Calculate percent increase and percent decrease

Percent increase and decrease describe multiplicative change relative to an original amount: the percent change is $(\text{new amount} - \text{original amount})/\text{original amount}$ , expressed as a percent, so a rate $r$ produces $\text{original}(1+r)$ for an increase and $\text{original}(1-r)$ for a decrease. This understanding applies to discounts, markups, tax, depreciation, and inflation, emphasizes the original quantity as the reference base, and distinguishes successive percentage changes from simply adding rates; continuous growth and advanced compound-interest models are not included.

Detailed Explanation: 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.

Learn by doing: Calculate percent increase and percent decrease

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Percent growth of a number (1% multiples)

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