Pupils should already be able to identify multiples of numbers, and common multiples of numbers within the multiplication tables (4NF–1 and 5MD–2). To be ready to progress to key stage 3, given 2 fractions pupils must be able to express them with the same denominator. Pupils should first work with pairs of fractions where one denominator is a multiple of the other, for example, 1/5 and 4/15 . They should learn that the denominator that is the multiple (here 15) can be used as a common denominator. Pupils should then be able to apply what they already know about writing equivalent fractions (5F–2) to express the fractions in a common denomination.
“We need to compare the denominators of 1/5 and 4/15.” “15 is a multiple of 5.”
“We can use 15 as the common denominator.” “We need to express both fractions in fifteenths.”
“We need to compare the denominators of 1/3 and 3/8 .” “8 is not a multiple of 3.”
“24 is a multiple of both 3 and 8.” “We can use 24 as the common denominator.”
“We need to express both fractions in twenty-fourths.”
Pupils must then learn to work with pairs of fractions where one denominator is not a multiple of the other, for example, 1/5 and 3/8. Pupils should recognise when 1 denominator is not a multiple of the other (here, 3 is not a factor of 8 and 8 is not a multiple of 3) and learn to identify a new denominator that is a common multiple of both denominators. Again, pupils should then be able to apply what they already know about writing equivalent fractions to express the fractions in a common denomination.
At key stage 3, pupils will learn to find the lowest common multiple of any 2 numbers. At key stage 2, being able to find a common multiple of the denominators by multiplying the 2 denominators is sufficient. This does not always result in the lowest common denominator (for example 1/6 and 2/9 can be expressed with a common denominator of 18 rather than 54), and if pupils can identify a lower common denominator then they should use it. Pupils may also recognise when the resulting pair of common denomination fractions can be simplified. Pupils should also be able to find a common denominator for more than 2 fractions, such as 1/3, 4/15 and 2/5, when 1 of the denominators is a multiple of the other denominators (in this case 15). Once pupils know how to express fractions with a common denominator, they can use this to compare and order fractions.