Understanding Percentage Increase and Decrease

Percentage is a way of expressing a number as a fraction of 100. In mathematics, it is frequently used to describe how much a quantity has increased or decreased in relation to its original value. This lesson will guide you through the concepts of percentage increase and decrease, as well as repeated percentage change.

Percentage Increase

Percentage increase refers to the amount a number grows in relation to its original value. To calculate the percentage increase, you can use the formula:

Percentage Increase = ((New Value - Original Value) / Original Value) x 100%

For example, if a student scores 70 on a test and later scores 80, the percentage increase is calculated as follows:

New Value = 80
Original Value = 70
Percentage Increase = ((80 - 70) / 70) x 100% = (10 / 70) x 100% ≈ 14.29%

Percentage Decrease

Percentage decrease is the measure of how much a number has decreased in relation to its original value. The formula for calculating percentage decrease is:

Percentage Decrease = ((Original Value - New Value) / Original Value) x 100%

For instance, if a price drops from £50 to £40, the percentage decrease is:

Original Value = 50
New Value = 40
Percentage Decrease = ((50 - 40) / 50) x 100% = (10 / 50) x 100% = 20%

Real-World Applications

Understanding percentage increase and decrease is crucial in various scenarios such as shopping discounts, calculating interest rates, and analyzing data trends. For example, if a product is on sale, knowing how to calculate the percentage decrease can help you determine the final price.

Repeated Percentage Change

Repeated percentage change occurs when a quantity increases or decreases by a certain percentage multiple times. This concept is important in finance, population studies, and growth models.

Calculating Repeated Percentage Change

To calculate the total change after multiple percentage changes, you can use the following approach:

Final Value = Initial Value x (1 + Percentage Change)^n

where n is the number of times the percentage change occurs.

For example, if an investment of £100 increases by 10% for three years, the final value can be calculated as:

Initial Value = 100
Percentage Change = 0.10
n = 3
Final Value = 100 x (1 + 0.10)^3 = 100 x (1.10)^3 ≈ 133.10

Practice Problems

1. A salary of £2000 is increased by 15%. What is the new salary?
2. A jacket originally priced at £80 is on sale for £60. What is the percentage decrease?

3. A population of 5000 increases by 5% every year for 4 years. What is the population at the end of 4 years?

Conclusion

In this lesson, we have explored the concepts of percentage increase, percentage decrease, and repeated percentage change. Mastery of these concepts will not only enhance your mathematical skills but also improve your ability to analyze real-world situations effectively.