Year 6 Maths Percentages

Find a fraction of a quantity - Non-unit fraction

Q: Can you multiply first?

Yes, (45 × 3) ÷ 5 = 27 too, but dividing first keeps numbers small.

Q: What is two thirds of 42?

42 ÷ 3 = 14, and 14 × 2 = 28.

Q: What if it does not divide exactly?

Write a mixed number: 2/3 of 7 is 4 2/3.

20 practice questions 0 video lessons Theory + worked examples

Practice 20 questions

Practice questions

Every question with a fully worked solution.

Start practising

Theory

To find a fraction such as $\dfrac{3}{5}$ of an amount, first find one fifth (divide by the denominator $5$), then take three of them (multiply by the numerator $3$). This Year 6 maths page shows how to find non-unit fractions of numbers, money and measurements, and how to work backwards to find the whole.

A non-unit fraction has a numerator bigger than $1$, like $\dfrac{3}{5}$ or $\dfrac{2}{3}$.

$\dfrac{3}{5}$ of an amount means $3$ of its $5$ equal parts. So divide by the denominator, then multiply by the numerator.

$\dfrac{3}{5}$ of $45$: $45 \div 5 = 9$ (one fifth), then $9 \times 3 = 27$.

To work backwards, find one part first: if $\dfrac{3}{5}$ of a number is $24$, one fifth is $24 \div 3 = 8$, and the whole is $8 \times 5 = 40$.

$\dfrac{3}{5}$ of $45$: three parts of $9$ make $27$.

$\dfrac{2}{3}$ of $42$: $2 \times 14 = 28$.

Three parts make $24$, so one part is $8$ and the whole is $40$.

A fraction of an amount:

\[ \dfrac{a}{b} \text{ of an amount} = (\text{amount} \div b) \times a \]

a / b of an amount = (amount \div b) \times a

\[ \dfrac{3}{5} \text{ of } 45 = (45 \div 5) \times 3 = 27 \]

3 / 5 of 45 = (45 \div 5) \times 3 = 27

\[ \text{whole} = (\text{part} \div a) \times b \]

whole = (part \div a) \times b

Divide first. Dividing first keeps the numbers small.

          Do not stop at one part. \(48 \div 8 = 6\) is only one eighth; \(\dfrac{3}{8}\) of \(48\) is \(18\).
        

How to find a fraction of an amount

Divide the amount by the denominator to find one part.
Multiply by the numerator to find that many parts.

How to find the whole

Divide the known amount by the numerator to find one part.
Multiply by the denominator.

Example 1 — Three fifths

Find $\dfrac{3}{5}$ of $45$.

Solution

$45 \div 5$	$=$	$9$
$9 \times 3$	$=$	$27$

45 \div 5 \times 3 = 27

$27$.

Example 2 — Several fractions

Find each amount.
(i) $\dfrac{2}{3}$ of $42$
(ii) $\dfrac{5}{8}$ of $56$
(iii) $\dfrac{4}{7}$ of $63$

Solution

$14 \times 2$	$=$	$28$
$7 \times 5$	$=$	$35$
$9 \times 4$	$=$	$36$

28, 35, 36

(i) $28$
(ii) $35$
(iii) $36$

Example 3 — Sale price

A shirt costs $\$36$. In a sale it costs $\dfrac{3}{4}$ of that price. What is the sale price?

Solution

$36 \div 4$	$=$	$9$
$9 \times 3$	$=$	$27$

36 \div 4 \times 3 = 27

$\$27$.

Example 4 — Measurements

Find each amount.
(i) $\dfrac{2}{5}$ of $35$ kg
(ii) $\dfrac{5}{6}$ of $48$ m
(iii) $\dfrac{2}{3}$ of $90$ minutes

Solution

$7 \times 2$	$=$	$14$
$8 \times 5$	$=$	$40$
$30 \times 2$	$=$	$60$

14 kg, 40 m, 60 minutes

(i) $14$ kg
(ii) $40$ m
(iii) $60$ minutes (one hour)

Example 5 — Work backwards

$\dfrac{3}{5}$ of a number is $24$. What is the number?

Solution

$24 \div 3$	$=$	$8$
$8 \times 5$	$=$	$40$

24 \div 3 \times 5 = 40

$40$, as in the third diagram.

Example 6 — Not exact

Find $\dfrac{2}{3}$ of $7$.

Solution

$7 \div 3$	$=$	$2\dfrac{1}{3}$
$2 \times 2\dfrac{1}{3}$	$=$	$4\dfrac{2}{3}$

2 / 3 of 7 = 42 / 3

$4\dfrac{2}{3}$.

Example 7 — Two steps

Work out $\dfrac{2}{3}$ of $42$, then add $\dfrac{1}{4}$ of $36$.

Solution

$\dfrac{2}{3} \times 42$	$=$	$28$
$36 \div 4$	$=$	$9$
$28 + 9$	$=$	$37$

28 + 9 = 37

$37$.

Example 8 — Find the mistake

To find $\dfrac{3}{8}$ of $48$, Max divided by $8$ and wrote $6$. What is right?

Solution

$48 \div 8$	$=$	$6$
$6 \times 3$	$=$	$18$

48 \div 8 \times 3 = 18

$6$ is only one eighth. Three eighths is $18$.

Common pitfalls

Stopping after dividing. Dividing gives one part; multiply by the numerator.

Dividing by the numerator. For $\dfrac{3}{8}$ of $48$, divide by $8$, not by $3$.

Working backwards the wrong way. If $\dfrac{3}{5}$ is $24$, divide by $3$ then multiply by $5$.

A fraction less than 1 that gives more. $\dfrac{3}{4}$ of an amount is always less than the amount.

Frequently asked questions

How do you find three fifths of a number?

Divide by 5, then multiply by 3.

Can you multiply first?

Yes, $(45 \times 3) \div 5 = 27$ too, but dividing first keeps numbers small.

What is two thirds of 42?

$42 \div 3 = 14$, and $14 \times 2 = 28$.

How do you find the whole from a fraction?

Divide by the numerator, then multiply by the denominator.

What if it does not divide exactly?

Write a mixed number: $\dfrac{2}{3}$ of $7$ is $4\dfrac{2}{3}$.

← Previous subtopic

Find a fraction of a quantity - Unit fraction

Next subtopic →

Benchmark fraction / decimal / percentage equivalence

\(45 \div 5\)	\(=\)	\(9\)
\(9 \times 3\)	\(=\)	\(27\)

\(14 \times 2\)	\(=\)	\(28\)
\(7 \times 5\)	\(=\)	\(35\)
\(9 \times 4\)	\(=\)	\(36\)

\(36 \div 4\)	\(=\)	\(9\)
\(9 \times 3\)	\(=\)	\(27\)

\(7 \times 2\)	\(=\)	\(14\)
\(8 \times 5\)	\(=\)	\(40\)
\(30 \times 2\)	\(=\)	\(60\)

\(24 \div 3\)	\(=\)	\(8\)
\(8 \times 5\)	\(=\)	\(40\)

\(7 \div 3\)	\(=\)	\(2\dfrac{1}{3}\)
\(2 \times 2\dfrac{1}{3}\)	\(=\)	\(4\dfrac{2}{3}\)

\(\dfrac{2}{3} \times 42\)	\(=\)	\(28\)
\(36 \div 4\)	\(=\)	\(9\)
\(28 + 9\)	\(=\)	\(37\)

Find a fraction of a quantity - Non-unit fraction

📖 Theory

How to find a fraction of an amount

How to find the whole

Common pitfalls

Frequently asked questions

Theory