Tukuk-OSPercent means “per hundred”, so 10% of anything is that thing shifted one decimal place left: 10% of 240 is 24. From there, 20% is double it, 5% is halve it, and 15% is the 10% plus half of the 5% — the tip-and-discount arithmetic that needs no calculator. Reversible percentages make the hard ones easy: 64% of 75 is painful, but percentages swap freely, so it is 75% of 64 — three quarters of 64, which is 48. Any percentage chain is just multiplication: a 20% cut followed by a 20% cut is 0.8 × 0.8 = 0.64, a 36% total reduction, not 40% — the shop applying “extra 20% off sale price” is counting on you to add percentages.
The most abused distinction in public conversation is percent versus percentage point. When a tax goes from 5% to 8%, that is a 3-percentage-point rise but a 60% increase — both true, wildly different feelings, and both used as weapons in politics and advertising. Whenever someone quotes a percentage change, ask “from what base?”: a 300% increase on a base of two sales is still five sales.
Percentages also hide in compounding, the quietest math in finance: 0.99 to the power 365 is about 0.03 — the “one percent worse every day for a year” meme is actually correct arithmetic — and 1.01^365 ≈ 37.8, the other direction. The same curve runs your loan, your subscription price rises and your savings; nothing in daily life grows in straight lines the way intuition expects.