Skill: Calculate percent increase and percent decrease

A percent change compares the change to the original amount:

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

• If the result is positive, it is a percent increase.
• If the result is negative, it is a percent decrease.

Example: Finding a percent increase

A movie ticket price increases from $10 to $12. What is the percent increase?

Step 1: Find the change.

$$12-10=2$$

The price increased by $2.

Step 2: Compare the change with the original price.

The original price is $10, so use $10 as the denominator:

$$\frac{2}{10}=0.2$$

Step 3: Convert the decimal to a percent.

$$0.2\times 100\%=20\%$$

The ticket price increased by 20%.

For a decrease, use the same idea: compare the amount lost with the original amount. For example, a change from $10 to $8 is

$$\frac{8-10}{10}\times100\%=-20\%$$

The negative sign shows a 20% decrease.