Introduction to Fractions (Cambridge International IGCSE Maths)

Introduction to fractions

What is a fraction?

• 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 each whole number is split into

  • The numerator is how many parts you have

    • For example, $\frac{2}{3}$ means that each whole number is divided into 3 parts and you have 2 of these parts

• A fraction is less than 1 if the numerator is smaller than the denominator

• A fraction is more than 1 if the numerator is bigger than the denominator

How do I shade a fraction on a diagram?

• 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

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

Answer:

Count the total number of squares in the grid

*Total of 21 squares ***

Divide 21 by 7

• 21 ÷ 7 = 3** *

Multiply by 5

*3 × 5 = 15 *

Shade 15 squares

• It doesn't matter which 15 you shade
• It's neater to group them together