Percentage of a Number

Multiply the number by the percent, then divide by 100: 15% of 80 is 80 × 15 ÷ 100 = 12. The division by 100 is not an extra rule to memorise — it is what the word means. Percent comes from the Latin per centum, "by the hundred", so a percentage is a fraction whose denominator is already fixed at 100. Written as a decimal, 15% is simply 0.15, and the whole calculation reduces to 80 × 0.15. That reframing is worth doing every time, because it removes the two errors people actually make: forgetting the ÷ 100 (giving an answer 100 times too big) and dividing when they should multiply. If the percent is under 100, the answer must come out smaller than the original number. That single check catches almost everything.

Almost any everyday percentage can be assembled from 10%, and 10% is free: move the decimal point one place to the left. 10% of 80 is 8. From that one number everything else follows by halving and doubling. 5% is half of 10% (4). 20% is double (16). 15% is 10% plus 5% (12). 30% is 10% tripled (24). 1% is the decimal moved two places (0.8), which then gives you 2%, 3% and the awkward in-between values. This is exactly how you tip without reaching for a phone. On a $47 restaurant check, 10% is $4.70, so a 20% tip is $9.40 and an 18% tip is a shade under that. The table above does the same laddering for whatever number you enter, showing 5%, 10%, 15%, 20%, 25% and 50% side by side so you can read off or interpolate any nearby value.

For a tip, a markup or sales tax, add the percentage back: 80 + 15% = 92. For a discount, subtract it: 80 − 15% = 68. The calculator reports both, which makes it a tip calculator and a sale-price calculator at the same time. The faster route is a single multiplication. Adding 15% is × 1.15; taking 15% off is × 0.85. One step instead of two, and far less prone to slips. Reversing an applied percentage is where people go wrong. If a jacket costs $68 after a 15% discount, the original price is not 68 + 15%. That would be $78.20, which is wrong, because the 15% was taken off the larger number. You have to divide by the factor: 68 ÷ 0.85 = $80. Whenever a percentage has already been applied to a figure, undo it with division, never by adding the same percent back.

A% of B is always equal to B% of A. Both are A × B ÷ 100, so swapping the two numbers cannot change the answer — and one of the two versions is usually much easier. Nobody wants to work out 4% of 75 mentally. But 75% of 4 is three quarters of 4, which is 3, and that is the same answer. Similarly, 18% of 50 looks tedious until you flip it into 50% of 18 = 9. And 12% of 25 becomes 25% of 12 = 3. The rule of thumb: if either number is close to 100, 50, 25 or 10, flip the problem so that number becomes the percentage. It costs nothing and turns most awkward percentages into a halving or a quartering.

Several common percentages are exact fractions in disguise, and recognising them is faster than any multiplication. 50% is 1/2, 25% is 1/4, 20% is 1/5, 10% is 1/10, 12.5% is 1/8 and 75% is 3/4. Finding 25% of 640 by halving twice (320, then 160) beats reaching for a keypad. Others never come out exactly. 33.3% is not one third — one third is 33.333… percent, repeating forever, because 1/3 has no exact decimal form. The same applies to 16.7% (1/6) and 66.7% (2/3). For an exact answer, divide by 3 rather than multiplying by 0.333. That rounding gap is small but real. Taking "33%" of $900 gives $297, while a true third is $300 — a $3 difference that matters when you are splitting a bill or allocating a budget in shares that must add back up to the whole.