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 and are equivalent fractions. They can both be shown to be equivalent to the simplest form of 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?
Find the larger of these two fractions: or .
and 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
= multiplying numerator and denominator by 8
= multiplying numerator and denominator by 3
So is the larger fraction