The Two Questions
Attendance percentage itself is simple:
``
attendance % = classes attended ÷ total classes held × 100
`
The questions that actually matter are the two derived ones.
How Many Can I Still Miss?
Given a required percentage r, total planned classes T and classes attended so far
a, the maximum you can miss for the rest of term is:
`
remaining misses = T − (r × T) − (classes already missed)
`
For a 75% requirement across 100 classes, you may miss 25 in total. If you have already
missed 18, you have 7 left — regardless of how many are remaining.
How Many Must I Attend Consecutively to Recover?
This is the one students get wrong, because the denominator grows as you attend. Attending
x more consecutive classes from a attended out of h held gives:
`
(a + x) ÷ (h + x) ≥ r → x ≥ (r × h − a) ÷ (1 − r)
`
At 60 attended of 90 held (66.7%) and a 75% requirement:
`
x ≥ (0.75 × 90 − 60) ÷ 0.25 = 7.5 → 8 classes
`
Note the 1 − r divisor. At a 90% requirement it is 0.1, so every missed class costs ten
attended ones to recover. High requirements are not slightly harder to recover from — they
are an order of magnitude harder.
| Requirement | Classes needed to recover one absence |
|---|---|
| 60% | 1.5 |
| 75% | 3 |
| 80% | 4 |
| 90% | 9 |
| 95% | 19 |
Attendance Is Usually Per-Subject
Most institutions calculate the requirement separately for each subject, not across your
whole timetable. A comfortable overall figure hides a single subject below threshold, which
is the one that stops you sitting the exam.
The Arithmetic Is Not the Advice
If illness, caring responsibilities or a crisis is driving the absences, the recovery
calculation is the wrong tool — every institution has a process for authorised absence, and
using it early is far more effective than attending eight consecutive classes to claw back a
percentage.
The Four Percentage Questions
Almost every percentage problem is one of these, and mixing them up is the most common
arithmetic error there is:
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | Y × (X ÷ 100) | 15% of 80 = 12 |
| X is what % of Y? | (X ÷ Y) × 100 | 12 is 15% of 80 |
| X is Y% of what? | X ÷ (Y ÷ 100) | 12 is 15% of 80 |
| % change from X to Y | ((Y − X) ÷ X) × 100 | 80 → 92 is +15% |
Percentage Points Are Not Percent
A rate moving from 4% to 5% is one percentage point, and a 25% increase. Both
statements are true and they are not interchangeable — headlines routinely use the smaller
one when reporting a rise and the larger one when reporting a fall.
Increases and Decreases Do Not Cancel
| Start | Change | Result |
|---|---|---|
| 100 | +50%, then −50% | 75 |
| 100 | −50%, then +50% | 75 |
| 100 | −20%, then +25% | 100 |
The reason is that the second percentage applies to a different base. To reverse a −20% you
need +25%, not +20%. This is why a stock that falls 50% must double to break even, and why
"we cut costs 30% then grew 30%" leaves you 9% down.Reversing a Percentage
To find the price before a 20% discount, divide by 0.8 — do not add 20%:
`
before = after ÷ (1 − discount)
$80 ÷ 0.8 = $100 ✓
$80 × 1.2 = $96 ✗
``
The same asymmetry applies to tax, tips, markups and platform fees.