How to Find a Fraction of a Number
Level 1 Fractions · Reviewed by The NumThink editorial team · Last reviewed
This page is part of the NumThink Fractions course. Read why the method works, watch it run on worked examples, then drill it in the practice box below until it feels automatic.
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The bottom number (the denominator) says how many equal parts to split the whole into; the top number (the numerator) says how many of those parts to take. 28 split into 4 equal parts gives 7 in each part, and 3 parts make 21.
Dividing first keeps the numbers small. Multiplying first gives the same answer (3 × 28 = 84, and 84 ÷ 4 = 21), but the middle number is bigger.
The steps
- Divide by the denominator. One quarter of 28: 28 ÷ 4 = 7.
- Multiply by the numerator. Three quarters: 7 × 3 = 21.
Worked examples
Easy 1/2 of 18
Show the thinking
Half of 18: 18 ÷ 2 = 9
So 1/2 of 18 = 9.
Answer: 9
Medium 3/4 of 28
Show the thinking
28 ÷ 4 = 7
7 × 3 = 21
So 3/4 of 28 = 21.
Answer: 21
Hard 5/8 of 72
Show the thinking
72 ÷ 8 = 9
9 × 5 = 45
So 5/8 of 72 = 45.
Answer: 45
When to use it
- Shares and recipes: 2/3 of 24 students is 16 students, and 3/4 of 200 ml is 150 ml.
- Any time the number divides exactly by the denominator.
When NOT to use it
- Tenths and hundredths are often quicker as percentages: 7/10 of 60 is 70% of 60, which is 42.
- When the number does not divide evenly (2/3 of 25): the answer is not a whole number — leave it as a fraction, 50/3.