Lesson 2: Percent Increase and Decrease

Property

To find the percent change:

• Step 1. Find the amount of change.

• Step 2. Find what percent the amount of change is of the original amount. The amount of change is what percent of the original amount?

Examples

• A shirt's price increased from 20 dollars to 25 dollars. Find the percent change. The change is $25 - 20 = 5$ dollars. The percent change is $\frac{5}{20} = 0.25$, which is a 25% increase.

• A car's value decreased from 15,000 dollars to 12,000 dollars. Find the percent change. The change is $12,000 - 15,000 = -3,000$ dollars. The percent change is$\frac{-3000}{15000} = -0.20$, a 20% decrease.

Property

A percentage $p\%$ must be applied to a quantity; it is not a standalone number to be added or subtracted.
First, find the amount of change by converting the percentage to a decimal and multiplying by the original value ($N$).

Property

To increase a number by a percentage, multiply by $(1 + \text{decimal})$.
For example, an increase of 5% means multiplying by $1.05$.
To decrease a number by a percentage, multiply by $(1 - \text{decimal})$.
For example, a decrease of 20% means multiplying by $0.80$.

Examples