Percentage Increase and Decrease

Introduction

Percentages are a way to express a number as a fraction of 100. Understanding percentage increase and decrease is essential in various real-life situations, such as calculating discounts, profits, and changes in prices.

Percentage Increase

To calculate the percentage increase between two values:

1. Find the difference between the new value and the original value.
2. Divide the difference by the original value.
3. Multiply the result by 100 to convert it to a percentage.

The formula for percentage increase is:

$$\text{Percentage Increase} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100$$

Example of Percentage Increase

If the price of a shirt increases from $20 to$25:

1. Difference: $25 -$20 = $5
2. Divide by original value: $\frac{5}{20} = 0.25$
3. Convert to percentage: $0.25 \times 100 = 25\\%$

Thus, the percentage increase is $25\%$.

Percentage Decrease

To calculate the percentage decrease:

1. Find the difference between the original value and the new value.
2. Divide the difference by the original value.
3. Multiply the result by 100 to convert it to a percentage.

The formula for percentage decrease is:

$$\text{Percentage Decrease} = \frac{\text{Original Value} - \text{New Value}}{\text{Original Value}} \times 100$$

Example of Percentage Decrease

If the price of a shirt decreases from $30 to$24:

1. Difference: $30 -$24 = $6
2. Divide by original value: $\frac{6}{30} = 0.2$
3. Convert to percentage: $0.2 \times 100 = 20\\%$

Thus, the percentage decrease is $20\%$.

Key Questions

• How do you calculate the percentage increase from one value to another?
• What steps are involved in finding the percentage decrease?
• Can you give an example of a real-life situation involving percentage increase or decrease?

Summary

Understanding percentage increase and decrease helps in making informed decisions based on changes in values and prices.