Find a fraction of a quantity - Unit fraction
Theory
A unit fraction has \(1\) on top, like \(\dfrac{1}{6}\). To find \(\dfrac{1}{6}\) of an amount, share it into \(6\) equal parts: divide by the denominator. This Year 6 maths page shows how to find unit fractions of numbers, money and measurements, and what to do when the amount does not divide exactly.
A unit fraction is a fraction with numerator \(1\): \(\dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{4}, \dfrac{1}{5}, \ldots\)
The denominator tells you how many equal parts to make. \(\dfrac{1}{6}\) of \(54\) is one of \(6\) equal parts: \(54 \div 6 = 9\).
The bigger the denominator, the smaller each part: \(\dfrac{1}{8}\) of an amount is less than \(\dfrac{1}{4}\) of it.
If the amount does not divide exactly, the answer is a mixed number: \(\dfrac{1}{4}\) of \(9\) is \(2\dfrac{1}{4}\).
Check by multiplying: \(9 \times 6 = 54\).
A unit fraction of an amount:
How to find a unit fraction of an amount
- Read the denominator: that is the number of equal parts.
- Divide the amount by the denominator.
- Write the units, and check by multiplying back.
| \(54 \div 6\) | \(=\) | \(9\) |
\(9\).
(i) \(\dfrac{1}{8}\) of \(64\)
(ii) \(\dfrac{1}{3}\) of \(\$27\)
(iii) \(\dfrac{1}{7}\) of \(63\) m
| \(64 \div 8\) | \(=\) | \(8\) |
| \(27 \div 3\) | \(=\) | \(9\) |
| \(63 \div 7\) | \(=\) | \(9\) |
(i) \(8\)
(ii) \(\$9\)
(iii) \(9\) m
| \(2 \times 60\) | \(=\) | \(120\) |
| \(120 \div 4\) | \(=\) | \(30\) |
\(30\) minutes.
| \(3 \times 1000\) | \(=\) | \(3000\) |
| \(3000 \div 5\) | \(=\) | \(600\) |
\(600\) g.
| \(45 \div 9\) | \(=\) | \(5\) |
\(5\) students.
| \(9 \div 4\) | \(=\) | \(2\dfrac{1}{4}\) |
\(2\dfrac{1}{4}\) (\(2\) remainder \(1\), and the \(1\) left over is shared into quarters).
| \(56 \div 8\) | \(=\) | \(7\) |
\(56 \div 8 = 7\).
| \(48 \div 6\) | \(=\) | \(8\) |
A sixth is one of six equal parts, so divide: \(8\). A part must be smaller than the whole.
Common pitfalls
Frequently asked questions
What is a unit fraction?
A fraction with \(1\) on top, such as \(\dfrac{1}{5}\).
How do you find a unit fraction of a number?
Divide the number by the denominator.
What is one sixth of 54?
\(54 \div 6 = 9\).
Which is bigger, one quarter or one eighth of the same amount?
One quarter, because the amount is shared into fewer parts.
What if it does not divide exactly?
Write a mixed number: \(\dfrac{1}{4}\) of \(9\) is \(2\dfrac{1}{4}\).