Year 6 Maths Percentages

Percentage discounts & sale price

Q: How do you find the original price after 50% off?

Double the sale price: $38 becomes $76.

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Theory

A discount is the amount taken off a price. When an item is $25\%$ off, the discount is $25\%$ of the original price, and the sale price is the original price minus the discount. This Year 6 maths page shows how to find discounts and sale prices for $10\%$, $25\%$ and $50\%$ off, how much of the price you still pay, and how to compare offers.

The original price is the price before the sale. The discount is the amount of money taken off.

Sale price = original price − discount.

$10\%$ off means the discount is one tenth of the price; $25\%$ off is one quarter; $50\%$ off is one half.

The percentage you still pay is $100\%$ minus the discount.

With $50\%$ off, the discount and the sale price are the same amount.

$25\%$ off $\$84$: the discount is $\$21$ and the sale price is $3 \times \$21 = \$63$.

$10\%$ of $\$70$ is $\$7$, so $\$70$ becomes $\$63$.

Discounts and sale prices:

\[ \text{discount} = \text{percentage} \times \text{original price} \]

discount = percentage \times original price

\[ \text{sale price} = \text{original price} - \text{discount} \]

sale price = original price - discount

Discount	You save	You pay
$10\%$ off	$\dfrac{1}{10}$	$90\%$
$25\%$ off	$\dfrac{1}{4}$	$75\%$
$50\%$ off	$\dfrac{1}{2}$	$50\%$

Two steps. First find the discount, then subtract it from the original price.

Check. The sale price must be less than the original price.

Finding the sale price

Find the discount: $10\%$ divide by $10$, $25\%$ divide by $4$, $50\%$ divide by $2$.
Subtract the discount from the original price.

Finding the original price after 50% off

Double the sale price, because the sale price is half of the original.

Example 1 — Ten per cent off

A jacket costs $\$70$ and has $10\%$ off.
(i) What is the discount?
(ii) What is the sale price?

Solution

$70 \div 10$	$=$	$7$
$70 - 7$	$=$	$63$

discount 7, sale price 63

(i) $\$7$
(ii) $\$63$

Example 2 — Twenty-five per cent off

A game costs $\$84$ with $25\%$ off. Find the sale price.

Solution

$84 \div 4$	$=$	$21$
$84 - 21$	$=$	$63$

84 \div 4 = 21, 84 - 21 = 63

$\$63$, as in the first diagram.

Example 3 — Half price

Boots cost $\$66$ and are $50\%$ off. Find the discount and the sale price.

Solution

$66 \div 2$

$=$

$33$

66 \div 2 = 33

The discount is $\$33$ and the sale price is also $\$33$.

Example 4 — Cents in the answer

A cap costs $\$45$ with $10\%$ off. What is the sale price?

Solution

$45 \div 10$	$=$	$4.5$
$45 - 4.5$	$=$	$40.5$

45 - 4.50 = 40.50

$\$40.50$.

Example 5 — What you pay

A shop takes $20\%$ off everything.
(i) What percentage of the price do you pay?
(ii) Use it to find the sale price of a $\$130$ item.

Solution

$100\% - 20\%$	$=$	$80\%$
$130 \div 10 \times 8$	$=$	$104$

100 % - 20 % = 80 %, 130 \div 10 \times 8 = 104

(i) $80\%$
(ii) $\$104$

Example 6 — Compare two offers

A bike costs $\$160$.
(i) Find the sale price with $25\%$ off.
(ii) Find the sale price with $50\%$ off.
(iii) How much more does the $50\%$ offer save?

Solution

$160 - 40$	$=$	$120$
$160 - 80$	$=$	$80$
$120 - 80$	$=$	$40$

120, 80, difference 40

(i) $\$120$
(ii) $\$80$
(iii) $\$40$ more

Example 7 — Original price

After $50\%$ off, a lamp costs $\$38$. What was the original price?

Solution

$38 \times 2$

$=$

$76$

38 \times 2 = 76

$\$76$.

Example 8 — Find the mistake

Shoes cost $\$120$ with $25\%$ off. Ivy says the sale price is $\$30$. What went wrong?

Solution

$120 \div 4$	$=$	$30$
$120 - 30$	$=$	$90$

120 - 30 = 90

$\$30$ is the discount. She must subtract it: the sale price is $\$90$.

Common pitfalls

Giving the discount as the sale price. With $25\%$ off $\$120$, $\$30$ is the discount; the sale price is $\$90$.

Adding the discount. A discount makes the price smaller, so subtract it.

Dividing by the percentage. $25\%$ off means divide by $4$, not by $25$.

Forgetting the cents. $10\%$ off $\$45$ gives $\$40.50$, not $\$40$.

Frequently asked questions

What is a discount?

The amount of money taken off the original price.

How do you find the sale price?

Find the discount, then subtract it from the original price.

What percentage do you pay with 50% off?

$50\%$ of the original price.

Is 50% off the same as half price?

Yes. The discount and the sale price are equal.

How do you find the original price after 50% off?

Double the sale price: $\$38$ becomes $\$76$.

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

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Find a fraction of a quantity - Unit fraction

Discount	You save	You pay
\(10\%\) off	\(\dfrac{1}{10}\)	\(90\%\)
\(25\%\) off	\(\dfrac{1}{4}\)	\(75\%\)
\(50\%\) off	\(\dfrac{1}{2}\)	\(50\%\)

\(70 \div 10\)	\(=\)	\(7\)
\(70 - 7\)	\(=\)	\(63\)

\(84 \div 4\)	\(=\)	\(21\)
\(84 - 21\)	\(=\)	\(63\)

\(45 \div 10\)	\(=\)	\(4.5\)
\(45 - 4.5\)	\(=\)	\(40.5\)

\(100\% - 20\%\)	\(=\)	\(80\%\)
\(130 \div 10 \times 8\)	\(=\)	\(104\)

\(160 - 40\)	\(=\)	\(120\)
\(160 - 80\)	\(=\)	\(80\)
\(120 - 80\)	\(=\)	\(40\)

Percentage discounts & sale price

📖 Theory

Finding the sale price

Finding the original price after 50% off

Common pitfalls

Frequently asked questions

Theory