Percent Increase and Decrease
Learn how to calculate percent increase and percent decrease to measure changes in quantities.
Definition
- If the result is positive, it's a percent increase
- If the result is negative, it's a percent decrease
- For a 20% increase: multiply by (which is )
- For a 20% decrease: multiply by (which is )
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Worked Examples
A pair of sneakers was 80 dollars last year. This year it costs 100 dollars. What is the percent increase?
Identify the values
Original = 80 dollars, New = 100 dollars → Original: 80, New: 100
Find the change
dollars → Change = 20
Divide by original
→ 0.25
Convert to percent
→ 25% increase
Answer: The price increased by 25%.
Common Mistakes
Using the new value instead of the original value in the denominator
Why it's wrong: Percent change is always relative to where you started, not where you ended up.
Correct: Always divide by the ORIGINAL value:
Thinking a 50% increase followed by a 50% decrease returns to the original
Why it's wrong: After a 50% increase, the new base is larger. A 50% decrease of a larger number takes away more.
Correct: Example: 100 increases by 50% to 150. Then 150 decreases by 50% to 75, not back to 100!
Confusing percent increase with the new total
Why it's wrong: A 20% increase doesn't mean the new value is 20% - it means you ADD 20% to 100%.
Correct: For 20% increase, multiply by 1.20 (not 0.20). The new value is 120% of the original.
Forgetting to convert the decimal to a percent
Why it's wrong: 0.15 and 15% look different but represent the same amount. Forgetting to multiply by 100 gives the wrong answer format.
Correct: After dividing, multiply by 100 to express as a percent:
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Practice Problems
18 problemsA shirt's price increased from 40 dollars to 50 dollars. What is the percent increase?
Why It Matters
- Shopping: A shirt originally 40 dollars is now 25% off. What's the sale price?
- Salary: Your hourly wage increases from 15 to 18 dollars. What percent raise is that?
- Investments: A stock rises from 50 to 65 euros. What's the percent gain?
- Population: A town grows from 10,000 to 12,500 people. What's the growth rate?
- Grades: Your test score improved from 70 to 84. How much did you improve?
Real World Applications
Shopping and Discounts
Stores use percent decrease to show how much you save during sales.
Example:
A 40% off sale on a 90 dollar item means you pay dollars.
A store advertises '30% off everything!' You want to buy headphones originally priced at 80 dollars.
How much will you pay?
Step 1: Write the mathematical expression
Calculate the sale price:
Salary and Wages
Employers and employees use percent increase to discuss raises and cost-of-living adjustments.
Example:
A 5% raise on a 50,000 dollar salary means a new salary of dollars.
Your monthly salary is 3,000 euros. You receive a 8% raise.
What is your new monthly salary?
Step 1: Write the mathematical expression
Calculate the new salary:
Population Growth
Demographers use percent change to track how populations grow or shrink over time.
Example:
A city with 500,000 people that grows by 4% will have people.
A town had 25,000 residents last year. This year it has 27,500 residents.
What is the percent increase in population?
Step 1: Write the mathematical expression
Calculate the percent change:
Key Takeaways
- 1Percent change =
- 2Positive result = percent increase; Negative result = percent decrease
- 3For X% increase, multiply by . Example: 15% increase uses multiplier 1.15
- 4For X% decrease, multiply by . Example: 15% decrease uses multiplier 0.85
- 5Always use the ORIGINAL value as the base for calculations
Frequently Asked Questions
Glossary
- Percent increase
- A positive percent change indicating growth from the original value
- Percent decrease
- A negative percent change indicating reduction from the original value
- Multiplier
- A decimal used to calculate the new value directly (e.g., 1.20 for 20% increase)
- Original value
- The starting value before any percent change is applied
- Markup
- A percent increase added to cost to determine selling price
- Discount
- A percent decrease from the regular price
Formula Card
Percent Change
Calculates the percent increase (positive) or decrease (negative)
Increase Multiplier
Find new value after percent increase
Decrease Multiplier
Find new value after percent decrease
Find Original
Work backwards from new value to find original