The idea, step by step
Use the original price as the whole
A percentage discount is a part taken off the original price. For 20% off 50 dollars, the whole is the original 50 dollars. Find the amount saved, then subtract it from the original price.
Keep the two answers separate: saving 10 dollars and paying 40 dollars describe different quantities. Label them so a reader can see which one you mean.
Compare the final prices
A larger percentage is not automatically a cheaper purchase when the original prices differ. Calculate what each offer actually costs. If delivery or a required fee applies, include it before deciding.
You can also find the percentage left to pay. A 25% discount leaves 75% of the original price. This is a useful second way to check a calculation.
A common trap
A 20% discount on 35 dollars means subtract 20 dollars.
Instead: 20% is a proportion, not a fixed money amount. One fifth of 35 is 7, so the sale price is 28 dollars.
See the thinking
Worked example 1
A jacket originally costs 90 dollars. It is reduced by 30%. Find the saving and sale price.
- 10% of 90 is 9, so 30% is 27 dollars.
- Subtract the saving: 90−27=63.
Worked example 2
A bag costs 80 dollars and has 15% off. How much is paid?
- 10% of 80 is 8 dollars; 5% is half of that, 4 dollars.
- The saving is 8+4=12 dollars.
- 80−12=68 dollars.
Check your understanding
An item costs 48 dollars. What is its price after 25% off?
Show answer
36 dollars.
A quarter of 48 is 12; 48−12=36.
Your turn
6 questions · 11 marks · Work at your own pace.
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%=1/4; 48÷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÷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.
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 ↗