Reverse calculation, also known as working backwards, involves determining the original value before a percentage increase or decrease was applied. It's essentially undoing the percentage change. Here's how to calculate it:
Steps to Calculate Reverse Percentage:
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Determine the resulting percentage: If the problem states a percentage increase, add that percentage to 100%. If it states a percentage decrease, subtract that percentage from 100%. This tells you what percentage of the original value you now have.
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Find 1%: Divide the new value (the value after the percentage change) by the percentage you calculated in step 1. This gives you the value of 1% of the original amount.
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Calculate the original value (100%): Multiply the value of 1% (from step 2) by 100. This gives you the original value before the percentage change.
Example 1: Reverse Calculation with a Percentage Increase
Let's say a shirt costs \$33 after a 10% price increase. What was the original price?
- Determine the resulting percentage: 100% (original price) + 10% (increase) = 110%
- Find 1%: \$33 / 110 = \$0.30
- Calculate the original value (100%): \$0.30 * 100 = \$30
Therefore, the original price of the shirt was \$30.
Example 2: Reverse Calculation with a Percentage Decrease
A shop is selling a television for \$360 after applying a 20% discount. What was the original price?
- Determine the resulting percentage: 100% (original price) - 20% (discount) = 80%
- Find 1%: \$360 / 80 = \$4.50
- Calculate the original value (100%): \$4.50 * 100 = \$450
Therefore, the original price of the television was \$450.
Formula Summarization:
Let:
- New Value = The value after the percentage change
- Original Value = The value before the percentage change
- Percentage Change = The percentage increase or decrease (expressed as a decimal)
If there is an increase:
- Original Value = New Value / (1 + Percentage Change as a decimal)
If there is a decrease:
- Original Value = New Value / (1 - Percentage Change as a decimal)
Common Pitfalls to Avoid:
- Incorrectly Adding/Subtracting: Make sure you are adding for an increase and subtracting for a decrease.
- Dividing by the Wrong Value: Always divide the new value by the adjusted percentage (either 100% + increase or 100% - decrease). Do not divide by the original percentage change alone.
- Incorrectly Converting Percentage to Decimal: If using formulas, divide the percentage by 100 to get a decimal (e.g., 10% becomes 0.10).
Reverse calculation involves understanding how percentages affect original values and applying the correct steps to "undo" the change, ultimately revealing the starting amount.
