Fractions of amounts

There are many methods to find fractions of amounts, including:

Find \(\frac{2}{5}\) of 40.

Multiply \(\frac{2}{5}\) by 40.

\(\frac{2}{5} \times 40\)

\(= \frac{2}{5} \times \frac{40}{1}\) (40 can be written as \(\frac{40}{1}\))

\(= \frac{80}{5}\)

= 16

A unitary method simply means finding out what 1 of something is worth first.

Work out \(\frac{3}{4}\) of 16.

First work out \(\frac{1}{4}\)of 16, by dividing 16 by 4.

\(\frac{1}{4}\) of 16 is 4.

Then multiply the answer by 3 to work out \(\frac{3}{4}\).

\(\frac{3}{4}\) of 16 is \(3 \times 4 = 12\).

\(\frac{1}{4}\) of 16 is the same as \(16 \div 4\) which is 4.

If \(\frac{1}{4}\) of 16 = 4, then \(\frac{3}{4}\) of 16 must be three times this amount, so \(\frac{3}{4}\) of 16 = 12 (\(4 \times 3 = 12\)).

Question

Which is larger, \(\frac{2}{3}\) of 24 or \(\frac{3}{4}\) of 20?