How percentage math works
A percentage is just a fraction with 100 as the denominator, so every percentage problem reduces to one multiplication or division once you convert the percent to a decimal. "15% of 240" is 0.15 × 240. "30 is what percent of 150" flips it around: divide the part by the whole and multiply by 100. Percent change compares the difference to where you started, which is why the direction matters - going from 80 to 110 is a 37.5% rise, but falling from 110 back to 80 is only a 27.3% drop.
The asymmetry in percent change trips people up constantly: a 50% loss needs a 100% gain to recover, and a price that rises 20% then falls 20% ends up below where it started. Whenever a headline quotes a percentage, ask "percent of what?" - the base value is where misleading statistics usually hide.
Frequently asked questions
How do I calculate a percentage of a number?
Convert the percentage to a decimal by dividing by 100, then multiply. 15% of 240 is 0.15 × 240 = 36. For quick mental math, find 10% by moving the decimal point one place, then scale: 10% of 240 is 24, so 15% is 24 plus half of 24.
How do I reverse a percentage?
Divide by the decimal instead of multiplying. If $80 is the price after a 20% discount, the original was 80 ÷ 0.80 = $100. A common mistake is adding the 20% back on, which gives $96 - wrong, because the 20% was taken off the larger original number.
What's the difference between percent change and percentage points?
Percentage points measure the simple difference between two percentages; percent change measures it relative to the starting value. An interest rate going from 3% to 4% is a rise of 1 percentage point, but a 33% increase - the rate itself grew by a third.