WTMaths logo
Fractions as Operators

Fractions as Operators

A fraction can be seen as a division waiting to happen: for example, `frac(1)(4)` of a pizza means a whole pizza split, or divided, into four equal slices.

When a fraction of an amount is required, the fraction acts as an operator or function on the amount. The original amount is multiplied by the numerator and divided by the denominator. Note that the multiplication and division can be calculated in either order.

When using a mixed fraction as a multiplier, turn the mixed fraction into an improper fraction first.

Example 1

Three quarters of the passengers at a train station are waiting for a train to Birmingham. If there are 120 passengers at the station, how many are waiting for the train to Birmingham?

120 x `frac(3)(4)`

= 120 x 3 ÷ 4

= 360 ÷ 4

= 90

Answer: 90

Example 2

After a flood in the stock room, `frac(3)(8)` of the boxes of chocolates were found to be damaged. If there were originally 400 boxes of chocolates, how many were damaged?

`frac(3)(8)` x 400

= 3 x 50 (Divide 400 ÷ 8 = 50)

= 150

Answer: 150