A unit fraction has 1 as the numerator: \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\), etc. To find a unit fraction of an amount, simply divide by the denominator.
\(\frac{1}{n} \text{ of } A = A \div n\)
Example 1 — Find \(\frac{1}{4}\) of 60
Step 1
Divide by the denominator: \(60 \div 4 = 15\).
Step 2
\(\frac{1}{4}\) of 60 = 15
Example 2 — Find \(\frac{1}{6}\) of £540
Step 1
\(540 \div 6 = 90\)
Step 2
\(\frac{1}{6}\) of £540 = £90
✓ Quick Check 1 — Unit fractions of an amount
Question 1 of 10
Non-Unit Fractions of an Amount
For fractions like \(\frac{3}{4}\) or \(\frac{2}{5}\), first find one part (divide by denominator), then scale up (multiply by numerator).
In real-life problems, fractions of amounts appear in wages, discounts, measurements and statistics. Some problems require multiple steps. On a calculator: type amount ÷ denominator × numerator.
Example 5 — \(\frac{3}{5}\) of a class of 30 passed. Of those, \(\frac{2}{3}\) got a grade A. How many got grade A?
Step 1
Find \(\frac{3}{5}\) of 30: \(30 \div 5 = 6\), \(6 \times 3 = 18\) students passed.
Step 2
Find \(\frac{2}{3}\) of 18: \(18 \div 3 = 6\), \(6 \times 2 = 12\) got grade A.
Step 3
12 students got grade A.
Example 6 — Calculator: \(\frac{7}{12}\) of £2340
Step 1
Press: 2340 ÷ 12 × 7 =
Step 2
2340 ÷ 12 = 195. Then 195 × 7 = 1365.
Step 3
\(\frac{7}{12}\) of £2340 = £1365
Calculator tip: Always divide first, then multiply. Press = after the division before multiplying, or chain it as: amount ÷ denominator × numerator =
✓ Quick Check 3 — Real-life fractions of amounts
Question 1 of 10
Practice: Find each fraction of the given amount
Work out each answer and type it in, then click Check All.
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Question
Answer
Result
1
1/3 of 90
2
3/4 of 80
3
2/5 of 50
4
5/8 of 64
5
2/3 of 120
6
7/10 of 300
7
3/7 of 56
8
4/5 of 450
9
5/6 of 180
10
3/8 of 240
⚠ Things to Watch Out For
Dividing by the numerator instead of the denominator: For ¾ of 60: divide by 4 (the denominator) to get 15, then multiply by 3 (the numerator) to get 45. Many students accidentally divide by 3 first.
Stopping after finding the unit fraction: ¾ of 60 — students find ¼ of 60 = 15 and stop there. Remember: ¾ means 3 lots of ¼, so multiply 15 × 3 = 45.
Using the wrong whole: "⅔ of the 24 girls in a class" — the whole is 24, not the total class size. Identify the correct whole before calculating.
Not simplifying before multiplying: ¾ × 60: you can cross-cancel — 60÷4=15, then 15×3=45. This avoids large numbers.
Confusing "of" with division: "of" in maths means multiply. ¾ of 60 = ¾ × 60. Do not treat "of" as a division sign.