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Find a fraction of a quantity - Unit fraction

20 practice questions 0 video lessons Theory + worked examples
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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.

Twenty shared into four equal groups of five 5 5 5 5 20 shared into 4 equal groups
\(\dfrac{1}{4}\) of \(20 = 20\div 4 = 5\). Each of the four equal groups holds \(5\), and one group is one quarter.

Each unit fraction of a quantity is found by dividing by its denominator.

FractionCalculationResult
\(\dfrac{1}{4}\) 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

  1. Read the denominator — it is the number of equal groups.
  2. Divide the quantity by that denominator.
  3. Take one group; that is the answer.
Example 1 — Quarter
Find \(\dfrac{1}{4}\) of \(20\).
Solution

Share into \(4\) equal groups.

\(\dfrac{1}{4}\text{ of }20\)\(=\)\(20\div 4=5\)
Example 2 — Third
Find \(\dfrac{1}{3}\) of \(18\).
Solution
\(\dfrac{1}{3}\text{ of }18\)\(=\)\(18\div 3=6\)
Example 3 — Sixth
Find \(\dfrac{1}{6}\) of \(30\).
Solution
\(\dfrac{1}{6}\text{ of }30\)\(=\)\(30\div 6=5\)
Example 4 — Pocket money
Mia saves \(\dfrac{1}{8}\) of $40. How much is that?
Solution
\(\dfrac{1}{8}\text{ of }40\)\(=\)\(40\div 8=5\)

Mia saves $5.

Common pitfalls

Dividing by the numerator. Divide by the bottom number; \(\dfrac{1}{4}\) of \(20\) is \(20\div 4\), never \(20\div 1\).
Multiplying instead. A fraction of a quantity makes it smaller, so divide — do not multiply by the denominator.
Unequal groups. The groups must be equal; sharing unevenly does not give a fraction of the quantity.

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 \(\dfrac{1}{10}\).