Fractions of a Quantity
Every question with a fully worked solution.
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Theory
To find a fraction of a quantity, divide by the denominator to find one part, then multiply by the numerator. In maths, of means multiply. This Year 7 maths page shows how to find fractions of numbers, money, time and measurements, change units first when needed, compare discounts and work backwards to the whole.
In maths, of means multiply: \(\dfrac{2}{3}\) of \(12\) is \(\dfrac{2}{3} \times 12\).
Step 1. Find one part: divide by the denominator. \(12 \div 3 = 4\). Step 2. Find the parts you need: multiply by the numerator. \(2 \times 4 = 8\).
A unit fraction (numerator \(1\)) needs Step 1 only: \(\dfrac{1}{4}\) of \(20\) is \(20 \div 4 = 5\).
Decimals: write the decimal as a fraction first: \(0.5 = \dfrac{1}{2}\), \(0.25 = \dfrac{1}{4}\), \(0.6 = \dfrac{3}{5}\). Units: if the answer must be in a smaller unit, change units first (\(1\) h \(= 60\) min, \(1\) kg \(= 1000\) g).
Divide by the bottom, multiply by the top:
How to find a fraction of a quantity
- Change units first if the answer needs a smaller unit.
- Divide by the denominator to find one part.
- Multiply by the numerator.
- Check the size against half the amount.
| \(2 \times 60\) | \(=\) | \(120\) |
| \(120 \div 3\) | \(=\) | \(40\) |
| \(2 \times 40\) | \(=\) | \(80\) |
\(80\) minutes
| \(210 \div 5\) | \(=\) | \(42\) |
| \(4 \times 42\) | \(=\) | \(168\) |
\(168\) m
(i) \(\dfrac{1}{6}\) of \(42\)
(ii) \(\dfrac{5}{8}\) of \(72\) kg
| \(42 \div 6\) | \(=\) | \(7\) |
| \(72 \div 8\) | \(=\) | \(9\) |
| \(5 \times 9\) | \(=\) | \(45\) |
(i) \(7\)
(ii) \(45\) kg (more than half of \(72\), as expected)
(i) \(0.6\) of \(\$45\)
(ii) \(\dfrac{2}{5}\) of \(3\) kg, in grams
| \(45 \div 5 \times 3\) | \(=\) | \(27\) |
| \(3000 \div 5 \times 2\) | \(=\) | \(1200\) |
(i) \(0.6 = \dfrac{3}{5}\), so \(\$27\)
(ii) \(3\) kg \(= 3000\) g, so \(1200\) g
| \(96 - 96 \div 8 \times 3\) | \(=\) | \(96 - 36 = 60\) |
| \(88 - 88 \div 4\) | \(=\) | \(88 - 22 = 66\) |
Shop A is cheaper by \(\$6\), even though its full price is higher.
| \(48 \div 2\) | \(=\) | \(24\) |
| \(5 \times 24\) | \(=\) | \(120\) |
There are \(120\) students. Check: \(\dfrac{2}{5}\) of \(120\) is \(48\).
Common pitfalls
Frequently asked questions
What does of mean in maths?
Multiply. \(\dfrac{2}{3}\) of \(12\) means \(\dfrac{2}{3} \times 12 = 8\).
How do you find a fraction of an amount?
Divide by the denominator, then multiply by the numerator.
How do you find 0.75 of an amount?
Write \(0.75\) as \(\dfrac{3}{4}\): divide by \(4\), then multiply by \(3\).
How do you find the whole if you know a fraction of it?
Find one part, then multiply by the denominator. If \(\dfrac{2}{5}\) is \(48\), the whole is \(120\).
Should I change units first?
Yes, if the answer must be in a smaller unit. \(2\) hours \(= 120\) minutes.