Unlike fractions are formed by combining different unit fractions. For example,

$\frac{2}{3}$ is formed combining two of

$\frac{1}{3}$ while

$\frac{2}{7}$ is formed by combining of two of

$\frac{1}{7}$. Hence the subtraction can be performed on unlike fractions, only after expressing them as equivalent fractions sharing a common denominator.

The lowest common multiple of the two denominators is used in this process as the common denominator and hence called the lowest common denominator (LCD). Then the difference between the equivalent fractions are found in the same manner as with like fractions.

### Solved Example

**Question: **Find the difference of

$\frac{1}{2}$ -

$\frac{3}{8}$ ** Solution: **

The first task is to find the common denominator to be used in the equivalent fractions $\frac{1}{2}$ and $\frac{3}{8}$.

The LCM of 2 and 8 is 8 and 8 is used as the common denominator.

Since the second fraction $\frac{3}{8}$ already has 8 as its denominator, it is only required to write $\frac{1}{2}$ in its equivalent form with denominator 8.

$\frac{1}{2}$ = $\frac{1\times 4}{2\times 4}$ = $\frac{4}{8}$.

Hence $\frac{1}{2}$ - $\frac{3}{8}$ = $\frac{4}{8}$ - $\frac{3}{8}$ = $\frac{1}{8}$.