Basic Fractions (Edexcel GCSE Maths: Foundation)

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Naomi C

Last updated

16 February 2024

Introduction to Fractions

What is a fraction?

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

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.

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, but it's neater to group them together

Fractions of Amounts

How do I find a fraction of an amount?

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 $\frac{5}{6} \times \frac{8}{3} = \frac{40}{18} = \frac{20}{9}$

Equivalent Fractions

What are equivalent fractions?

Equivalent fractions are two fractions that represent the same amount
- They are different ways of writing the same thing
- For example, $\frac{1}{2}$ and $\frac{6}{12}$ are equivalent fractions

How do I find an equivalent fraction?

To find an equivalent fraction, multiply the top and bottom of a fraction by the same number
- $\frac{5}{6}$ is equivalent to $\frac{5 \times 2}{6 \times 2} = \frac{10}{12}$ and $\frac{5 \times 3}{6 \times 3} = \frac{15}{18}$ and $\frac{5 \times 4}{6 \times 4} = \frac{20}{24}$ etc.
- For each fraction, there are an infinite number of equivalent fractions

Examiner Tip

Using equivalent fractions can help with shading parts of diagrams questions as well as adding and subtracting fractions without a calculator.
- Remember that if you have your calculator in the exam you can use it to check your work.

Simplifying Fractions

What is a simplified fraction?

A simplified fraction is a fraction that is written using the smallest possible integer values
- Simplifying turns a fraction into an 'easier' equivalent fraction
If both the numerator and denominator can be divided by the same number (called a common factor), the fraction can be simplified
Simplifying is also called cancelling a fraction

How do I simplify fractions?

To simplify the fraction, divide the top and bottom by the common factor

- $\frac{12}{18} = \frac{12 \div 6}{18 \div 6} = \frac{2}{3}$
- $\frac{25}{45} = \frac{25 \div 5}{45 \div 5} = \frac{5}{9}$

Examiner Tip

Make use of your calculator if you have it in your exam.
- Type any fraction into it and pressing equals will automatically simplify the fraction for you.
- If the question asks you to show your working, you must show which number you divided by.

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