Worked examples: choosing the right percentage calculation
“What is 15% of 80?” multiplies 80 by 0.15 and returns 12. “12 is what percent of 80?”
divides 12 by 80 and multiplies by 100, returning 15%. These questions use the same three
numbers, but switching which value is unknown changes the operation.
Percentage change depends on the starting value
A price rising from $80 to $100 increases by 25%: (100 − 80) / 80 × 100.
The reverse move, $100 down to $80, decreases by 20%. The difference is the denominator,
not a rounding error. Always use the original value as the base when reporting a change.
Two common traps
A 20% discount followed by another 10% discount is a 28% total discount, not 30%.
For a $100 item, the first discount leaves $80 and the next removes $8, leaving $72.
Similarly, raising a rate from 4% to 5% is an increase of one percentage point but a relative
increase of 25%. Use percentage points when subtracting two rates directly.
A percentage change from zero is undefined because the usual formula divides by the starting
value. Describe a move from zero in absolute units instead. Negative starting values can also
produce confusing signs; state the original amounts when discussing a move from a loss to a profit.
To check any result, convert the percentage to a decimal and multiply it by the base amount.
For money, round the final amount according to the actual billing rule; rounding every intermediate
step can change a tax or discount total by a cent.
Examples and assumptions updated September 28, 2026. Amounts are illustrative, not current product quotes.