How to solve it
- Write what fraction of the total the known quantity represents.
- Divide the quantity by the numerator: that gives one part.
- Multiply that part by the denominator: that gives the total.
- Check by taking the fraction of the total.
14 ÷ 2 = 7
7 × 3 = 21
Result: 21
Common mistake:Wrong: 18 × 3/5 = 54/5.Right: 18 ÷ 3/5 = 30.If 3/5 of the total is 18, the total is greater than 18. Multiplying 18 by 3/5 gives a smaller number; you have to divide.
Enter the part in “Known amount” and the fraction in “Known fraction”; you can add a unit, which is carried over to the whole. With 18 as the part and three fifths as the fraction, the result is 30 and the check appears below it. It accepts whole numbers, fractions, terminating decimals and mixed numbers. If you are looking for the part, use fraction of a number, and if you are looking for the fraction, what fraction is it.
Worked example: the capacity of a tank
A tank contains 18 gallons, and that amount fills 3/5 of its capacity. What is the total capacity?
- Identify the data. The 18 gallons are what is in the tank; the tank’s capacity is what is missing.
- Find what each fifth is worth. Three fifths are 18, so each fifth is 18 ÷ 3 = 6 gallons.
- Count all the fifths. The whole tank is 5 fifths, that is, 5 × 6 = 30 gallons.
- Write it as a single operation. 18 ÷ 3/5 = 18 × 5/3 = 90/3 = 30.
The result is 30 gallons.
Check. 3/5 of 30 is 18, the starting amount. Also, 30 is greater than 18, as it should be with a fraction less than 1.
18 ÷ 3 = 6 per fifth; 6 × 5 = 30
Why you divide by the fraction
The starting relationship is part = fraction × whole. To solve for the whole, you have to undo that multiplication, and undoing it means dividing by the fraction. Dividing by the fraction is the same as multiplying by its reciprocal, 5/3, because the product of the two is 1. Wikipedia sums it up in its section on division: to divide a number by a fraction, multiply that number by the reciprocal of the fraction.
Division gives the whole, and the inverse multiplication checks it. If the whole you get does not return the part when multiplied by the fraction, one of the values has been swapped.
What you are looking for: the part, the fraction or the whole
The three problems use the same three numbers, but each leaves a different one blank. First decide which one you do not know, then choose the operation.
| What you are looking for | Operation | Example |
|---|---|---|
| The part | Multiply the whole by the fraction | 5/8 of 80 = 50 |
| The fraction | Divide the part by the whole | 50 of 80 = 5/8 |
| The whole | Divide the part by the fraction | 50 ÷ 5/8 = 80 |
This page solves the last row. The first is solved by fraction of a number and the second by what fraction is one amount of another.
A similar shortcut fails the same way. Multiplying only by the denominator gives the whole only when the numerator is 1. With 2/7 you have to divide by 2 first.
Cases that change the setup
The method is always the same, but the wording sometimes hides which fraction is involved. The table collects the cases that cause the most confusion and what to write in each.
| Case | Calculation | Whole |
|---|---|---|
| Direct data | 28 is 2/7 of the whole: 28 ÷ 2/7 | 98 |
| Amount left over | You spend 1/4 and 24 is left: 24 ÷ 3/4 | 32 |
| Fraction greater than 1 | 15 is 5/4 of the whole: 15 ÷ 5/4 | 12 |
| Non-integer result | 10 is 4/7 of the whole: 10 ÷ 4/7 | 35/2, that is, 17 1/2 |
| Percentage | 25% is 40, and 25% = 1/4: 40 ÷ 1/4 | 160 |
In the second case, the fraction you write is the one that is left, 1 − 1/4 = 3/4, not the one that was spent. In the third, the part exceeds the whole because it is being compared with a smaller reference. The fourth does not come out even, and the calculator leaves it as a fraction; a rounded decimal would be an approximation, and fraction to decimal shows all its digits. In the last one, the percentage calculator does the same calculation with the percentage entered directly.
Where this calculation appears
Almost every problem of this kind gives you a part and asks you to recover the whole: a sale where you know what you paid, a book where you know the pages read, a group where you know how many are of one type. When the problem says “the 120 is 2/5,” you are facing this calculation, with 120 ÷ 2/5 = 300. If the problem chains several spends or splits, the guide to fraction of the remainder problems shows how to reduce it to a single fraction, and fraction word problems collects more problems to practice.
To divide a fraction by a whole number, which is a different problem, use divide fractions. A fraction equal to 0 does not work here: no whole turns it into a part other than zero, and the calculator rejects it.
Sources
Wikipedia, article Fraction, section “Arithmetic with fractions”, subsection “Division” (accessed October 17, 2026).
Frequently asked questions
Can I enter the fraction as a decimal?
Yes, as long as the decimal terminates. Enter 0.25 instead of 1/4 and the part 7: the result is 28, the same as with the fraction. If the decimal has repeating digits, such as 0.333…, use the fraction 1/3, because a rounded decimal would change the whole.
How do I solve a problem with two spends in a row?
Work out what fraction of the whole is left after both spends. If you spend half and then a third of what remains, 1/2 × 2/3 = 1/3 of the whole is left. With $20 left, the whole is 20 ÷ 1/3 = $60. The guide to fraction of the remainder problems works through more cases.
What do I do if the part is given in hours and minutes?
Convert it to a single unit first. If 1 h 30 min is 3/8 of a workday, enter 90 minutes as the part and you get 240 minutes, which is 4 hours. To convert with fractions of an hour, use fraction of an hour to minutes.