Percentage Increases & Decreases

Learn percentage calculations with clear formulas and step-by-step examples. Plus, practice with our interactive calculator and test your skills with the quiz below!"

🔢 How to Calculate Percentage Changes

For Percentage Increase: New Value = Original × (1 + percentage)
For Percentage Decrease: New Value = Original × (1 - percentage)

➕ Use + for increases | ➖ Use - for decreases

💡 Quick Tip: Convert percentages to decimals by dividing by 100. For example: 15% = 0.15, 12% = 0.12
Example 1: Price Increase

Problem: A shirt costs $40. If the price increases by 15%, what is the new price?

Step 1: Convert percentage: 15% = 0.15
Step 2: Use formula: New Value = $40 × (1 + 0.15)
Step 3: Calculate: New Value = $40 × 1.15 = $46
✅ Answer: $46
Example 2: Depreciation

Problem: A car worth $20,000 depreciates by 12% each year. What is its value after one year?

Step 1: Convert percentage: 12% = 0.12
Step 2: Use formula: $20,000 × (1 - 0.12)
Step 3: Calculate: $20,000 × 0.88 = $17,600
✅ Answer: $17,600

🔍 Finding the Original Amount

Original Value = Final Value1 ± percentage

➕ Use + if final value is after an increase
➖ Use - if final value is after a decrease

💡 Key Words to Watch: "after a discount", "is 25% of", "increased to" — these tell you what part of the total you are working with.
Example 3: Finding Original Price

Problem: After a 20% discount, a laptop costs $800. What was the original price?

Step 1: Convert percentage: 20% = 0.20
Step 2: Use formula: $8001 - 0.20
Step 3: Calculate: $8000.80 = $1,000
✅ Answer: $1,000
Example 4: Finding Total from Part

Problem: 75% of students passed the test. If 180 students passed, how many took the test?

Step 1: Convert percentage: 75% = 0.75
Step 2: Use formula: 1800.75
Step 3: Calculate: 1800.75 = 240
✅ Answer: 240 students

🧮 Percent Change Calculator

Practice with your own numbers using this calculator!

📊 Test Your Knowledge!

1. A shirt originally costs $40. After a sale, it costs $32. What is the percent decrease?
A) 20%
B) 25%
C) 8%
D) 12%
2. The population of a town increased from 5,000 to 6,500. What is the percent increase?
A) 25%
B) 23%
C) 30%
D) 1,500%
3. A stock price dropped from $80 to $60. What is the percent decrease?
A) 20%
B) 25%
C) 33.3%
D) 75%
4. A restaurant bill was $50. After adding an 18% tip, what is the total amount?
A) $59
B) $68
C) $58
D) $60
5. A laptop's price increased from $800 to $920. What is the percent increase?
A) 12%
B) 13%
C) 120%
D) 15%