Find a fraction of a quantity - Unit fraction
Theory
To find a unit fraction of a quantity, divide the quantity by the denominator. The denominator tells how many equal groups to share into, so \(\dfrac{1}{4}\) of a quantity is the quantity \(\div 4\).
A unit fraction has a numerator of \(1\), such as \(\dfrac{1}{4}\) or \(\dfrac{1}{6}\).
The denominator tells how many equal groups the quantity is shared into.
Finding \(\dfrac{1}{n}\) of a quantity is the same as dividing the quantity by \(n\) and taking one group.
Each unit fraction of a quantity is found by dividing by its denominator.
| Fraction | Calculation | Result |
|---|---|---|
| \(\dfrac{1}{4}\) of \(20\) | \(20\div 4\) | \(5\) |
| \(\dfrac{1}{3}\) of \(18\) | \(18\div 3\) | \(6\) |
| \(\dfrac{1}{6}\) of \(30\) | \(30\div 6\) | \(5\) |
| \(\dfrac{1}{8}\) of \(40\) | \(40\div 8\) | \(5\) |
How to find a unit fraction of a quantity
- Read the denominator — it is the number of equal groups.
- Divide the quantity by that denominator.
- Take one group; that is the answer.
Share into \(4\) equal groups.
| \(\dfrac{1}{4}\text{ of }20\) | \(=\) | \(20\div 4=5\) |
| \(\dfrac{1}{3}\text{ of }18\) | \(=\) | \(18\div 3=6\) |
| \(\dfrac{1}{6}\text{ of }30\) | \(=\) | \(30\div 6=5\) |
| \(\dfrac{1}{8}\text{ of }40\) | \(=\) | \(40\div 8=5\) |
Mia saves $5.
Common pitfalls
Frequently asked questions
How do you find a unit fraction of a number?
Divide the number by the denominator. For \(\dfrac{1}{4}\) of \(20\), work out \(20\div 4=5\).
Why do you divide by the denominator?
The denominator is how many equal groups the quantity is shared into, and one group is the unit fraction.
Is the answer bigger or smaller than the quantity?
Smaller. One group is only part of the whole amount, so \(\dfrac{1}{4}\) of \(20\) is \(5\), which is less than \(20\).
What is a unit fraction?
A fraction with a numerator of \(1\), such as \(\dfrac{1}{3}\), \(\dfrac{1}{5}\) or \(\dfrac{1}{10}\).