Basic Fractions (CIE IGCSE Maths: Core)

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Last updated

15 February 2024

A fraction is part of a whole
A fraction is written as $\frac{a}{b}$ where a and b are integers
- The number on the top, a, is called the numerator
- The number on the bottom, b, is called the denominator
The values of the numerator and denominator tell us about the size of the fraction
- The denominator is how many parts the whole is split into
- The numerator is how many parts you have
  - For example, $\frac{2}{3}$ means that the whole is divided into 3 parts and you have 2 of these parts

Divide by the denominator and multiply by the numerator
- To shade $\frac{3}{5}$ of a grid of 20 squares
  - Divide 20 squares by 5 to get 4 squares
  - Multiply this amount by 3 to get 12 squares
  - Shade 12 squares
- To shade $\frac{1}{4}$ of a circle
  - Divide the circle into four quarters by drawing a horizontal and a vertical line through the centre
  - 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

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 $\frac{1}{3}$ of , divide it by 3
  - $90 \div 3 = 30$
- To find $\frac{2}{5}$ of , divide it by 5 then multiply it by 2
  - $60 \div 5 = 12$ , then $12 \times 2 = 24$
Method 2
Change the fraction into a decimal, then multiply
- To find $\frac{1}{4}$ of , turn into then multiply
  - $0.25 \times 16 = 4$
- To find $\frac{9}{10}$ of , turn into then multiply
  - $0.9 \times 15 = 13.5$
Method 3
Write both numbers as fractions and multiply two fractions together
- To find $\frac{2}{3}$ of , write as
  - work out $\frac{2}{3} \times \frac{60}{1} = \frac{120}{3} = 40$
- To find $\frac{5}{6}$ of $\frac{8}{3}$
  - - work out $\frac{5}{6} \times \frac{8}{3} = \frac{40}{18} = \frac{20}{9}$

the (exam) results speak for themselves:

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