Fractions | Cambridge O Level Maths Revision Notes 2025

Introduction to Fractions

A fraction is part of a whole
A fraction is written as $\frac{a}{b}$ where a and b are whole numbers (integers)

Divide by the denominator and multiply by the numerator
To shade $\frac{3}{5}$ of a grid of 20 squares...
- first divide 20 squares by 5 to get 4 squares
- then multiply this amount by 3 to get 12 squares - this is how many to shade
Sometimes it will be obvious as the grid will be organised into the number of rows or columns given on the denominator
- For example, to shade $\frac{3}{5}$ of a grid of 20 squares, when the grid is in 4 rows of 5, shade 3 of the rows of 5 squares
To shade $\frac{1}{4}$ of a circle...
- divide the circle into four quarters (like sharing a pizza equally between four people)
- then shade one of these quarters

Shade $\frac{5}{7}$ of the grid below.

Count the total number of squares in the grid

total of 21 squares

Divide 21 by 7

21 ÷ 7 = 3 squares

It doesn't matter which 15 you shade, but it's neater to group them together

Method 1: divide by the denominator and multiply by the numerator
- To find $\frac{1}{2}$ of an amount, divide it by 2
- To find $\frac{1}{3}$ of an amount, divide it by 3
- To find $\frac{2}{5}$ of an amount, divide it by 5 then multiply it by 2
  - $\frac{2}{5}$ of 60: do 60 ÷ 5 = 12, then 12 × 2 = 24
Method 2 (if you know how to change fractions into decimals): change the fraction into a decimal, then multiply
- To find $\frac{1}{4}$ of an amount, multiply the amount by 0.25
- To find $\frac{9}{10}$ of an amount, multiply the amount by 0.9
Method 3 (if you know how to multiply fractions): write both numbers as fractions and multiply two fractions together
- To find $\frac{2}{3}$ of 60, work out $\frac{2}{3} \times \frac{60}{1}$
- To find $\frac{5}{6}$ of $\frac{8}{3}$ , work out $\frac{5}{6} \times \frac{8}{3}$