🏷️ Percentage Increase & Decrease

Cambridge Lower Secondary · Grade 7 · Number & Percentages

Percentage Increase
20% of 80 = 16  →  80 + 16 = 96
or: 80 × 1.20 = 96
Percentage Decrease
15% of 200 = 30  →  200 − 30 = 170
or: 200 × 0.85 = 170
% Change Formula
(Change ÷ Original) × 100
e.g. (12 ÷ 80) × 100 = 15%

Watch a 25% increase in action! 🏷️

$80
Original
→
× 1.25
?
New Price

What you'll learn:

  • Percentage increase: find the increase, then add
  • Percentage decrease: find the decrease, then subtract
  • The multiplier method: increase by 15% → × 1.15
  • Percentage change formula: (change ÷ original) × 100
  • Profit and loss percentage
  • VAT calculations (adding 5% or 15%)
  • Discount problems: original vs sale price
Created by Mr Josh

📖 Learn: Percentage Increase & Decrease

Part 1: Percentage Increase (Two-Step Method)

To increase a value by a percentage:

📌 Step 1: Find the percentage of the original amount.
📌 Step 2: Add it to the original.
Example: Increase $80 by 20%
   20% of 80 = 0.20 × 80 = 16  →  80 + 16 = $96
Example: Increase 450 g by 30%
   30% of 450 = 0.30 × 450 = 135  →  450 + 135 = 585 g
💡 Always identify the original value — this is what you find the % of.

Part 2: Percentage Decrease (Two-Step Method)

To decrease a value by a percentage:

📌 Step 1: Find the percentage of the original amount.
📌 Step 2: Subtract it from the original.
Example: Decrease $200 by 15%
   15% of 200 = 0.15 × 200 = 30  →  200 − 30 = $170
Example: A jacket costs $120. It's reduced by 25%.
   25% of 120 = 0.25 × 120 = 30  →  120 − 30 = $90
💡 A "discount" is always a decrease. A "sale" means the price goes down.

Part 3: The Multiplier Method

The multiplier method combines both steps into one multiplication.

Change Multiplier Why?
Increase 20%× 1.20100% + 20% = 120% = 1.20
Increase 15%× 1.15100% + 15% = 115% = 1.15
Decrease 20%× 0.80100% − 20% = 80% = 0.80
Decrease 35%× 0.65100% − 35% = 65% = 0.65
Example: Increase $340 by 15%  →  340 × 1.15 = $391
Example: Decrease $80 by 20%  →  80 × 0.80 = $64
💡 For an increase: multiplier > 1. For a decrease: multiplier < 1.

Part 4: Percentage Change Formula

% Change = (Change ÷ Original) × 100

Where Change = New Value − Original Value
Example: A price rises from $50 to $62. Find the % increase.
   Change = 62 − 50 = 12  →  (12 ÷ 50) × 100 = 24% increase
Example: A score falls from 80 to 68. Find the % decrease.
   Change = 80 − 68 = 12  →  (12 ÷ 80) × 100 = 15% decrease
💡 Always divide by the original value — the value before the change.

Part 5: Profit, Loss, VAT & Discounts

Profit & Loss:

Profit = Selling Price − Cost Price  (when SP > CP)
% Profit = (Profit ÷ Cost Price) × 100
Loss = Cost Price − Selling Price  (when CP > SP)
Example: Buy for $40, sell for $52.   Profit = $12.   % Profit = (12 ÷ 40) × 100 = 30%

VAT (Value Added Tax):

VAT is added to the cost price. VAT of 15% → multiply by 1.15
Example: Item costs $200 + 15% VAT  →  200 × 1.15 = $230

Discounts:

Discount = Original Price × (Discount % ÷ 100)
Sale Price = Original Price × Multiplier  (e.g. 30% off → × 0.70)
💡 "30% off" means you pay 70% of the original price.
Created by Mr Josh

💡 Worked Examples

Example 1: Percentage Increase (Two-Step)

A shirt costs $65. The price increases by 20%. Find the new price.

Step 1: Find 20% of 65:   0.20 × 65 = 13
Step 2: Add to original:   65 + 13 = $78
Answer: $78
✅ Check with multiplier: 65 × 1.20 = 78 ✓

Example 2: Percentage Decrease (Discount)

A bicycle costs $320. There is a 35% sale discount. Find the sale price.

Step 1: Find 35% of 320:   0.35 × 320 = 112
Step 2: Subtract:   320 − 112 = $208
Answer: $208
✅ Multiplier method: 320 × 0.65 = 208 ✓

Example 3: Percentage Change Formula

A painting was bought for $500 and sold for $620. Find the percentage profit.

Step 1: Find the change:   620 − 500 = 120
Step 2: Apply formula:   (120 ÷ 500) × 100 = 24%
Answer: 24% profit
💡 Always divide by the original ($500 here, the cost price).

Example 4: VAT Calculation

A phone costs $850 before VAT. VAT is 15%. Find the total price including VAT.

Step 1: Find 15% VAT:   0.15 × 850 = $127.50
Step 2: Total:   850 + 127.50 = $977.50
Answer: $977.50
✅ Multiplier: 850 × 1.15 = 977.50 ✓
Created by Mr Josh

🏷️ Visualizer

Animated Price Tag

Enter a starting price and a % change (positive = increase, negative = decrease).



$100
Original
→
× 1.20
$?
New Price

Multiplier Explorer

Drag the slider to explore how the multiplier changes the value.

−50% decrease0% (no change)+100% increase
+20% increase
Multiplier: × 1.20
$100
Original
$120
New Value

100 × 1.20 = $120

🛍️ Shop Sale Game

Calculate the sale price for each item, then add it to your basket!

