Concept

Unlike fractions are fractions with different denominators.

A fraction is said to be in simplest form if its numerator and denominator have no common factors other than 1.

Rule

To subtract fractions with unlike denominators,

1. If the denominators are not the same, find an equivalent fraction with a common denominator. 
2. Simplify, if needed, by dividing the numerator and the denominator by their greatest common factor. 

Example

Subtract. 

Write the difference.

$\frac{1}{6}-\frac{1}{10}$

Solution

If the denominators are not the same, find an equivalent fraction with a common denominator. 

Multiples of 6 are: 6, 12, 18, 24, 30
Multiples of 10 are: 10, 20, 30, 40, 50

The least common multiple of 6 and 10 is 30.

Rewrite the fractions with the common denominator 30.

To rewrite $\frac{1}{6}$multiply the numerator and denominator by the factor 5.
 $\frac{1 \times 5}{6 \times 5} \mathrm{=} \frac{5}{30}$

To rewrite $\frac{1}{10}$multiply the numerator and denominator by the factor 3.
 $\frac{1 \times 3}{10 \times 3} \mathrm{=} \frac{3}{30}$

Subtract $\frac{5}{30}-\frac{3}{30}$

 Simplify $\frac{2}{30}$by dividing the numerator and denominator by their greatest common factor.

Factors for 2 are: 1, 2
Factors for 30 are: 1, 2, 3, 5, 6, 10, 15, 30

The greatest common factor of 2 and 30 is 2.

$\frac{2 ÷ 2}{30 ÷ 2} \mathrm{=} \frac{1}{15}$

 Answer: $\frac{1}{15}$

Pre-requisite Skills

Equivalent Fractions (4.14.5)

Simplifying fractions (5.10.6)