Fraction of a quantity

Often we wish to find out what fraction (or percentage) a 'part' of a quantity is of a 'whole'.

Example 1

The class was told that each student must read \(\dfrac{3}{8}\) of a 496-page book before the first day of term. How many pages must each student read?

Solution

The 'whole' is the 496-page book.

The 'part' is \(\dfrac{1}{8}\) so 8 parts is 496 pages.

Hence 1 part is 496 ÷ 8 = 62 pages.

Thus 3 parts = 62 × 3 = 186 pages.

So the students must read 186 pages.

This is called the unitary method of solving problems, where calculations are based on one part of the whole. The most important step is the first line – identifying which is the 'part' and which is the 'whole'.

Example 2

Binh's farm has produced 4008 cubic metres of hay. If he keeps \(\dfrac{7}{12}\) of this to feed his stock, how much will he have to sell at the market?

Solution

The whole is 4008 m³.

The part is \(\dfrac{1}{12}\).

Hence 1 part = 4008 ÷ 12 = 334 m³.

He keeps \(\dfrac{7}{12}\) so he sells \(\dfrac{5}{12}\).

So the amount of hay he sells = 5 × 334 = 1670 m³ of hay.