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Calculate percent increase and decrease
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Have you ever wondered how much something increased or decreased? Percent of change tells us exactly that - how much a quantity changed relative to its original amount. This is everywhere in real life: price changes, population growth, sale discounts, and more!
Percent of change tells us how much a quantity has increased or decreased as a percentage of the original amount.
Formula:
Percent of Change = (Amount of Change / Original Amount) × 100%
Or: (New - Original) / Original × 100%
When a value gets larger.
Examples:
A shirt was originally 15. What is the percent decrease?
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When a value gets smaller.
Examples:
Steps:
A shirt costs 25. What is the percent increase?
Step 1: Amount of increase
Step 2: Divide by original
Step 3: Convert to percent
Answer: The price increased by 25%
A town's population was 8,000 last year. This year it's 8,800. Find the percent increase.
Step 1: Increase
Step 2: Divide by original
Step 3: Convert to percent
Answer: Population increased by 10%
Maria scored 72 on her first test and 90 on her second test. What was her percent increase?
Step 1: Increase
Step 2: Divide by original
Step 3: Convert to percent
Answer: Her score increased by 25%
Steps:
A jacket originally costs 60. What is the percent decrease?
Step 1: Amount of decrease
Step 2: Divide by original
Step 3: Convert to percent
Answer: The price decreased by 25% (25% off!)
Sam weighed 180 pounds and now weighs 162 pounds. Find the percent decrease.
Step 1: Decrease
Step 2: Divide by original
Step 3: Convert to percent
Answer: Weight decreased by 10%
The temperature was 85°F and dropped to 68°F. What was the percent decrease?
Step 1: Decrease
Step 2: Divide by original
Step 3: Convert to percent
Answer: Temperature decreased by 20%
Common mistake: Using the new amount as the denominator.
Example: Price drops from 40.
❌ WRONG: 40 = 0.25 = 25%
✓ RIGHT: 50 = 0.20 = 20%
Always divide by the original (starting) amount!
Sometimes you know the percent change and need to find the new amount.
Method: New Amount = Original × (1 + percent increase as decimal)
Example: A $40 item increases by 15%. What's the new price?
Solution:
Answer: $46
Why it works: 100% of original + 15% increase = 115% of original = 1.15 × original
Method: New Amount = Original × (1 - percent decrease as decimal)
Example: A $60 item decreases by 20%. What's the new price?
Solution:
Answer: $48
Why it works: 100% of original - 20% decrease = 80% of original = 0.80 × original
Problem: A $120 coat is on sale for 35% off. What's the sale price?
Solution:
Answer: $78
Problem: You invest $1,000 and it grows by 8%. What's your new total?
Solution:
Answer: $1,080
Problem: A player's average went from 15 points per game to 18 points per game. What's the percent increase?
Solution:
Answer: 20% increase
Problem: A city's population was 250,000 and decreased to 225,000. What's the percent decrease?
Solution:
Answer: 10% decrease
Markup is when a store adds to the cost to set a selling price.
Example: A store buys a shirt for $20 and marks it up 60%. What's the selling price?
Solution:
Answer: $32
Markdown is when a store reduces the price (a discount).
Example: A $50 item is marked down 30%. What's the sale price?
Solution:
Answer: $35
When something changes multiple times, you can't just add the percents!
Example: A $100 item increases by 10%, then decreases by 10%. What's the final price?
Wrong way: +10% - 10% = 0%, so still $100? NO!
Right way:
Answer: 100!)
Why? The 10% decrease is calculated from 100!
❌ Mistake 1: Using the new amount as the original
❌ Mistake 2: Forgetting to multiply by 100
❌ Mistake 3: Adding percents for multiple changes
❌ Mistake 4: Confusing increase vs decrease
❌ Mistake 5: Sign errors
Tip 1: Use the formula relationship
Think of it like this: Amount of Change = Original × Percent
If you know any two values, you can find the third!
Tip 2: Check reasonableness
Tip 3: Identify what's given
Tip 4: Set up carefully
Finding Percent of Change:
Finding New Amount:
Finding Original Amount:
Percent of change measures how much something increased or decreased compared to the original amount.
Key Points:
Master percent of change and you'll be able to analyze real-world data, understand sales and discounts, and make informed decisions about money and statistics!
Step 1: Find the amount of change Change = Original - New = 20 - 15 = $5
Step 2: Use the percent of change formula Percent of change = (Change/Original) × 100% Percent of change = (5/20) × 100% Percent of change = 0.25 × 100% = 25%
Since the price went down, this is a 25% decrease.
Answer: 25% decrease
A plant grew from 8 inches to 10 inches tall. What is the percent increase?
Step 1: Find the amount of change Change = New - Original = 10 - 8 = 2 inches
Step 2: Use the percent of change formula Percent of change = (2/8) × 100% Percent of change = 0.25 × 100% = 25%
Since it grew, this is a 25% increase.
Answer: 25% increase
A store marks up a watch by 40%. If the store paid $50 for the watch, what is the selling price?
Method 1: Calculate the markup amount Markup = 40% of 20 Selling price = 20 = $70
Method 2: Use multiplier Multiplier = 1 + 0.40 = 1.40 Selling price = 70
Answer: $70
A jacket is marked down 30% from its original price of $80. What is the sale price?
Method 1: Calculate the discount Discount = 30% of 24 Sale price = 24 = $56
Method 2: Use multiplier Multiplier = 1 - 0.30 = 0.70 Sale price = 56
Answer: $56
A stock price increased by 20% on Monday and then decreased by 20% on Tuesday. If it started at $100, what is the final price? Did it return to the original price?
Monday (20% increase): Multiplier = 1.20 Price after Monday = 120
Tuesday (20% decrease): Multiplier = 0.80 Price after Tuesday = 96
Final price: $96
No, it did NOT return to the original price! The 20% decrease is calculated on the larger amount ($120), so it loses more money than it gained.
Difference from original: 96 = $4 loss
Answer: $96 (not back to original)