What are common mistakes when reversing percentages?

How to Avoid the Classic Trap When Reversing Percentages

Working backward from a final price or value often trips people up. The single most common mistake when reversing a percentage is applying the percentage rate directly to the final number. For instance, if an item is discounted by 30% and now costs $70, calculating 30% of $70 ($21) and adding it back gives $91—which is wrong. The original price was actually $100.

To reverse a percentage accurately, you must always calculate relative to the original baseline of 100%. A 30% decrease means the final value represents 70% (100% - 30%) of the starting amount. Instead of multiplying by the discount percentage, you divide the final amount by the remaining proportion—in this case, dividing $70 by 0.70 to retrieve the true original price. By focusing on what remains rather than what was removed or added, you can easily avoid this common math pitfall.