Skill: Subtract fractions with unlike denominators

To subtract fractions with unlike denominators, first rewrite them with a common denominator. Then subtract the numerators and keep the common denominator. The denominators show the size of the pieces, so they are not subtracted.

Example

Subtract:

$$4\frac14-1\frac23$$

1. Find a common denominator

The denominators are $4$ and $3$. Their least common denominator is $12$.

Rewrite each fraction:

$$\frac14=\frac{3}{12} \qquad\text{and}\qquad \frac23=\frac{8}{12}$$

So the problem becomes:

$$4\frac{3}{12}-1\frac{8}{12}$$

2. Regroup because $\frac{3}{12}$ is smaller than $\frac{8}{12}$

Borrow $1$ whole from $4$:

$$4\frac{3}{12}=3\frac{15}{12}$$

This works because $1=\frac{12}{12}$, so:

$$3\frac{3}{12}+\frac{12}{12}=3\frac{15}{12}$$

Now subtract:

$$3\frac{15}{12}-1\frac{8}{12}$$

3. Subtract the whole numbers and fractions

$$3-1=2$$

and

$$\frac{15}{12}-\frac{8}{12}=\frac{7}{12}$$

Therefore,

$$\boxed{4\frac14-1\frac23=2\frac7{12}}$$

Remember: Make equivalent fractions with a common denominator, subtract only the numerators, and keep the denominator.