Introduction

Percentages are an essential part of daily life, whether you use them for calculating discounts, tax, or even determining success rates. While most people are familiar with finding percentages of numbers, reversing a percentage calculation is a skill that comes in handy when solving real-world problems. In this article, we’ll walk you through the process of reversing a percentage calculation step by step.

Step 1: Understand the Problem

To reverse a percentage calculation, first, make sure you have a clear understanding of the problem. This involves identifying the original value (the base), the final value (the result after applying the percentage), and the percentage change.

For instance, let’s say you bought a product that costs $150 after a 20% discount. To find the original price before the discount, you need to reverse the percentage calculation.

Step 2: Convert Percentage to Decimal

Before proceeding with calculations involving percentages, it’s crucial to convert percentages into decimals. Simply divide the given percentage by 100 to get the decimal equivalent.

In our example above, the 20% discount would be converted to:

20 ÷ 100 = 0.2

Step 3: Reverse Percentage Calculation

Once you’ve converted the percentage to its decimal form, there are two methods available for reversing the calculation:

Method 1 – Division

The simplest approach to reversing a percentage reduction or increase is dividing the final value by one minus/plus the decimal equivalent of the percentage change.

For example, if we have a final value V and a percentage decrease p:

Original Value = V / (1 – p)

For our sample problem:

Original Value = $150 / (1 – 0.2) = $150 / 0.8 = $187.50

If it was instead an increase in price by p%:

Original Value = V / (1 + p)

Method 2 – Algebraic Approach

Another method for reversing a percentage calculation involves working through the algebraic formula:

Original Value * (1 +/ – p) = Final Value

Here, you need to isolate the “Original Value” by rearranging the formula and then solving for it.

Let’s revisit our example problem:

Original Value * (1 – 0.2) = $150

Original Value * 0.8 = $150

To find the original value, divide both sides of the equation by 0.8:

Original Value = $150 / 0.8 = $187.50

Conclusion

Reversing a percentage calculation might seem daunting initially, but with a proper understanding of the problem and following either of these straightforward methods, you can effortlessly find the original value. From determining the pre-discount prices to solving various other real-life scenarios, this skill will surely prove to be valuable in your everyday calculations.