Find a Unit Fraction of a Number
Finding a unit fraction of a number means splitting a group into equal parts and taking one part. In Year 3 (ACARA v9), students connect unit fractions like 1/2, 1/3 and 1/4 to sharing a collection equally — finding 1/3 of 12 is the same as sharing 12 into 3 equal groups and taking one group. The key idea: the denominator tells you how many equal groups to make, and a unit fraction (1 on top) means you take just one of those groups. This links fractions to division, so a child who knows 12 / 3 = 4 can see straight away that 1/3 of 12 is 4.
Worked examples
Find 1/2 of 10.
The denominator is 2, so share 10 into 2 equal groups: 10 / 2 = 5. Take 1 group.
Answer: 5
Find 1/3 of 12 lollies.
Share 12 into 3 equal groups: 12 / 3 = 4. A unit fraction means take 1 group.
Answer: 4 lollies
Find 1/4 of 20.
Share 20 into 4 equal groups: 20 / 4 = 5. Take 1 group.
Answer: 5
Real-world: 15 marbles are shared so you keep 1/5 of them. How many do you keep?
Share 15 into 5 equal groups: 15 / 5 = 3. Keep 1 group.
Answer: 3 marbles
Tips
- •Turn the fraction into a sharing question. 1/4 of 16 means 'share 16 into 4 equal groups' — the denominator tells you how many groups.
- •Use the division facts you already know. Finding 1/3 of a number is the same as dividing by 3, so times-table knowledge does the heavy lifting.
- •Common mistake to watch for: children sometimes multiply by the denominator instead of dividing, working out 1/3 of 12 as 36. Remind them a fraction of a number is smaller than the number — you are sharing it out, not making more.
- •Start with real objects. Sharing counters, blocks or grapes into equal piles shows what 'one part of the whole' really means before using numbers alone.