Percent (II): discount
Foundation20% off = price × 80%.
After this lesson, you can:
- 20% off = pay 80% (original × 0.8)
- Amount saved = original − selling price
- Half price means paying 50%
1Summary 重點摘要
20% off = price × 80%.
2Vocabulary cards Vocabulary
D
Discount折扣
A price reduction; "20% off" means you pay 80% of the original price.
O
Original price原價
The price before the discount, e.g. $100.
S
Selling price售價
The price actually paid after discounting.
P
Percent百分數
A fraction of 100, e.g. 80% = 80100 = 0.8.
A
Amount saved節省金額
Original price − selling price, e.g. 100 − 80 = $20.
H
Half price五折（半價）
Paying 50%, e.g. half of $60 is $30.
C
Convert to decimal轉成小數
Turn the percentage into a decimal before multiplying: 80% = 0.8.
S
Successive discounts折上折
Discounting twice — multiply in turn, e.g. 20% off then 10% off = ×0.8 then ×0.9.
3Step by step Steps
- Step 1: Understand what a discount meansA 20% off sale means you pay 80% of the original price, because the shop takes 20% off. Note that the discount is not $8 less, and not 80% less: you pay 80%. Understanding this sentence is the foundation of every discount calculation.
- Step 2: The basic calculationThe basic formula is selling price = original price × the percentage you pay. For a $100 item at 20% off: 100 × 80% = 100 × 0.8 = $80. Change the percentage into a decimal or a fraction, then multiply directly.
- Step 3: How much is savedOriginal price minus selling price gives the saving: 100 − 80 = $20. This is exactly 20% of the original price, because the percentage paid plus the percentage saved always adds up to 100%. The two sides check each other.
- Step 4: The half-price caseHalf price means paying 50% of the original price. For a $60 item: 60 × 50% = 60 × 0.5 = $30. Whenever you see half price, just divide the original price by 2 and you have the answer at once.
- Step 5: Successive discounts multiply in turnWith a discount on a discount, calculate one step at a time. A $200 item at 20% off then 10% off: first 200 × 0.8 = 160, then 160 × 0.9 = $144. Never add 80% and 90% together, because the second discount works on the reduced price.
- Step 6: Compare the real pricesTo compare two shops, work out each actual selling price first. Shop A sells at $150 with 20% off: 150 × 0.8 = $120. Shop B sells at $140 with 30% off: 140 × 0.7 = $98. Shop B is $22 cheaper, so it is the better buy. The bigger discount is not always the cheaper price.
4Diagrams Diagrams
5Worked example Example
Example: a camera costs $800 and is now sold at 15% off. What is the selling price? How much is saved?
- 15% off means you pay 85% of the original price, because 100% − 15% = 85%.
- Selling price = original price × the percentage paid = 800 × 85% = 800 × 0.85.
- 800 × 0.85 = 680, so the camera sells for $680.
- Money saved = original price − selling price = 800 − 680 = $120.
- Check: the saving is 15% of the original price, and 800 × 15% = 800 × 0.15 = 120, the same amount.
- Answer: The $800 camera sells for $680 at 15% off, so the buyer saves $120, which is 15% of the original price. We first turned the discount into paying 85%, multiplied to get 680, and subtracted to find the saving of 120. The check 800 × 15% = 120 agrees with the subtraction, so the answer is correct.
6Common mistakes Mistakes
✗ Thinking 20% off means $8 less.
✓ 20% off means paying 80%: on $100 you pay $80, saving $20.
✗ Thinking 20% off means paying 20%: $100 becomes $20.
✓ The discount tells you what you PAY: pay 80%, so you save 20%.
✗ Adding successive discounts: 20% + 10% = 30% off.
✓ Multiply in turn: × 0.8 then × 0.9 = 0.72 — you pay 72%.
✗ Forgetting to convert % before multiplying: 100 × 80.
✓ Convert first: 80% = 0.8, so 100 × 0.8 = 80.
7Quick check Quick check
Q1A $200 item at 40% off. What is the selling price?
Answer: 200 × 60% = $120.
Did you get it right?
Q2A $50 book at 10% off. Selling price?
Answer: 50 × 90% = $45.
Did you get it right?
Q3$300 trainers at 30% off. How much is saved?
Answer: 300 × 30% = $90.
Did you get it right?
Q4Paying by "20% off" means paying what percent of the original?
Answer: 80%.
Did you get it right?
Q5Which is cheaper: $120 at 30% off, or $100 with no discount?
Answer: 120 × 70% = $84 < $100, the discounted one is cheaper.
Did you get it right?
8Recap Recap
- 20% off = pay 80% (original × 0.8)
- Amount saved = original − selling price
- Half price means paying 50%
- Successive discounts multiply in turn — never add them
- Convert % to a decimal before multiplying (80% → 0.8)