All three percentage questions, answered exactly with the working shown.
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The Coddy math course teaches the method itself - you work each step on an interactive board and get told exactly where a move went wrong.
Every percentage problem is a fraction problem wearing different clothes. 25% is the fraction 25/100, which is 1/4 - and once you write it that way, "what is 25% of 60" stops being a formula to memorise and becomes one multiplication: a quarter of 60 is 15. The word "of" in a percentage question always means multiply.
There are only three questions a percentage problem can ask, and they are the same equation solved for a different letter. The part equals the percent times the whole. Know two of those three quantities and the third follows: multiply to find the part, divide to find the percent, divide the other way to find the whole. This calculator answers all three and shows which division it did and why.
Everything here is exact. One sixth as a percentage is 16⅔%, and this page will never hand you 16.67% - a rounded percentage is a different number, and on money, doses and marks the difference is not academic.
Percent means per hundred, so put the number over 100 and reduce: 25% = 25/100 = 1/4, and 12.5% = 12.5/100 = 1/8.
"What is 25% of 60" is 1/4 × 60 = 15. The word "of" is always a multiplication.
"15 is what percent of 60" is 15/60 = 1/4, then multiply by 100% to read it as a percentage: 25%.
"15 is 25% of what" means 1/4 × w = 15, so w = 15 ÷ 1/4 = 60. Dividing by a fraction is multiplying by its reciprocal.
The benchmark percentages and the fraction each one is. Everything else, the calculator above will work out exactly.
| Percentage | As a fraction | Of 60, for instance |
|---|---|---|
| 1% | 1/100 | 0.6 |
| 5% | 1/20 | 3 |
| 10% | 1/10 | 6 |
| 12.5% | 1/8 | 7.5 |
| 20% | 1/5 | 12 |
| 25% | 1/4 | 15 |
| 33⅓% | 1/3 | 20 |
| 50% | 1/2 | 30 |
| 66⅔% | 2/3 | 40 |
| 75% | 3/4 | 45 |
| 100% | 1 | 60 |
| 150% | 3/2 | 90 |
25% of 60Write 25% as 25/100 and reduce it to 1/4. Then "of" means multiply: 1/4 × 60 = 15. Two lines, and the first one is the one worth internalising - once a percent is a fraction, the rest is arithmetic you already know.
15 of 60Write the part over the whole: 15/60, which reduces to 1/4. Multiplying by 100% reads that fraction as a percentage: 25%. The order matters - the number after "of" is the whole and goes on the bottom.
15 at 25%This time the whole is unknown: 1/4 × w = 15. Divide both sides by 1/4 - that is, multiply by 4 - and w = 60. This is the question behind "the deposit was 25% and I paid 15", and it is the one people most often set up backwards.
33⅓% of 50A third of 50 is 50/3, which is 16⅔ - not 16.67. The answer is a repeating decimal, so the exact form is the mixed number, and this page gives exactly that with the plain fraction 50/3 beside it. Any rounded version is a different number.
Write the percentage over 100, reduce, and multiply. 25% of 60 is 25/100 × 60 = 1/4 × 60 = 15. On a calculator, the same thing is 0.25 × 60 - moving the decimal point two places left IS dividing by 100.
Divide the part by the whole and multiply by 100%. 15 out of 60 is 15/60 = 1/4 = 25%. The number after "of" - the whole - always goes on the bottom of the fraction.
One equation covers all three questions: part = percent × whole. Multiply when the part is missing, divide part by whole when the percent is missing, and divide part by the percent (as a fraction) when the whole is missing. This calculator switches between the three with the buttons above the boxes.
Because the decimal would be wrong. A third of 50 is 50/3, which is 16⅔ exactly; any decimal you could write down - 16.67, 16.6667 - is a different, nearby number. When the exact answer terminates, you get the decimal; when it repeats, you get the exact fraction.
Yes, whenever the part is bigger than the whole. 150 is 250% of 60. Above 100% simply means "more than the whole" - prices after markup and growth over time routinely pass it.
Exactly the same - both are 8 × 25 / 100 = 2, because multiplication does not care about order. It is a genuinely useful trick: 16% of 50 looks awkward, but 50% of 16 is instantly 8.
