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Teaching mathematics
Teaching mathematics

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2.2 Ordering fractions

The understanding of equivalence among fractions can also cause a challenge because numbers which effectively have different labels can mean the same quantity of proportion (depending on how they are being used). As an example four divided by six and 10 divided by 15 are equivalent fractions. They can both be shown to be equivalent to the simplest form of two divided by three by ‘cancelling down’ i.e. dividing the numerator and denominator in each fraction by the same common factor.

Since the value of the fraction is determined by the relation between the numerator and the denominator it can be difficult to compare the sizes of the two fractions. The usual method when comparing the size of two fractions is to find equivalences which have the same denominator.

Activity 5 Which fraction is larger?

Timing: Allow 10 minutes

Find the larger of these two fractions: two divided by three or five divided by eight.


two divided by three and five divided by eight which is larger?

Both the denominators 3 and 8 are factors of 24 (the least common multiple or LCM) so you can find equivalent fractions whose denominators are 24

two divided by three = 16 divided by 24 multiplying numerator and denominator by 8

five divided by eight = 15 divided by 24 multiplying numerator and denominator by 3

So two divided by three is the larger fraction