Reverse through the retained multiplier
Translate the final amount into the percentage it represents, then divide by that multiplier.
AQA 8300 · R9 subset
Reverse percentages: stop reversing in the wrong direction.
This reviewed journey separates the multiplier method from the original value, diagnoses five common wrong paths, then changes the direction of the percentage change to test method choice.
Reviewed family · Studara-authored items · No grade-uplift claim
The lost mark
One answer. Several places the method can fail.
Studara does not reduce the response to right or wrong. The reviewed contract checks these states independently.
Recover the original value
State the exact original amount supported by the reverse operation.
Why it goes wrong
The diagnosis stays uncertainty-safe.
A wrong response can support a specific measured diagnosis. A blind multiple-choice diagnostic records only a possible cause until later working provides stronger evidence.
01
Wrong-direction multiplier
An increase is treated like a decrease, or a decrease like an increase.
02
Rate instead of retained percentage
The change rate is used as the multiplier instead of 100% plus or minus the rate.
03
The final amount is multiplied
The forward operation is repeated when the question asks for the value before it happened.
04
A percentage of the final is adjusted
The percentage change is applied directly to the final amount, which uses the wrong base.
05
Correct method, arithmetic error
The division method is right but the exact original amount is not.
The worked repair
Repair the smallest broken step.
Teaching is not evidence. This sequence is the repair; the proof checks begin after it disappears.
- 1
Decide whether the final amount is above or below 100% of the original.
- 2
Write the retained percentage as a multiplier—for example, 80% becomes 0.80.
- 3
Divide the final amount by that multiplier to move back to 100%.
- 4
Check by applying the percentage change forward to the recovered value.
What happens after the repair
Correction is the start, not the result.
Immediate
Same method, new values
A fresh one-step original-value problem checks the reverse operation without the repair visible.
Delayed
Parallel form later
The same invariant method returns on a different authored item after a calendar delay.
Transfer
Increase replaces decrease
Both the values and required method choice change, so the student must discriminate between 100 + r and 100 − r.
Exam
Two minutes, exam-like
The final form is timed, source-aligned and carries its mark tariff.
REVIEWED BOUNDARY
This reviewed family covers one exact price increase or decrease with an exact penny result. Compound change, repeated change, interest and multi-step financial contexts remain outside it.
Straight answers
Before you use this guide.
What is the quickest reliable reverse-percentage method?
Represent the final amount as its retained percentage of the original, convert that percentage to a multiplier, then divide the final amount by it.
Why not subtract the percentage from the final value?
The stated percentage is of the original value, not the final value. Taking that percentage of the final changes the base and usually produces the wrong answer.
What does the transfer check change?
The reviewed transfer form changes both the values and the direction of change, requiring the learner to choose between an increase and decrease multiplier.
Turn this method into evidence