Calculating discounts | Year 6

01 / LEARN

Understand the idea.

Use the original price as the whole

A percentage discount uses the original price as the whole. Find the stated fraction of that price to calculate the saving. Then subtract the saving to find the sale price: these are two different money amounts.

Use familiar percentages to build the saving. Ten percent is one tenth, five percent is half of ten percent, and twenty-five percent is one quarter. Label saving and price paid so they cannot be confused.

Compare the final prices

The percentage left to pay provides another approach. A discount of $25 %$ leaves $75 %$ of the original price. The saved part and the paid part must together account for the full original price.

Compare final amounts when offers have different starting prices. A larger percentage discount does not by itself guarantee the cheaper purchase. Include any delivery charge or required fee supplied in the problem before comparing totals.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Worked example 1

A jacket originally costs 90 dollars. It is reduced by 30%. Find the saving and sale price.

Worked solution

1
Find ten percent of the original price.
$90 \div 10 = 9 dollars$
Ten percent is one tenth of the original 90 dollars.
2
Build the thirty-percent saving.
$3 \times 9 = 27 dollars$
Thirty percent is three lots of ten percent.
3
Subtract the saving.
$90 - 27 = 63 dollars$
The discount is removed from the original price to get the sale price.
4
Check the two labelled amounts.
$27 + 63 = 90$
The 27-dollar saving and 63-dollar sale price together make the original price.

Answer

Saving 27 dollars; sale price 63 dollars.

EXAMPLE 02

Worked example 2

A bag costs 80 dollars and has 15% off. How much is paid?

Worked solution

1
Find ten percent.
$80 \div 10 = 8 dollars$
One tenth of the original price gives a convenient starting part.
2
Find five percent.
$8 \div 2 = 4 dollars$
Five percent is half of ten percent.
3
Combine the parts of the discount.
$8 + 4 = 12 dollars$
Ten percent plus five percent gives the fifteen-percent saving.
4
Find the amount paid.
$80 - 12 = 68 dollars$
The sale price is the original amount minus the saving.

Answer

68 dollars.

03 / YOUR TURN

Try it yourself.

Check your understanding

An item costs 48 dollars. What is its price after 25% off?

Show answer & reasoning

36 dollars.

$25 % = \frac{1}{4}$ , so the saving is $48 \div 4 = 12$ dollars. The sale price is $48 - 12 = 36$ dollars.

Keep practising

6 worksheet questions · 11 marks

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Read the questions online

A game costs 65 dollars. Find the price after $10 %$ off.
2 marks
A hat costs 48 dollars. Find the saving with $25 %$ off.
1 mark
A ball costs 35 dollars. Find the price after $20 %$ off.
2 marks
A backpack costs 86 dollars. It is half price. How much is paid?
1 mark
Mina has 60 dollars. A coat normally costs 80 dollars and has $25 %$ off. Can she afford it with no extra fees?
2 marks
Shop A offers $20 %$ off a 50-dollar bag. Shop B offers 5 dollars off a 43-dollar bag of the same model. Which final price is lower, and by how much?
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

A game costs 65 dollars. Find the price after $10 %$ off.
2 marks
$10 %$ of 65 is 6.50; $65 - 6.50 = 58.50$ .
58.50 dollars.
A hat costs 48 dollars. Find the saving with $25 %$ off.
1 mark
$25 % = \frac{1}{4}$ ; $48 \div 4 = 12$ .
12 dollars.
A ball costs 35 dollars. Find the price after $20 %$ off.
2 marks
$20 %$ is 7 dollars; $35 - 7 = 28$ .
28 dollars.
A backpack costs 86 dollars. It is half price. How much is paid?
1 mark
Half price means a $50 %$ discount; $86 \div 2 = 43$ .
43 dollars.
Mina has 60 dollars. A coat normally costs 80 dollars and has $25 %$ off. Can she afford it with no extra fees?
2 marks
A quarter of 80 is 20; $80 - 20 = 60$ .
Yes, exactly.
Shop A offers $20 %$ off a 50-dollar bag. Shop B offers 5 dollars off a 43-dollar bag of the same model. Which final price is lower, and by how much?
3 marks
A: $50 - 10 = 40$ dollars.
B: $43 - 5 = 38$ dollars. The difference is 2 dollars.
Shop B is 2 dollars cheaper.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Fraction/decimal/percentage quantities; discounts; budgets/cost predictions; comparing choices, risks and consequences.

Official curriculum source ↗

In this lesson

Understand the idea.

Use the original price as the whole

Compare the final prices

See the method in action.

Worked example 1

Find ten percent of the original price.

Build the thirty-percent saving.

Subtract the saving.

Check the two labelled amounts.

Worked example 2

Find ten percent.

Find five percent.

Combine the parts of the discount.

Find the amount paid.

Try it yourself.

Check your understanding

Keep practising