Ever needed to figure out the original price of something before tax or a discount was applied? That’s where a reverse percentage comes in handy. A reverse percentage calculation helps you find the original number when you only know what a percentage of it is.
The key is dividing the known value by the decimal form of the percentage. Keep reading to see how it works.
Reverse percentage: the formula
The formula for calculating reverse percentage is:
Original Number = Given Number / (Percentage / 100)
In this formula, the “Given Number” is the value you know, and “Percentage” refers to the percentage it represents.
For an accurate calculation, you’ll need to convert the percentage to a decimal.
Here’s how to convert to a decimal:
Percentage / 100 = Decimal Value
Then, you’ll use the decimal value in the formula:
Original Number = Given Number / Decimal Value
How to Calculate Reverse Percentages: Step-by-Step
Here’s how to calculate the original number when you only know a percentage of it:
- Step 1: Figure out what number you have and what percentage of the original number it represents.
- Step 2: Turn the percentage into a decimal. For example, 25% becomes 0.25.
- Step 3: Divide the number you have by the decimal. This gives you the original number.
- Step 4: Double-check your answer. Calculate the percentage of the original number you calculated. Does it match the number you started with?
Examples of reverse percentage calculations
Reverse percentage calculations can be tricky, but they’re pretty easy once you get the hang of them. Here are a few examples to help you understand how they work:
Example 1: Simple reverse percentage
Problem: 100 is 25% of what number?
Solution: 100 / 0.25 = 400
Explanation: Twenty-five percent of 400 is 100, so 400 is the original number.
Example 2: More complex reverse percentage
Problem: 121 is 32% of what number?
Solution: 121 / 0.32 = 378.125
Explanation: Thirty-two percent of 378.125 is 121, so 378.125 is the original number.
Example 3: Real-world application (sales tax)
Problem: A shirt costs $25 after a 6% sales tax. What was the original price?
Solution: $25 / 1.06 = $23.58 (approximately).
Explanation: The original price was about $23.58. The 1.06 represents 100% of the original price plus 6% sales tax.
Closing Thoughts
Reverse percentages are a handy tool for working out the original amount when you only know the final value.
Remember our formula: Original Number = Given Number / Decimal Value. It’s simple and effective.
For best results, try working through a few examples. The more you practice, the easier it’ll be to calculate those original numbers.