Reverse Percentage Calculations

This page provides a comprehensive guide on how to perform reverse percentage calculations in various scenarios, including both increases and decreases. The information is crucial for students learning to find the original number of a percentage increase or decrease.

Reverse Percentage for Increases

To calculate the original value from a percentage increase, follow these steps:

1. Convert the percentage to a decimal
2. Add 1 to the decimal
3. Divide the new amount by the result from step 2

Highlight: This method is particularly useful when you need to find the original price after a percentage increase.

Reverse Percentage for Decreases

The process for decreases is slightly different:

1. Convert the percentage to a decimal
2. Subtract the decimal from 1.00
3. Divide the new amount by the result from step 2

Vocabulary: Reverse percentage formula - The mathematical expression used to find the original value before a percentage change was applied.

Practical Example

The guide provides an example to illustrate the reverse percentage increase calculation:

Patrick invested money in a bank account that earns 4% interest annually. After one year, the account balance is £291.20. To find Patrick's original investment:

1. Convert 4% to 0.04
2. Add 1: 1.00 + 0.04 = 1.04
3. Divide the new amount by 1.04: £291.20 ÷ 1.04 = £280

Example: This demonstrates how to find the original amount after a percentage increase, which is a common application in financial calculations.

Highlight: Understanding these steps to find original price after percentage increase is crucial for solving various real-world problems, from finance to data analysis.

The page emphasizes the importance of these calculations, making it a valuable resource for those learning to work with percentages and their applications in practical scenarios.