Add and subtract fractions: Denominators are multiples

In a nutshell

To add and subtract fractions, they must have the same denominator. The lowest common denominator (LCD) is the smallest common multiple of the denominators of several fractions.

Common denominators

procedure

1.	Note which fraction has the larger denominator. This is the common denominator you need to use.
2.	Work out what you need to multiply the smaller denominator by to match the common denominator found in Step 1.
3.	Multiply the top and bottom of the fraction by the number you found in Step 2.

Example 1

Which is larger $\frac{3}{5}$ or $\frac{7}{10}$ ?

Find the common denominator (the larger denominator of the pair):

$10$ 

Work out the multiplier for the fraction with the smaller denominator:

$5 \times 2 = 10$ 

Multiply the numerator and denominator of the fraction by the multiplier:

$\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}$ 

Compare the two fractions:

$\frac{6}{10} < \frac{7}{10}$ 

 $\frac{7}{10}$ is larger than $\frac{6}{10}$ $( = \frac{3}{5})$ . Therefore $\frac{7}{10}$ is the larger fraction.

Adding and subtracting fractions

procedure

1.	Multiply up the fraction with the smallest denominator so both fractions have the same denominator.
2.	Add or subtract the numerators. Note: Remember not to add or subtract the denominators.
3.	Simplify the fraction if possible.

Example 2

What is $\frac{7}{12}+\frac{1}{6}$ ?

Multiply up the fraction with the smaller denominator ( $6$ ) to match the lowest common denominator ( $12$ ).

$6 \times 2 = 12$ 

$\frac{1}{6} \times 2 = \frac{1\times2}{6\times2} = \frac {2}{12}$ 

Add the numerators together.

$\frac{7}{12}+\frac{2}{12} = \frac{7+2}{12} = \frac{9}{12}$ 

Simplify the fraction. The numerator and denominator are both multiples of 3.

$\frac{9\div3}{12\div3} = \frac{3}{4}$ 

Note: Not all fractions can be simplified.