Year 6 Maths Percentages

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

Q: How do you find 50% of an amount?

Divide it by 2. 50% of 96 is 48.

Q: How do you find 25% of an amount?

Divide it by 4, or halve it twice.

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Theory

$50\%$ is one half and $25\%$ is one quarter. So to find $50\%$ of an amount, divide it by $2$; to find $25\%$, divide it by $4$; and $75\%$ is three of those quarters. This Year 6 maths page shows how to find these percentages of numbers, money and measurements, and how to find the whole when you know a part.

$50\% = \dfrac{50}{100} = \dfrac{1}{2}$. To find $50\%$, divide by 2 (halve).

$25\% = \dfrac{25}{100} = \dfrac{1}{4}$. To find $25\%$, divide by 4, or halve and halve again.

$75\% = \dfrac{3}{4}$. To find $75\%$, find $25\%$ and multiply by $3$ (or take $25\%$ away from the whole).

The answer can be a decimal: $50\%$ of $9$ is $4.5$.

$25\% + 25\% + 50\% = 100\%$, the whole amount.

Four quarters of $96$: each $25\%$ is $24$, so $50\%$ is $48$.

$75\%$ is three quarters: $3 \times 90 = 270$ L.

Percentages that are halves and quarters:

\[ 50\% = \dfrac{1}{2} \;\Rightarrow\; \div 2 \]

50 = 1 / 2, divide by 2

\[ 25\% = \dfrac{1}{4} \;\Rightarrow\; \div 4 \]

25 = 1 / 4, divide by 4

\[ 75\% = \dfrac{3}{4} \;\Rightarrow\; \div 4, \text{ then } \times 3 \]

75 = 3 / 4, divide by 4 then multiply by 3

          Halve and halve again. \(25\%\) of \(140\): half is \(70\), half again is \(35\).
        

          Not divide by 25. \(25\%\) means one quarter, so divide by \(4\), not by \(25\).
        

How to find 50% or 25%

50%: divide the amount by $2$.
25%: divide the amount by $4$ (or halve twice).

How to find 75%

Find $25\%$.
Multiply by $3$.

How to find the whole

From 50%: multiply by $2$.
From 25%: multiply by $4$.

Example 1 — Half and quarter

Find $50\%$ and $25\%$ of $96$.

Solution

$96 \div 2$	$=$	$48$
$96 \div 4$	$=$	$24$

96 \div 2 = 48, 96 \div 4 = 24

$50\%$ is $48$ and $25\%$ is $24$.

Example 2 — Seventy-five per cent

Find $75\%$ of $96$.

Solution

$96 \div 4$	$=$	$24$
$3 \times 24$	$=$	$72$

3 \times 24 = 72

$72$.

Example 3 — A decimal answer

Find $50\%$ of $9$.

Solution

$9 \div 2$

$=$

$4.5$

9 \div 2 = 4.5

$4.5$.

Example 4 — Money and mass

Find each amount.
(i) $25\%$ of $140$ kg
(ii) $25\%$ of $\$30$

Solution

$140 \div 4$	$=$	$35$
$30 \div 4$	$=$	$7.5$

140 \div 4 = 35, 30 \div 4 = 7.5

(i) $35$ kg
(ii) $\$7.50$

Example 5 — A class survey

A class has $28$ students. $25\%$ walk to school and $50\%$ come by car.
(i) How many walk?
(ii) How many come by car?
(iii) How many do neither?

Solution

$28 \div 4$	$=$	$7$
$28 \div 2$	$=$	$14$
$28 - 7 - 14$	$=$	$7$

7 walk, 14 by car, 7 neither

(i) $7$
(ii) $14$
(iii) $7$ (the last $25\%$)

Example 6 — Work backwards

(i) $50\%$ of a number is $23$. What is the number?
(ii) $25\%$ of a number is $11$. What is the number?

Solution

$23 \times 2$	$=$	$46$
$11 \times 4$	$=$	$44$

23 \times 2 = 46, 11 \times 4 = 44

(i) $46$
(ii) $44$

Example 7 — Three quarters of a tank

A tank holds $360$ L. How much is $75\%$ of the tank?

Solution

$360 \div 4$	$=$	$90$
$3 \times 90$	$=$	$270$

360 \div 4 \times 3 = 270

$270$ L, as in the second diagram.

Example 8 — Find the mistake

Leo found $25\%$ of $64$ by dividing by $25$ and got $2.56$. What is right?

Solution

$64 \div 4$

$=$

$16$

64 \div 4 = 16

$25\%$ is one quarter, so divide by $4$. The answer is $16$.

Common pitfalls

Dividing by 25 or 50. Divide by $4$ for $25\%$ and by $2$ for $50\%$.

Stopping at one quarter for 75%. $75\%$ is three quarters: multiply the quarter by $3$.

Rounding off a half. $50\%$ of $9$ is $4.5$, not $4$.

Halving when working backwards. If $50\%$ is $23$, the whole is $46$ (double it).

Frequently asked questions

How do you find 50% of an amount?

Divide it by $2$. $50\%$ of $96$ is $48$.

How do you find 25% of an amount?

Divide it by $4$, or halve it twice.

How do you find 75%?

Find $25\%$ and multiply by $3$.

Why is 25% the same as one quarter?

$25$ out of $100$ is $\dfrac{25}{100} = \dfrac{1}{4}$.

If 25% is 11, what is the whole?

$4 \times 11 = 44$.

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Percentage discounts & sale price

\(96 \div 2\)	\(=\)	\(48\)
\(96 \div 4\)	\(=\)	\(24\)

\(96 \div 4\)	\(=\)	\(24\)
\(3 \times 24\)	\(=\)	\(72\)

\(140 \div 4\)	\(=\)	\(35\)
\(30 \div 4\)	\(=\)	\(7.5\)

\(28 \div 4\)	\(=\)	\(7\)
\(28 \div 2\)	\(=\)	\(14\)
\(28 - 7 - 14\)	\(=\)	\(7\)

\(23 \times 2\)	\(=\)	\(46\)
\(11 \times 4\)	\(=\)	\(44\)

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

📖 Theory

How to find 50% or 25%

How to find 75%

How to find the whole

Common pitfalls

Frequently asked questions

Theory