Do you often find yourself struggling with reverse percentage problems? Don't worry, you're not alone. Many people find reverse percentages challenging, but with a little bit of practice and some simple calculations, you can master them too. In this article, we'll show you how to do reverse percentage in a step-by-step guide.
What is Reverse Percentage?
Before we dive into the details, let's first understand what reverse percentage means. Reverse percentage is the process of finding the original value of a percentage increase or decrease. In other words, if you know the percentage increase or decrease and the final value, you can use reverse percentage to find the original value.
Step-by-Step Guide to Reverse Percentage
Here's a step-by-step guide to help you solve reverse percentage problems:
Step 1: Convert the Percentage to a Decimal
The first step is to convert the percentage to a decimal. To do this, divide the percentage by 100. For example, if you have a percentage of 25%, divide it by 100 to get 0.25.
Step 2: Divide the Final Value by the Decimal
The next step is to divide the final value by the decimal from step 1. For example, if you have a final value of 125 and a decimal of 0.25, divide 125 by 0.25 to get 500.
Step 3: Subtract the Original Value from the Final Value
Once you have the original value, you can verify your answer by subtracting the original value from the final value. The result should be equal to the percentage increase or decrease. For example, if you had a percentage increase of 25% and a final value of 125, the original value would be 100. If you subtract 100 from 125, you get 25, which is the percentage increase.
Example Problems
Let's take a look at a few example problems to help you understand how to use reverse percentage.
Example 1:
A shirt is on sale for 20% off, and the sale price is $24. What was the original price of the shirt?
Step 1: Convert the percentage to a decimal: 20/100 = 0.2
Step 2: Divide the final value by the decimal: $24/0.2 = $120
Step 3: Subtract the original value from the final value: $120 - $96 = $24
Therefore, the original price of the shirt was $120.
Example 2:
A stock has increased in value by 15%, and the new value is $690. What was the original value of the stock?
Step 1: Convert the percentage to a decimal: 15/100 = 0.15
Step 2: Divide the final value by the decimal: $690/0.15 = $4,600
Step 3: Subtract the original value from the final value: $4,600 - $3,990 = $690
Therefore, the original value of the stock was $3,990.
Tips for Solving Reverse Percentage Problems
Here are a few tips to help you solve reverse percentage problems more easily:
- Always convert the percentage to a decimal first.
- Be careful with the order of operations when dividing or multiplying.
- Double-check your answer by subtracting the original value from the final value.
Conclusion
Reverse percentage can be a challenging concept, but with practice and a good understanding of the steps, you can master it. Remember to always convert the percentage to a decimal, divide the final value by the decimal, and double-check your answer by subtracting the original value from the final value. With these tips and the step-by-step guide we've provided, you'll be able to solve reverse percentage problems with ease.
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