Percentages: increase, decrease and reverse percentages
Mathematics · Year 8
Name: ______________________Date: ____________
A percentage change can be handled with a multiplier: add the percentage to 100% for an increase and subtract it from 100% for a decrease. Reverse percentages divide the final amount by that multiplier to recover the original.
Example
After a 20% discount a jacket costs $72. The multiplier is 0.80, so the original price was 72 / 0.80 = $90.
Key terms
Multiplier:
A decimal factor used to apply a percentage change.
Original value:
The amount before a percentage change.
Reverse percentage:
Working backwards from a changed amount to the original.
Questions
1. What does Multiplier mean?
The amount before a percentage change.
A decimal factor used to apply a percentage change.
Working backwards from a changed amount to the original.
A value selected without mathematical context.
2. Which statement correctly describes Original value?
A decimal factor used to apply a percentage change.
Working backwards from a changed amount to the original.
The amount before a percentage change.
A step that removes the need to calculate.
3. Which definition matches Reverse percentage?
Working backwards from a changed amount to the original.
A decimal factor used to apply a percentage change.
The amount before a percentage change.
A label that can be ignored when solving.
4. Which worked example belongs to percentages: increase, decrease and reverse percentages?
An example that changes the given values before starting.
An example that gives a result without a mathematical method.
Finding the percentage of the final amount when the question asks for the original value.
After a 20% discount a jacket costs $72. The multiplier is 0.80, so the original price was 72 / 0.80 = $90.
5. Which practice approach is most reliable?
Translate the percentage change into a decimal multiplier before multiplying or dividing.
Finding the percentage of the final amount when the question asks for the original value.
Apply a familiar rule before identifying what the quantities represent.
Round every value at the beginning and do not check the effect.
6. Which action is a sensible accuracy check?
Assume the first answer is correct because a calculator produced it.
Check only that an answer has several digits.
Apply the stated percentage change to the recovered original and confirm the final amount.
Change the units after calculating without using a conversion.
7. Where could percentages: increase, decrease and reverse percentages be applied?
In a situation with no quantities or relationships.
Compare sale prices, population changes or price rises using percentage multipliers.
Only in a memorised classroom example.
In place of reading the conditions of a problem.
8. A student is beginning a percentages: increase, decrease and reverse percentages problem. What should they do?
Finding the percentage of the final amount when the question asks for the original value.
Apply a familiar rule before identifying what the quantities represent.
Round every value at the beginning and do not check the effect.
Translate the percentage change into a decimal multiplier before multiplying or dividing.
9. Which mistake is most important to avoid here?
Writing down the units supplied in the question.
Finding the percentage of the final amount when the question asks for the original value.
Showing intermediate working.
Checking the result using the original information.
10. After calculating, which step gives the strongest evidence that the result is valid?
Apply the stated percentage change to the recovered original and confirm the final amount.
Assume the first answer is correct because a calculator produced it.
Check only that an answer has several digits.
Change the units after calculating without using a conversion.
11. Which task transfers this mathematics into a meaningful context?
Copy a completed answer without its method.
List unrelated numbers from the question.
Compare sale prices, population changes or price rises using percentage multipliers.
Repeat a definition without using it.
12. Why is the worked percentages: increase, decrease and reverse percentages example valid?
It avoids the defining relationship in the topic.
A percentage change can be handled with a multiplier: add the percentage to 100% for an increase and subtract it from 100% for a decrease. Reverse percentages divide the final amount by that multiplier to recover the original.
It treats every numerical operation as interchangeable.
It relies on the answer being visually complicated.
13. Which statement best connects Multiplier and Original value?
Multiplier and Original value are unrelated labels.
Multiplier removes the need for Original value.
The meanings of Multiplier and Original value can be swapped.
A decimal factor used to apply a percentage change. The amount before a percentage change.
14. Which response shows mathematical reasoning rather than guessing?
Translate the percentage change into a decimal multiplier before multiplying or dividing. Then apply the stated percentage change to the recovered original and confirm the final amount.
Finding the percentage of the final amount when the question asks for the original value.
Apply a familiar rule before identifying what the quantities represent.
Round every value at the beginning and do not check the effect.
