason as before. It names the size of the pieces, and taking some pieces away does not resize the ones that are left.

You can check a difference by adding back what you took away: $\frac{7}{15}+\frac{5}{15}$ is $\frac{12}{15}$, the fraction you started from. And as always, simplify at the end if the top and the bottom share a factor.