Choose a method
Convert percent to a multiplier and write part = rate × whole. Reverse a percentage by dividing the final quantity by its multiplier.
Avoid this trap
Successive percent changes act on different bases. An increase followed by the same percent decrease does not generally return to the start.
Check and transfer
Check whether the answer should be a percent, a number of objects or a monetary amount. Estimate the direction before calculating.
Worked example with a numerical check
A reading group completes 4 of its 20 planned books. What percentage of the plan has it completed? Use the planned count as the whole. Divide completed books by the whole and multiply by one hundred. The requested value is 20.
Contrast and diagnose
A coat costs $32 after a 20% discount. What was its original price in dollars? The sale price is 80 percent of the original price. Divide the final price by 0.8 to reverse the discount. The requested value is 40. An incorrect approach: Apply a second 20 percent discount rather than reverse it.
Transfer practice
A club grows from 40 members to 48 members. What is the percentage increase? Try first. Check: 20. Calculate the increase, then compare it with the original membership. Convert that ratio into a percentage.
A reading group completes 4 of its 20 planned books. What percentage of the plan has it completed?
- Use the planned count as the whole.
- Divide completed books by the whole and multiply by one hundred.
- The requested value is 20.
Compare the other answer choices
Report books rather than percentage.
Reverse total/completed and report that ratio as a percent without multiplying by 100.
Report the proportion without converting to percent.
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.
Math specifications