Percent Increase and Decrease

What You’ll Learn

In this lesson you’ll learn how to find percent increase (growth) and percent decrease (reduction), including the formula and examples.

The Concept

Percent increase/decrease measures change relative to the original amount.

Formula:

$$\text{Percent change} = \frac{\text{new} - \text{original}}{\text{original}} \times 100\%$$

• Positive result = increase
• Negative = decrease

Shortcut for increase: Add the percent of original. Example: 20% increase on 50 = $50 + (0.20 \times 50) = 60$

For decrease: Subtract the percent. 30% decrease on 80 = $80 - (0.30 \times 80) = 56$

Worked Examples

A salary of 40,000 dollars increases by 8%.

1. Increase amount: $0.08 \times 40{,}000 = 3{,}200$ dollars
2. New salary: $40{,}000 + 3{,}200 = 43{,}200$ dollars
3. Percent increase: $\frac{3{,}200}{40{,}000} \times 100\% = 8\%$

Price of 120 dollars decreases by 25%.

1. Decrease: $0.25 \times 120 = 30$ dollars
2. New price: $120 - 30 = 90$ dollars

Real-World Applications

Percent increase/decrease appears in raises (5% salary bump), discounts (30% off sale), inflation (prices up 4%), or fuel efficiency changes. It helps understand how much things really change relative to the starting amount.

You’ve Got This

Percent change is just “how much bigger/smaller compared to the original.” Multiply the percent by the original, then add/subtract. Check by seeing if the change makes sense (a 50% increase doubles the number). Practice with sale prices or bills and it’ll click fast.

Quiz

A 50-dollar item increases by 20%. New price?

• A.60 dollars
• B.70 dollars
• C.55 dollars
• D.40 dollars

A price drops from 80 dollars to 64 dollars. Percent decrease?

• A.20%
• B.25%
• C.16%
• D.30%

Salary of 50,000 dollars increases by 6%. New salary?

• A.53,000 dollars
• B.52,000 dollars
• C.56,000 dollars
• D.50,600 dollars

A 200-dollar bill decreases by 15%. New amount?

• A.170 dollars
• B.185 dollars
• C.230 dollars
• D.160 dollars

A stock was 40 dollars and is now 50 dollars. What is the percent increase?

• A.25%
• B.20%
• C.10%
• D.50%