15. Which explanation would best justify a final answer?
The answer must be right because it was completed quickly.
The method does not need to match the quantities or conditions.
A percentage change can be handled with a multiplier: add the percentage to 100% for an increase and subtract it from 100% for a decrease. Reverse percentages divide the final amount by that multiplier to recover the original. The result can be checked by this step: Apply the stated percentage change to the recovered original and confirm the final amount.
A different result was ignored because it was inconvenient.
16. A result seems unreasonable. What is the best diagnostic response?
Keep the result and remove the working.
Check for this common error: Finding the percentage of the final amount when the question asks for the original value. Then apply the stated percentage change to the recovered original and confirm the final amount.
Change the original question so the result fits.
Choose a new answer without revisiting the method.
17. Which plan would produce the clearest solution for another reader?
Finding the percentage of the final amount when the question asks for the original value.
Apply a familiar rule before identifying what the quantities represent.
Round every value at the beginning and do not check the effect.
Translate the percentage change into a decimal multiplier before multiplying or dividing. Show the working clearly and label the final result.
18. Which check is most closely tied to the mathematics in this topic?
Apply the stated percentage change to the recovered original and confirm the final amount.
Assume the first answer is correct because a calculator produced it.
Check only that an answer has several digits.
Change the units after calculating without using a conversion.
19. Which application requires the ideas from this topic?
A task with no measurable information or decision.
A task that forbids using the stated mathematical relationship.
Compare sale prices, population changes or price rises using percentage multipliers.
A task solved by copying an unrelated formula.
20. Which critique identifies a genuine flaw in a solution?
The solution states the relevant units.
Finding the percentage of the final amount when the question asks for the original value.
The solution shows an intermediate step.
The solution checks its answer.
21. What is the strongest summary of percentages: increase, decrease and reverse percentages?
It is a topic where units, conditions and checks never matter.
It is solved by choosing any operation that gives a whole number.
It has no connection to mathematical reasoning or real situations.
A percentage change can be handled with a multiplier: add the percentage to 100% for an increase and subtract it from 100% for a decrease. Reverse percentages divide the final amount by that multiplier to recover the original.
Answer key (parent copy)
1. A decimal factor used to apply a percentage change.
2. The amount before a percentage change.
3. Working backwards from a changed amount to the original.
4. After a 20% discount a jacket costs $72. The multiplier is 0.80, so the original price was 72 / 0.80 = $90.
5. Translate the percentage change into a decimal multiplier before multiplying or dividing.
6. Apply the stated percentage change to the recovered original and confirm the final amount.
7. Compare sale prices, population changes or price rises using percentage multipliers.
8. Translate the percentage change into a decimal multiplier before multiplying or dividing.
9. Finding the percentage of the final amount when the question asks for the original value.
10. Apply the stated percentage change to the recovered original and confirm the final amount.
11. Compare sale prices, population changes or price rises using percentage multipliers.
12. A percentage change can be handled with a multiplier: add the percentage to 100% for an increase and subtract it from 100% for a decrease. Reverse percentages divide the final amount by that multiplier to recover the original.
13. A decimal factor used to apply a percentage change. The amount before a percentage change.
14. Translate the percentage change into a decimal multiplier before multiplying or dividing. Then apply the stated percentage change to the recovered original and confirm the final amount.
15. A percentage change can be handled with a multiplier: add the percentage to 100% for an increase and subtract it from 100% for a decrease. Reverse percentages divide the final amount by that multiplier to recover the original. The result can be checked by this step: Apply the stated percentage change to the recovered original and confirm the final amount.
16. Check for this common error: Finding the percentage of the final amount when the question asks for the original value. Then apply the stated percentage change to the recovered original and confirm the final amount.
17. Translate the percentage change into a decimal multiplier before multiplying or dividing. Show the working clearly and label the final result.
18. Apply the stated percentage change to the recovered original and confirm the final amount.
19. Compare sale prices, population changes or price rises using percentage multipliers.
20. Finding the percentage of the final amount when the question asks for the original value.
21. A percentage change can be handled with a multiplier: add the percentage to 100% for an increase and subtract it from 100% for a decrease. Reverse percentages divide the final amount by that multiplier to recover the original.