Fractions
Fractions as operators
A unit fraction can act like an instruction. To find one-fifth of a quantity you divide by 5, and to find one-sixth you divide by 6.
What is a unit fraction?
A unit fraction is a fraction with a numerator of 1, such as 1/2, 1/5 or 1/10. Unit fractions are useful because you can use them as an operator — a rule that tells you what to do to a number.
Finding a fraction of a quantity
To find a unit fraction of a quantity, divide the quantity by the denominator. • 1/5 of a number: divide by 5. • 1/6 of a number: divide by 6. • 1/10 of a number: divide by 10. For example, 1/4 of $12 is 12 ÷ 4 = $3.
Comparing unit fractions
For unit fractions, the larger the denominator, the smaller the fraction. So 1/6 is smaller than 1/4, which is smaller than 1/3. This also means 1/6 of a quantity is smaller than 1/3 of the same quantity.
Worked examples
One-quarter of an amount
- Find 1/4 of $12.
- The denominator is 4, so divide by 4.
- 12 ÷ 4 = 3.
Answer: 1/4 of $12 is $3.
One-fifth of a quantity
- Find 1/5 of 45.
- The denominator is 5, so divide by 5.
- 45 ÷ 5 = 9.
Answer: 1/5 of 45 is 9.
Comparing two unit fractions
- Compare 1/6 and 1/4.
- The larger the denominator, the smaller the fraction.
- 6 is bigger than 4, so 1/6 is smaller.
Answer: 1/6 is smaller than 1/4.
Where you see this in real life
- Halving a recipe to cook for fewer people.
- Working out one-quarter of your pocket money to save.
- Sharing a quantity of sweets equally into groups.
Key words
- Unit fraction
- A fraction with a numerator of 1, such as 1/5.
- Operator
- A rule that tells you what to do to a number, like 'divide by 5'.
- Denominator
- The bottom number of a fraction — the number you divide by to find that fraction of a quantity.
- Quantity
- An amount, such as 12 sweets or $30.