👟
Trainers — Original: $12020% OFF
✓ Added!
👗
Dress — Original: $8530% OFF
✓ Added!
🎒
Backpack — Original: $6015% OFF
✓ Added!
🕶️
Sunglasses — Original: $4050% OFF
✓ Added!
⌚
Watch — Original: $15040% OFF
✓ Added!
🛒 Basket Total: $0.00

💰 Profit / Loss Calculator



Enter prices above to see the result!
Created by Mr Josh

✏️ Exercise 1: Percentage Increase (Step-by-Step)

For each question, fill in both the increase amount and the new value.

1. Increase $50 by 10%.   Increase = $   New value = $
2. Increase $200 by 15%.   Increase = $   New value = $
3. Increase $80 by 25%.   Increase = $   New value = $
4. Increase $350 by 20%.   Increase = $   New value = $
5. Increase $60 by 5%.   Increase = $   New value = $
6. A salary of $2000 rises by 8%. New salary = $
7. A population of 5000 grows by 12%. New population =
8. A shop increases all prices by 7%. Find the new price of an item costing $300. New price = $
Created by Mr Josh

✏️ Exercise 2: Percentage Decrease (Step-by-Step)

1. Decrease $100 by 20%.   Decrease = $   New value = $
2. Decrease $250 by 30%.   Decrease = $   New value = $
3. Decrease $80 by 5%.   Decrease = $   New value = $
4. Decrease $400 by 15%.   Decrease = $   New value = $
5. Decrease $1200 by 25%.   Decrease = $   New value = $
6. A phone costs $600 and has a 35% discount. Sale price = $
7. A class of 40 students loses 10% due to transfers. Students remaining =
8. A car valued at $18 000 depreciates by 12% in a year. New value = $
Created by Mr Josh

✏️ Exercise 3: Multiplier Method

First write the multiplier, then find the result using one multiplication.

1. Increase $90 by 10%.  Multiplier:   Result: $
2. Decrease $160 by 20%.  Multiplier:   Result: $
3. Increase $240 by 15%.  Multiplier:   Result: $
4. Decrease $500 by 35%.  Multiplier:   Result: $
5. Increase $75 by 40%.  Multiplier:   Result: $
6. Decrease $3000 by 5%.  Multiplier:   Result: $
7. Increase $48 by 50%.  Multiplier:   Result: $
8. Decrease $280 by 12.5%.  Multiplier:   Result: $
Created by Mr Josh

📐 Exercise 4: Percentage Change Formula

Use: % Change = (Change ÷ Original) × 100

1. Price goes from $50 to $60. % increase = %
2. Score goes from 80 to 64. % decrease = %
3. A crowd grows from 200 to 250. % increase = %
4. Rainfall drops from 40 mm to 30 mm. % decrease = %
5. A shirt rises from $40 to $52. % change = %
6. A plant grows from 25 cm to 35 cm. % increase = %
7. A jar of peanut butter drops from 500 g to 425 g. % decrease = %
8. An investment rises from $1000 to $1150. % return = %
Created by Mr Josh

🛒 Exercise 5: VAT, Profit/Loss & Discounts

1. A TV costs $400 + 15% VAT. Total price = $
2. A book costs $30 + 5% VAT. Total price = $
3. Buy for $50, sell for $65. Profit = $   % Profit = %
4. Buy for $120, sell for $90. Loss = $   % Loss = %
5. A jacket has 40% off its original price of $180. Sale price = $
6. A shop buys goods for $2000 and sells them for $2500. % profit = %
7. A laptop costs $950 before 15% VAT. VAT amount = $   Total = $
8. Trainers cost $220 with 30% discount. A friend gets an extra 10% off the sale price. Final price = $
Created by Mr Josh

📝 Practice (20 Questions)

1. Increase $40 by 10%. Answer: $
2. Decrease $80 by 25%. Answer: $
3. Increase $150 by 20% using the multiplier. Answer: $
4. Decrease $500 by 40% using the multiplier. Answer: $
5. Price goes from $60 to $75. % increase = %
6. Score drops from 120 to 90. % decrease = %
7. A $90 bag has 30% off. Sale price = $
8. A salary of $3600 increases by 5%. New salary = $
9. Buy for $200, sell for $260. % profit = %
10. A coat costs $250 + 15% VAT. Total = $
11. Multiplier for 35% increase =
12. Multiplier for 12% decrease =
13. Increase 640 by 12.5%. Answer:
14. Price falls from $180 to $144. % decrease = %
15. Buy for $75, sell for $60. % loss = %
16. A $5000 car loses 18% value per year. Value after 1 year = $
17. Item costs $320 + 5% VAT. Total = $
18. Crowd increases from 450 to 504. % increase = %
19. Decrease 720 by 37.5%. Answer:
20. A phone costs $800 with 25% discount. After the discount, 15% VAT is added. Final price = $
Created by Mr Josh

🏆 Challenge (8 Questions)

These require careful thinking. Show your working on paper first!

1. A price increases by 20%, then decreases by 20%. Is the final price the same as the original? If not, what is the % change overall? (Start with $100.) Answer:
2. After a 25% increase, a value is $375. What was the original value? $
3. After a 30% decrease, a price is $105. What was the original price? $
4. A shop increases a price by 40% and then offers 30% off. What single percentage change is this equivalent to? % (increase or decrease?)
5. An item is sold for $234 at a 30% profit. What was the cost price? $
6. A store marks up goods by 60% to get the selling price. During a sale, everything is 25% off the selling price. What is the % profit on the original cost? %
7. A laptop depreciates by 20% per year. What percentage of its original value remains after 2 years? %
8. An article sells for $345 including 15% VAT. What is the pre-VAT price? $
Created by Mr Josh