Total or difference
Decide whether the given quantity is the whole or the gap between shares.
AQA 8300 · R5 · Ratio cues
Ratio: is the number a total or a difference?
The interpretation mark. Dividing by the sum of the parts is only correct when the given quantity is the whole; when it is the gap between two shares, the divisor is the difference of the parts.
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.
Value of one part
Divide by the sum of the parts for a total, or by their difference for a gap.
Required share
Multiply the part value by the number of parts the question asks for.
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
The error
Dividing the given quantity by the sum of the ratio parts when the question actually gave a difference — “Alex has £24 more than Ben” treated as “they have £24 altogether”.
02
Why it survives revision
“Add the parts, divide, multiply back” is taught first and works on every total-type question, which is the majority of introductory practice. The procedure is never wrong on the questions used to establish it.
The worked repair
Repair the smallest broken step.
Teaching is not evidence. This one move is the repair; the proof checks begin after it disappears.
Read what the number describes — the whole, or the gap — before touching the parts at all.
What happens after the repair
Correction is the start, not the result.
Immediate
Asked again straight away, on a different question
The repair leaves the screen and a new authored item checks the method unassisted. Being taught something is never evidence that it was learned, so this is the first stage that counts at all.
Delayed
Asked again after at least 1 day
A parallel form of the same method, unassisted, with the repair no longer on screen. A retest in the same session does not count.
Transfer
Asked again when the surface changes
The transfer form states one person's share and asks for the other, so neither the total nor the difference is given and the ratio has to be used directly.
Exam
Asked again under exam conditions
Timed, carrying the mark tariff, in an exam-like response format and aligned to the specification. Any one of those missing and the evidence is refused.
REVIEWED BOUNDARY
This page covers one reviewed family: R5 · Ratio cues. Decide whether a total means add the parts or a difference means subtract them. Other families within the same GCSE Maths topic are outside this reviewed journey, and Studara does not apply the proof label to material that has not been reviewed. No grade-uplift claim is made anywhere on this site.
Straight answers
Before you use this guide.
When do I divide by the difference instead of the total?
When the number given is how much MORE one share is than another. Dividing by the sum of the parts is only correct when the number given is the whole amount.
How do I spot which one a question means?
Read what the number describes before touching the ratio. 'They have £24 altogether' is a total; 'Alex has £24 more than Ben' is a difference.
Does Studara guarantee a higher grade?
No. Studara has not run a controlled outcome study and publishes no grade-uplift claim. What has been measured, what is withheld, and the metric that failed its bar are all on the public evidence page.
Turn this method into evidence