How to solve it
- Identify the total: it is the denominator.
- Identify the part you are asked about: it is the numerator.
- Write part/total.
- Simplify the fraction.
15/24 = 5/8
Result: 5/8
Common mistake:Wrong: 20/12.Right: 12/20 = 3/5.The part goes on top and the total on the bottom. If 12 of 20 students passed, the fraction is 12/20 = 3/5, not 20/12.
Enter the amount you are comparing in “Part” and the reference amount in “Whole,” then select “Calculate.” If you already know the fraction and want the part, use fraction of an amount; if you want the whole, use find the whole from a fraction. To reduce the result by hand, there is the greatest common divisor calculator.
Worked example: 18 out of 30
On a 30-question test, you get 18 right. What fraction of the test did you get right, and what percent is that?
- Put the part over the whole. 18 correct out of 30 questions is 18/30.
- Reduce with the GCF. GCF(18, 30) = 6, so 18/30 = 3/5.
- Multiply by 100. (3/5) × 100 = 60%.
You got 3/5 of the test right, which is 60%.
Check. 3/5 of 30 is 30 ÷ 5 × 3 = 18, the part we started with.
How the fraction is found
A fraction says what part of one amount another amount is. That is why you divide the part by the whole, and why it helps to reduce: 3/5 and 18/30 are the same proportion, but the reduced one shows at a glance that you got three out of every five questions right. To reduce, divide top and bottom by the GCF (also called the GCD); the greatest common divisor calculator finds it for two or more numbers.
A percent is the same fraction written with a denominator of 100, so you multiply by 100. OpenStax puts it this way: a percent is a ratio whose denominator is 100 (accessed October 17, 2026). When the percent is not a whole number, it is computed exactly, as with 1/8, which is 12.5%. If the decimal does not terminate, as with 100/3%, the result is marked with ≈ and rounded to two decimal places (100/3% ≈ 33.33%, with an error below 0.005 percentage points). To convert any fraction to a percent with decimals, use fraction to percent. The same division of favorable outcomes by possible outcomes appears in the guide to probability with fractions.
Fraction of the whole or ratio between groups
A fraction compares a part with the whole set, while a ratio compares two parts with each other. The difference is which number goes on the bottom.
| Question | Part and whole | Result |
|---|---|---|
| What fraction of the group are boys (15 boys and 45 girls) | 15 out of 60 | 1/4, or 25% |
| How many boys there are for each girl | ratio 15 to 45 | 1/3, that is, 1 : 3 |
| What fraction of 2 hours is 45 minutes | 45 out of 120 minutes | 3/8, or 37.5% |
| How much is 90 compared with 60 | 90 out of 60 | 3/2, or 150% |
For the same group, the first two questions have different answers. If your question is a ratio between two groups, the right tool is ratio to fraction, and the guide to ratios, proportions and fractions explains the difference in depth.
Decimals, fractions and mixed numbers
Part and whole can be decimals, fractions or mixed numbers, and the result is reduced the same way. With 1 1/2 out of 3, the part is 3/2, and (3/2) ÷ 3 = 1/2, or 50%. With 0.5 out of 2, the part is 0.5 and the quotient is 0.25 = 1/4, or 25%. Check by multiplying: half of 3 is 1.5, and a quarter of 2 is 0.5.
Units, larger parts and special cases
Part and whole must be in the same unit. For 45 minutes out of 2 hours, convert the hours to minutes and enter 45 out of 120; if you enter 45 out of 2, you get 45/2, which is correct as a quotient but means nothing as a fraction of time. Units are not converted for you.
A part larger than the whole gives a fraction greater than 1. That is not an error but a comparison: 7 out of 4 is 7/4, or 175%, and the notice reminds you that the percent is over 100%. In a count of subsets, that usually means part and whole are swapped.
If another value is missing
This page solves for the unknown fraction. The other two questions in the same family have their own calculators.
| What you know | What you want | Calculator |
|---|---|---|
| Fraction and whole | The part | Fraction of an amount |
| Part and fraction | The whole | Find the whole from a part |
| Part and whole | The fraction | This page |
All three share the same relationship, part = fraction × whole, and each solves for a different unknown. If you work with sets of objects, the guide to fractions of a set explains why the whole changes when you add items. For increases, discounts and other percent problems, use the percentage calculator.
Frequently asked questions
What if the whole is 0?
There is no fraction, because you cannot divide by 0. A whole of 0 means there is no set to take a part of, so “5 out of 0” makes no sense; enter a positive whole.
Does 125% mean an increase of 125%?
No. If one number is 125% of another, it is 5/4 of it, but the increase is only the difference. With 40 and 50: 50 − 40 = 10, and 10/40 = 1/4, or 25%. Subtract first, then compare that difference with the starting number.