How to solve it
- Divide the quantity by the denominator: that gives the value of one part.
- Multiply that value by the numerator.
- Check that the result is smaller than the quantity when the fraction is proper.
40 ÷ 5 = 8
8 × 3 = 24
Result: 24
Common mistake:Wrong: 20 ÷ 2 × 5 = 50.Right: 20 ÷ 5 × 2 = 8.The denominator divides and the numerator multiplies. For 2/5 of 20, divide by 5 and multiply by 2; doing it the other way gives 50, more than the total.
Enter the fraction and the amount at the top and select “Calculate.” The first line is the part, and below it you will see the complement and what is left of the total. If you are looking for the total, use find the whole from a fraction, and if you are looking for the fraction, use what fraction is it?.
Worked example: 3/4 of 80
A box holds 80 pieces and 3/4 of them are used. How many pieces are used, and how many are left?
- Split the total into equal parts. The denominator is 4, so 80 ÷ 4 = 20 pieces per part.
- Take the number of parts the numerator gives. That is 3 parts: 3 × 20 = 60.
- Find what is left. 1 part of the 4 remains: 80 − 60 = 20 pieces.
Answer: 60 pieces are used and 20 are left.
Check: 60 + 20 = 80, and 60 is more than half of 80, as it should be for 3/4.
80 ÷ 4 = 20; 3 × 20 = 60
Multiplying by that fraction is the same as dividing by 4 and multiplying by 3, which is why the calculation is a fraction multiplication in which the amount is the second factor. Wikipedia explains that to multiply fractions you multiply the numerators and multiply the denominators; writing the amount as 80/1 gives (3 × 80)/(4 × 1) = 240/4 = 60.
Three questions that look alike
Three problems use the same three pieces of information, the total, the part and the fraction, and each one is missing a different piece. Before you calculate, identify which one you are looking for.
| What you are looking for | Example | Where |
|---|---|---|
| The part | 2/7 of 42 is 12 | This page |
| The total | 12 is 2/7 of the total: 42 | Find the whole from a fraction |
| The fraction | 12 out of 42 is 2/7 | What fraction is it? |
The table separates the problems by the missing piece: if the unknown is the part, you multiply, and if it is the total, you divide. For more general sharing problems, the guide to fractions of a set separates the whole, the parts and the units.
When the result is not a whole number
Not every fraction divides the amount exactly. The result stays as a fraction and as a mixed number, unrounded; if you need the decimal, convert it with fraction to decimal.
| Case | Calculation | Result |
|---|---|---|
| Part is not a whole number | 2/3 of 10 | 20/3 = 6 2/3 |
| Unit is kept | 5/8 of 2 lb | 10/8 = 5/4 = 1.25 lb |
| Decimal amount | 3/8 of 2.5 | 15/16 |
| Fraction of a fraction | 1/3 of 3/5 | 1/5 |
In all four cases you multiply the numerators together and the denominators together, then simplify. The second row shows that 1.25 lb is the same value as 5/4 lb, written as a decimal.
Common fractions of three amounts
Use this table as a quick reference for time, money or angles: the minutes in an hour, an amount of 100 such as $100, and the degrees in a full turn.
| Fraction | Of 60 | Of 100 | Of 360 |
|---|---|---|---|
| 1/2 | 30 | 50 | 180 |
| 1/3 | 20 | 100/3 (33 1/3) | 120 |
| 2/3 | 40 | 200/3 (66 2/3) | 240 |
| 1/4 | 15 | 25 | 90 |
| 1/10 | 6 | 10 | 36 |
| 1/5 | 12 | 20 | 72 |
| 1/6 | 10 | 50/3 (16 2/3) | 60 |
| 1/8 | 15/2 (7 1/2) | 25/2 (12 1/2) | 45 |
60 and 360 have many divisors, so almost all of their fractions come out as whole numbers. With 100, thirds and sixths give fractions that are not whole numbers. For more cases of turning fractions of an hour into minutes, use the fraction of an hour to minutes page.
Practice and reference
The amount you enter must be zero or positive, and the fraction can be proper, improper or negative. Enter the amount already in the unit you want in the answer. To practice the calculation with worked answers, try the fraction of a number worksheets.
Sources
Wikipedia, article Fraction (mathematics), section “Arithmetic with fractions,” subsection “Multiplication”: to multiply fractions, multiply the numerators and multiply the denominators (accessed October 17, 2026).
Frequently asked questions
What is the difference between “of” and “×” in 1/6 of 54?
None: in a fraction of an amount, “of” means multiply. 1/6 of 54 is 1/6 × 54 = 54/6 = 9. The word “of” shows up in word problems and the × sign in the operation, but they describe the same calculation. If a problem says “half of,” think 1/2 ×.
How do I find the total if I know the part?
Divide the part by the fraction, which means multiplying by the flipped fraction. If 21 is 3/7 of the total, the total is 21 × 7/3 = 49. The calculator to find the whole from a fraction does this inverse operation and checks the result.
Can the result be larger than the amount?
Yes, when the fraction is greater than 1. 5/4 of 40 is 50: the whole amount plus one more fourth, which is 10. With a fraction less than 1 the result is always smaller than the amount, and with 1 it is equal to it.
How do I find a percent of an amount?
Write the percent as a fraction with denominator 100 and simplify. 40% of 55 is 40/100 of 55 = 2/5 of 55 = 22. To turn a percent into a fraction without working out the amount, use percent to fraction.