Fractions of amounts

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

  • multiplying fractions
  • a unitary method

Multiplying fractions

Example

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

Unitary method

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

Example

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?

Multiplying fractions method

Find \frac{2}{3} of 24 by multiplying \frac{2}{3} by 24:

\frac{2}{3} \times \frac{24}{1} = \frac{48}{3} = 16

So: \frac{2}{3} of 24 = 16

Find \frac{3}{4} of 20 by multiplying \frac{3}{4} by 20:

\frac{3}{4} \times \frac{20}{1} = \frac{60}{4} = 15

So: \frac{3}{4} of 20 = 15

Compare the answers - 16 is the bigger number, so \frac{2}{3} of 24 is larger than \frac{3}{4} of 20.

This answer can also be written using an inequality sign:

\frac{2}{3} of 24 > \frac{3}{4} of 20

Unitary method

Work out \frac{2}{3} of 24 by first finding \frac{1}{3} of 24 and then multiplying the answer by 2.

\frac{1}{3} of 24 = 8 ( 24 \div 3 = 8).

8 \times 2 = 16, so \frac{2}{3} of 24 = 16.

Work out \frac{3}{4} of 20 by first finding \frac{1}{4} of 20, then multiplying the answer by 3.

\frac{1}{4} of 20 = 5 ( 20 \div 4 = 5).

5 \times 3 = 15, so \frac{3}{4} of 20 = 15.

Compare the answers - 16 is the bigger number, so \frac{2}{3} of 24 is larger than \frac{3}{4} of 20.

This answer can also be written with an inequality sign:

\frac{2}{3} of 24 > \frac{3}{4} of 20

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