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Numbers, units and arithmetic
Numbers, units and arithmetic

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1.6 Fractions

A fraction is written as one number over another (such as three divided by 10) and means the top number divided by the bottom number. The top number, 3, is called the numerator and the bottom number, 10, is called the denominator. Whole numbers can be written as fractions with the denominator 1. Thus, 2 can be written as two divided by one. The same fraction may be written in different ways, depending upon the context.

The top of a fraction is called the numerator.

The bottom of a fraction is called the denominator.

Click on the tabs below and note that all of the shaded areas represent the same fraction of the circle: one third of it. So

equation sequence part 1 one divided by three equals part 2 two divided by six equals part 3 four divided by 12
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Fractions which are equal in value but are written with different numerators and denominators are called equivalent fractions.

You can find equivalent fractions for any given fraction by multiplying top and bottom by the same whole number.

Decimals are themselves a special form of fractions (0.3 is three divided by 10). There are situations where it is simpler to use fractions. For example, if you wanted to divide a circle into six equal pieces, you think of the fraction one divided by six. There is no exact decimal equivalent of one divided by six (because dividing 6 into 1.0000 … produces a never-ending string of 6s: 0.1666 …). Recipes often ask for fractions, such as ‘half a pint of milk’ or a cooking time of ‘three-quarters of an hour’.

Example 5

What fraction of the circle is shaded in the diagram below?


The fraction is number of shaded parts divided by total number of parts. The circle is divided into 8 equal sections, so each section is one divided by eight. Three of them are shaded so the shaded part is three divided by eight of the circle.

However there are other equivalent fractions which represent the same shaded area, obtained by multipying the numerator and the denominator by the same whole number, e.g. six divided by 16.