A reliable method
Write an increase as a multiplier above one and a decrease as a multiplier below one. To reverse a percent change, divide by the multiplier that was applied.
The common trap
A ten percent discount followed by a ten percent increase does not return to the starting price. The second percentage uses a smaller base.
Check and transfer
Use simple interest only when the prompt specifies that interest is calculated on the original principal. Compound growth uses a changing balance and a different model.
Worked comparison: why the alternative fails
A $60 price after a 25% discount solves 0.75p = 60, so p = 80. Adding 25% of 60 gives 75, which fails: 75×0.75 = 56.25. Reversing an operation requires dividing by its multiplier.
Transfer and explain
A $100 account earns 5% simple interest for 3 years: interest is $15, ending balance $115. State which of these two quantities the question requests.
A tool priced at $100 is discounted by 15%. What is the sale price before tax, in dollars?
- A 15% discount leaves 85% of the original price.
- Apply the multiplier to the original price, not to the discount amount.
- The requested value is 85. Check its units and meaning against the original question.
Compare the other answer choices
Report the discount amount instead of the amount paid.
Apply a markup instead of a discount.
Convert the percent to a decimal twice.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
GED Mathematical Reasoning overviewSiyavula Grade 10 mathematics foundation reference