Adding & Subtracting Fractions

How do I add or subtract two fractions?

Addition and subtraction are treated in exactly the same way when dealing with fractions
- Find the lowest common denominator
- Write each fraction as an equivalent fraction over this denominator
- Add (or subtract) the numerators and write this over a single denominator
  - do not add the denominators
- Simplify the fraction by cancelling common factors

What do I do if any of the fractions are mixed numbers?

Convert any mixed numbers into top heavy fractions
- Then add or subtract the fractions as usual
- Remember to convert the answer back to a mixed number if required

Worked example

(a) Find $\frac{2}{3} + \frac{1}{5}$ .

Find the lowest common denominator of 3 and 5
15 is the smallest number that can be divided by both 3 and 5

The lowest common denominator is 15

Write both fractions as equivalent fractions with a common denominator of 15
Multiply the numerator and denominator of the first fraction by 5
Multiply the numerator and denominator of the second fraction by 3

\frac{2 \times 5}{3 \times 5} + \frac{1 \times 3}{5 \times 3} = \frac{10}{15} + \frac{3}{15}

Add the numerators and write over a single denominator

$\frac{10 + 3}{15} = \frac{13}{15}$

There are no common factors that will cancel

$\frac{13}{15}$

(b) Find $3 \frac{3}{4} - \frac{5}{8}$ giving your answer as a mixed number.

Change the mixed number into a top heavy fraction

Multiply the denominator by the whole part and add to the numerator

Write this value over the denominator

$\frac{4 \times 3 + 3}{4} = \frac{15}{4}$

Find the lowest common denominator of 4 and 8
8 is the smallest number that by divided by both 4 and 8

The lowest common denominator is 8

Write both fractions as equivalent fractions over 8
Multiply the numerator and denominator of the first fraction by 2

$\frac{15 \times 2}{4 \times 2} - \frac{5}{8} = \frac{30}{8} - \frac{5}{8}$

Subtract the numerators and write over a single denominator

$\frac{30 - 5}{8} = \frac{25}{8}$

Change into a mixed number
Divide 25 by 8 to get 3 remainder 1

$3 \frac{1}{8}$

Adding & Subtracting Fractions (Edexcel GCSE Maths: Foundation)

Revision Note