Skill: Calculate percent increase and percent decrease

A percent change compares the change with the original amount, also called the baseline.

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

• If the new amount is greater, it is a percent increase.
• If the new amount is smaller, it is a percent decrease.

Example

A backpack originally costs 80$. Its price increases to$$92$. What is the percent increase?

Step 1: Find the change.

$$\$92-\$80=\$12$$

The price increased by 12$.

Step 2: Divide by the original amount.

$$\frac{12}{80}=0.15$$

Use 80$, not$$92$, because the original amount is the baseline.

Step 3: Convert the decimal to a percent.

$$0.15\times 100\%=15\%$$

The price increased by $(15\%)$.

You can also use a multiplier to find the new price:

$$1+0.15=1.15$$ $$\$80(1.15)=\$92$$

For a decrease, subtract the decimal from $1$. For example, a $(15\%)$ decrease uses the multiplier

$$1-0.15=0.85.$$

Remember: a percent change is different from a percentage-point change. Percent change compares amounts, while percentage points compare percentages directly.