Percentages — typical problems with the formula and an explanation of every step
X% of a number
What percent is A of B
Percent change (was → now)
Original before discount / markup
Add / subtract a percent
The number if X% of it equals A
📚 Theory: how to think about percentages
A percent is just one hundredth: 1% = 1/100 = 0.01. So “15% of 240” is 240 × 0.15 = 36. Every percent problem comes down to multiplying or dividing by such a fraction.
A common trap: a discount can’t be “undone” by the same percent. If a price went up 20% and then down 20%, you don’t get back to where you started: 100 → 120 → 96. That’s why “the number before the discount” is found by division, not by subtracting the percent.
Percent change is always measured from the starting value: growth from 80 to 100 is +25% (20/80), while a drop from 100 to 80 is −20% (20/100). The same difference — different percentages!
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