Understanding percentages is a fundamental skill in everyday life, and being able to calculate inverse percentages is just as important. Whether you’re working on a mathematical problem or trying to calculate discounts while shopping, knowing how to determine the original value from a given percentage can save you time and effort. In this step-by-step guide, we’ll walk you through the process of calculating inverse percentages.

What is an inverse percentage?

An inverse percentage refers to the process of finding the original value before a percentage was applied. For example, if you know that 80% of an item’s original value is $100, you can use inverse percentage calculations to determine the item’s original price.

Step 1: Convert the percentage to a decimal

The first step in calculating an inverse percentage is to convert the given percentage to a decimal. To do this, divide the percentage value by 100. For instance, if the given percentage is 80%, divide 80 by 100, which equals 0.8.

Step 2: Divide the known value by the decimal

In the second step, divide the known value obtained after the percentage was applied by the decimal obtained in the previous step. Using the previous example, divide $100 by 0.8: $100 ÷ 0.8 = $125.

Step 3: Calculate the original value

The final step is to determine the original value before the percentage was applied. To do this, subtract the value obtained in step 2 from the known value. Continuing with the same example, subtract $125 from $100 to get $25. So, the original value is $25.

Using these three steps, you can easily calculate the inverse percentage for various scenarios. Just remember to convert the percentage to a decimal, divide the known value by the decimal, and subtract the result from the known value to find the original value.

Example:

Let’s work through an example to ensure you fully grasp the concept. Imagine a jacket initially priced at $120 is reduced by 30%. To find the original price, you would:

  • Step 1: Convert the percentage to a decimal: 30 ÷ 100 = 0.3.
  • Step 2: Divide the reduced price by the decimal: $120 ÷ 0.3 = $400.
  • Step 3: Calculate the original price: $400 – $120 = $280.

Calculating inverse percentages may seem challenging at first, but by following these simple steps, you can easily find the original value. Remember to convert the percentage to a decimal, divide the known value by the decimal, and subtract the result from the known value. With this guide, you can confidently tackle any inverse percentage calculation that comes your way, whether it’s for everyday life situations or more complex mathematical problems.

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