More fractions
Fractions of numbers
Finding a fraction of a number is just like sharing it into equal groups. Whenever you find an equal part of a whole, you are using fractions!
A fraction is like dividing
To find a fraction of a number, share the number into equal groups. Finding 1/2 means 2 equal groups, so 1/2 of 10 is 10 ÷ 2 = 5. Finding 1/4 means 4 equal groups, so 1/4 of 12 is 12 ÷ 4 = 3.
Unit fractions
A unit fraction has 1 on top, like 1/2, 1/3, 1/4 or 1/10. The bottom number tells you how many equal groups to make. For 1/5 of 60, make 5 groups: 60 ÷ 5 = 12.
Non-unit fractions
A non-unit fraction has more than 1 on top, like 3/4. First find one part, then take that many copies. For 3/4 of 20: find 1/4 of 20 = 5, then take 3 lots of 5 = 15.
Using fraction strips
A paper strip helps you find a fraction. A 15 cm strip marked in thirds has marks at 5 cm and 10 cm, because 15 ÷ 3 = 5. Each equal part is one third of the strip.
Worked examples
Half of a number
- Half means 2 equal groups.
- Share 10 into 2 equal groups: 10 ÷ 2.
- Each group is 5.
Answer: 1/2 of 10 = 5
A quarter of a number
- A quarter means 4 equal groups.
- Share 12 into 4 equal groups: 12 ÷ 4.
- Each group is 3.
Answer: 1/4 of 12 = 3
A fifth of a number
- A fifth means 5 equal groups.
- Share 60 into 5 equal groups: 60 ÷ 5.
- Each group is 12.
Answer: 1/5 of 60 = 12
A non-unit fraction
- Find 1/4 of 20 first: 20 ÷ 4 = 5.
- 3/4 means 3 of those parts.
- Take 3 lots of 5: 3 × 5 = 15.
Answer: 3/4 of 20 = 15
Where you see this in real life
- Sharing 60 party lanterns into 5 colours, getting 12 of each.
- Giving one of four apples to a friend, which is a quarter of the pack.
- Marking thirds along a 15 cm paper strip at 5 cm and 10 cm.
Key words
- Unit fraction
- A fraction with 1 on top, like 1/2, 1/4 or 1/5.
- Non-unit fraction
- A fraction with more than 1 on top, like 3/4.
- Numerator
- The top number — how many parts you take.
- Denominator
- The bottom number — how many equal groups the whole makes.
- Fraction strip
- A strip split into equal parts, used to find fractions.