Year 6 Maths Percentages

Find percentages of a quantity - Find 10%

Q: How do you find 10% of an amount?

Divide the amount by 10. 10% of $340 is $34.

Q: Why do you divide by 10?

10% is 10 out of 100, which is one tenth.

Q: How do you find the whole if you know 10%?

Multiply by 10. If 10% is 7, the whole is 70.

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Theory

Ten per cent ($10\%$) means $10$ out of every $100$, which is one tenth. So to find $10\%$ of an amount, divide it by 10. This Year 6 maths page shows how to find $10\%$ of numbers, money and measurements, how to build $20\%$, $30\%$ or $40\%$ from it, and how to find the whole amount when you know $10\%$.

Per cent means out of 100. $10\%$ is $\dfrac{10}{100}$, which simplifies to $\dfrac{1}{10}$.

Finding one tenth means sharing into $10$ equal parts, so $10\%$ of an amount = amount $\div 10$. Each digit moves one place to the right.

$10\%$ can be a decimal: $10\%$ of $65$ is $6.5$, and $10\%$ of $3$ L is $0.3$ L.

Other multiples of ten per cent are built from $10\%$: $20\%$ is two lots of $10\%$, $30\%$ is three lots, and so on.

The whole is $100\%$, which is ten lots of $10\%$. If you know $10\%$, multiply by $10$ to get the whole.

$\$340$ split into ten equal parts: each part is $10\%$, worth $\$34$.

$30\%$ is three tenths: $3 \times 16 = 48$.

$10\%$ of $65$: divide by $10$ to get $6.5$.

Ten per cent is one tenth:

\[ 10\% = \dfrac{10}{100} = \dfrac{1}{10} \]

10 = 10 / 100 = 1 / 10

\[ 10\% \text{ of an amount} = \text{amount} \div 10 \]

10 of an amount = amount \div 10

\[ 20\% = 2 \times 10\%, \quad 30\% = 3 \times 10\% \]

20 = 2 \times 10, 30 = 3 \times 10

\[ \text{whole} = 10\% \times 10 \]

whole = 10 \times 10

          Divide, do not subtract. \(10\%\) of \(130\) is \(130 \div 10 = 13\), not \(130 - 10\).
        

          Check the size. \(10\%\) is a small part: it must be much less than the whole amount.
        

How to find 10%

Divide the amount by $10$: move each digit one place to the right.
Keep the units (dollars, metres, litres) in your answer.

How to find 20%, 30%, 40%, ...

Find $10\%$ first.
Multiply by the number of tens: $30\%$ is $3$ lots of $10\%$.

How to find the whole from 10%

Multiply the $10\%$ amount by $10$.

Example 1 — Ten per cent of money

Find $10\%$ of $\$340$.

Solution

$340 \div 10$

$=$

$34$

340 \div 10 = 34

$\$34$, as in the first diagram.

Example 2 — A decimal answer

Find $10\%$ of $65$.

Solution

$65 \div 10$

$=$

$6.5$

65 \div 10 = 6.5

$6.5$. A tenth does not have to be a whole number.

Example 3 — Measurements

Find $10\%$ of each amount.
(i) $720$ m
(ii) $3$ L
(iii) $5$ kg

Solution

$720 \div 10$	$=$	$72$
$3 \div 10$	$=$	$0.3$
$5 \div 10$	$=$	$0.5$

720 \div 10 = 72, 3 \div 10 = 0.3, 5 \div 10 = 0.5

(i) $72$ m
(ii) $0.3$ L
(iii) $0.5$ kg

Example 4 — Thirty per cent

Find $30\%$ of $\$160$.

Solution

$160 \div 10$	$=$	$16$
$3 \times 16$	$=$	$48$

10 = 16, 30 = 3 \times 16 = 48

$\$48$.

Example 5 — Forty per cent

Find $40\%$ of $35$.

Solution

$35 \div 10$	$=$	$3.5$
$4 \times 3.5$	$=$	$14$

10 = 3.5, 40 = 4 \times 3.5 = 14

$14$.

Example 6 — Work backwards

(i) $10\%$ of a number is $7$. What is the number?
(ii) $10\%$ of a team is $2$ players. How many players are in the team?

Solution

$7 \times 10$	$=$	$70$
$2 \times 10$	$=$	$20$

7 \times 10 = 70, 2 \times 10 = 20

(i) $70$
(ii) $20$ players

Example 7 — In a school

A school has $380$ students and $10\%$ of them ride a bike to school.
(i) How many ride a bike?
(ii) How many do not?

Solution

$380 \div 10$	$=$	$38$
$380 - 38$	$=$	$342$

380 \div 10 = 38, 380 - 38 = 342

(i) $38$ students
(ii) $342$ students

Example 8 — Find the mistake

Ella found $10\%$ of $130$ by taking away $10$, and wrote $120$. What went wrong?

Solution

$130 \div 10$

$=$

$13$

130 \div 10 = 13

$10\%$ means one tenth, so she should divide by $10$, not subtract $10$. The answer is $13$.

Common pitfalls

Subtracting 10. $10\%$ of $130$ is $13$, not $120$.

Dividing by 100. Dividing by $100$ gives $1\%$. For $10\%$ divide by $10$.

Dropping the decimal. $10\%$ of $65$ is $6.5$, not $6$ or $65$.

Forgetting to multiply for 20% or 30%. $30\%$ of $160$ is $3 \times 16 = 48$, not $16$.

Frequently asked questions

How do you find 10% of an amount?

Divide the amount by $10$. $10\%$ of $\$340$ is $\$34$.

Why do you divide by 10?

$10\%$ is $10$ out of $100$, which is one tenth.

How do you find 30% of an amount?

Find $10\%$, then multiply by $3$.

Can 10% be a decimal?

Yes. $10\%$ of $65$ is $6.5$.

How do you find the whole if you know 10%?

Multiply by $10$. If $10\%$ is $7$, the whole is $70$.

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Find percentages of a quantity - Find 25% & 50%

\(720 \div 10\)	\(=\)	\(72\)
\(3 \div 10\)	\(=\)	\(0.3\)
\(5 \div 10\)	\(=\)	\(0.5\)

\(160 \div 10\)	\(=\)	\(16\)
\(3 \times 16\)	\(=\)	\(48\)

\(35 \div 10\)	\(=\)	\(3.5\)
\(4 \times 3.5\)	\(=\)	\(14\)

\(7 \times 10\)	\(=\)	\(70\)
\(2 \times 10\)	\(=\)	\(20\)

\(380 \div 10\)	\(=\)	\(38\)
\(380 - 38\)	\(=\)	\(342\)

Find percentages of a quantity - Find 10%

📖 Theory

How to find 10%

How to find 20%, 30%, 40%, ...

How to find the whole from 10%

Common pitfalls

Frequently asked questions

Theory