Percentages — Revision Notes

⚡ 30-Second Revision

Percentage = part ÷ stated whole × 100.
Growth uses the original value as base.
Percentage points compare rates by subtraction.
Successive changes multiply their factors.
Reverse a change by dividing by its factor.
Combined rates need the underlying group sizes.

2-Minute Revision

Identify the denominator before calculating a percentage. A rate rising from 20% to 25% increases by five percentage points and by 25% relative to its original rate. A 20% increase followed by a 20% decrease leaves 96% of the starting amount because the second change uses a different base. To recover an original value from a changed amount, divide by the change factor. When combining group percentages, recover or use the underlying counts rather than assuming equal group sizes.

5-Minute Revision

A workshop has 80 participants in group A and 120 in group B. Completion rates are 75% and 60%, giving 60 and 72 completions. The combined rate is 132/200 = 66%, not the unweighted average 67.5%. Next, a fee rises from 500 to 600 and later falls to 540. The first change is +20%, the second −10%, and the net change is +8% from 500. Explain each denominator and verify the net multiplier 1.2 × 0.9 = 1.08.

Vyyuha Quick Recall

Name the base, multiply changes, weight groups. A percentage is incomplete without its denominator.