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Everyday maths 1 (Wales)
Everyday maths 1 (Wales)

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3 Fractions

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Figure 10 Looking at fractions

What is a fraction?

A fraction is defined as a part of a whole. So for example one divided by three, or ‘one third’, is one part of three parts, all of equal size.

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Figure 11 Presenting a fraction: one third

Fractions are an important feature of everyday life. They could ensure that you get the best deal when shopping – or that you receive the largest slice of pizza! As you go through this section, you’ll see how fractions could be used when you are shopping or within the workplace.

Fractions are related to decimals and percentages, which you’ll look at in the sections that follow this one.

This section will help you to:

  • order and compare fractions
  • identify equivalencies between fractions
  • calculate parts of whole quantities and measurements (e.g. calculate discounts in sales).

Please look at the following example before you carry out the activity:

A half can be written as one divided by two, i.e. one of two equal parts.

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Figure 12 Presenting a fraction: one half

A quarter can be written as one divided by four, i.e. one of four equal parts.

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Figure 13 Presenting a fraction: one quarter

An eighth can be written as one divided by eight, i.e. one of eight equal parts.

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Figure 14 Presenting a fraction: one eighth

Hint: The top of the fraction is called the numerator. The bottom of the fraction is called the denominator. Any fraction with a 1 on the top is called a ‘unit fraction’, so one divided by two, one divided by three and one divided by 12, for example, are all unit fractions.

A fraction may not have a 1 on the top. For example, two divided by three means ‘two out of three parts’, or ‘two thirds’.

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Figure 15 Presenting a fraction: two thirds

Example: Where there’s a will, there’s a fraction

Lord Walton draws up a will to decide who will inherit the family estate. He proposes to leave one divided by two of the estate to his son, one divided by three to his daughter and one divided by six to his brother.

  1. Who gets the biggest share?
  2. Who gets the smallest share?


When numerators of fractions are all 1, the larger the denominator of the fraction, the smaller the fraction.

Looking at the example above, the fractions can be put in order of size starting from the smallest:

one divided by six, one divided by three, one divided by two


  1. The biggest share (one divided by two) goes to his son.
  2. The smallest share (one divided by six) goes to his brother.

If you’re asked to arrange a group of fractions into size order, it’s sometimes helpful to change the denominators to the same number. This can be done by looking for the lowest common multiple – that is, the number that all of the denominators are multiples of.