Fractions are used commonly in everyday life, eg sale prices at 1/3 off, or recipes using 1/2 a tablespoon of an ingredient. Knowing how to use fractions is an important mathematical skill.
There are many methods to find fractions of amounts, including:
multiplying fractions
a unitary methodA mathematical method often used with proportional work. The method uses multiplication and division to calculate the value of one item.
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 one of something is worth first.
Example
Find \(\frac{3}{4}\) of 16.
First work out \(\frac{1}{4}\) of 16, then multiply the answer by 3 to get \(\frac{3}{4}\).
\(\frac{1}{4}\) 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:
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 inequalityA statement showing that an expression is less than, greater than, or not equal to another expression. sign:
\(\frac{2}{3}\) of 24 > \(\frac{3}{4}\) of 20
Unitary method
Find \(\frac{2}{3}\) 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, no matter which method is used.
Find \(\frac{3}{4}\) 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: