A reliable method
Name the base explicitly, convert the percent to a multiplier, and write one equation before calculating.
The common trap
A discount and a tax use potentially different bases. Undoing a 20% discount means dividing by 0.8, not adding 20%.
Make the connection
Distinguish percentage points from relative percent change. Moving from 20% to 30% adds 10 percentage points but increases the rate by 50%.
State the base before calculating
A price rises from $80 to $100. The increase is $20, and relative to the original $80 that is 25%. Dividing by the final $100 yields 20%, which describes the decrease needed to return from $100 to $80. Percent change is directional because its denominator changes.
Reverse a discount with an equation
After a 30% discount, an item costs $84. The original price p satisfies 0.70p=84, so p=120. Adding 30% of $84 gives $109.20 and does not reverse the discount; the original discount was based on $120. Reversing a multiplier means dividing by it.
Try, then check
A $200 price increases by 15% then falls by 15%. The result is 200(1.15)(0.85)=$195.50. The $4.50 net loss is 2.25% of the original price. Explain why equal percentage changes do not cancel. Distinguish this from a change from 15% to 20%, which is five percentage points.
What is 20% of 150?
- 20% equals 20/100 = 1/5.
- Multiply 150 by 1/5.
- The result is 30.
Compare the other answer choices
Found the amount remaining after a 20% reduction.
Multiplied by 20 without dividing by 100.
Converted the percentage 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.
Official mathematics skillsSiyavula Grade 10 mathematics