Lesson 5: Percents of Increase and Decrease

Property

If a quantity grows, then the increase in the quantity, determined as a percent of the original, is the percent increase. The new amount can be calculated with the expression: $Original(1) + Original(\text{percent increase}) = Original(1 + \text{percent increase})$. For example, an increase of 25% is calculated as $200(1) + 200(0.25) = 200(1.25) = 250$.

Examples

• A plant was 10 inches tall and grew by 30%. The increase is $10 \times 0.30 = 3$ inches. The new height is $10 + 3 = 13$ inches.

• The price of a video game increased from 40 dollars to 50 dollars. The increase is 10 dollars. The percent increase is $\frac{10}{40} = 0.25$, or 25%.

Property

If a quantity shrinks, then the decrease in the quantity, determined as a percent of the original, is the percent decrease. The new amount can be calculated with the expression: $Original(1) + Original(-\text{percent decrease}) = Original(1 - \text{percent decrease})$. For example, a decrease of 20% is calculated as $125(1) + 125(-0.20) = 125(0.80) = 100$.

Examples

• A sweater originally costing 60 dollars is on sale for 25% off. The discount is $60 \times 0.25 = 15$ dollars. The sale price is $60 - 15 = 45$ dollars.

• The number of daily visitors to a website dropped from 800 to 600. The decrease is 200. The percent decrease is $\frac{200}{800} = 0.25$, or 25%.

Property

When analyzing data tables and graphs for percent change, identify the original and new values, then apply the appropriate formula: percent of increase = $\frac{\text{new amount} - \text{original amount}}{\text{original amount}} \times 100\%$ or percent of decrease = $\frac{\text{original amount} - \text{new amount}}{\text{original amount}} \times 100\%$.

Examples