GCSE(F)

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. Similarly, `frac(3)(4)` of a pizza means splitting a pizza into four slices, then taking three of these slices: in other words, 3 x `frac(1)(4)`, or `frac(3)(4)`.

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.

For example, `frac(3)(5)` of 50 could be either:

• 50 x 3 ÷ 5, or

• 50 ÷ 5 x 3.

In this instance, the calculation is easier by dividing by 5 first and then multiplying by 3 to obtain an answer of 30. (Although BIDMAS says that Division happens before Multiplication, you can actually carry out a division and a multiplication in either order).

When using a mixed fraction as a multiplier, turn the mixed fraction into an improper fraction first. For example, 2 `frac(3)(8)` x 40:

= `frac(19)(8)` x 40

= `frac(19)(1)` x 5 (divide both 40 and 8 by 8)

= 95.

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?

Answer: 90

120 x `frac(3)(4)`

= 120 x 3 ÷ 4

= 360 ÷ 4

= 90

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?

Answer: 150

`frac(3)(8)` x 400

= 3 x 50 (Divide 400 ÷ 8 = 50)

= 150

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