UtilibyWritten by the Utiliby editorial team · Last updated October 17, 2026 · Rules and formulas reviewed October 2026
What this free fraction calculator does
Fractions turn up in school maths, recipes, woodworking, sewing, medicine doses and everyday sharing. A fraction calculator removes the slow part: finding common denominators, multiplying across and reducing the result. This free online tool adds, subtracts, multiplies and divides fractions, mixed numbers, whole numbers and decimals in one box each, and always gives the answer in simplest form.
Unlike a plain answer box, it explains the working line by line, so it is useful for checking homework as well as getting a result. It also gives the answer as a mixed number, a decimal with repeating digits marked, and a percent. Bar models draw both fractions and the answer so you can see the sizes. A conversion tab simplifies any fraction, turns decimals into exact fractions and finds the closest fraction up to a denominator you choose. A comparison tab sorts a list of fractions from smallest to largest. Everything runs in your browser.
How to use the fraction calculator
- Type the first fraction. Use 3/4, a mixed number such as 1 1/2, a whole number or a decimal.
- Choose an operation and type the second fraction.
- Read the answer as a fraction, mixed number, decimal and percent.
- Follow the steps under the bar models to see how it was done.
- Use the conversion tab to simplify a fraction or change a decimal into a fraction.
- Use the compare tab to sort several fractions.
Adding and subtracting fractions
Fractions can only be added or subtracted when they share a denominator. If they do not, find the least common denominator, which is the smallest number both denominators divide into. Rewrite each fraction over that number by multiplying top and bottom by the same factor, then add or subtract the numerators and keep the denominator. For 1/2 + 1/3, the denominators 2 and 3 have a least common denominator of 6, so the sum is 3/6 + 2/6 = 5/6. For 3/4 - 5/6 the common denominator is 12, which gives 9/12 - 10/12 = -1/12. A negative answer simply means the second fraction is larger.
Multiplying and dividing fractions
Multiplication is the easiest operation: multiply the numerators, multiply the denominators and simplify. 2/3 x 9/10 = 18/30 = 3/5. For division, take the reciprocal of the second fraction by swapping its top and bottom, then multiply. 1/2 divided by 3/4 is 1/2 x 4/3 = 4/6 = 2/3. Dividing by a fraction less than one makes the answer larger, which surprises many students, but it follows because you are asking how many of the small pieces fit into the first amount. You cannot divide by zero.
Working with mixed numbers
A mixed number combines a whole number and a fraction, such as 2 3/4. To calculate with mixed numbers, convert each to an improper fraction by multiplying the whole number by the denominator and adding the numerator: 2 3/4 = (2 x 4 + 3)/4 = 11/4. Do the operation, then convert back by dividing the numerator by the denominator. For 1 1/2 + 2 3/4, that is 3/2 + 11/4 = 6/4 + 11/4 = 17/4 = 4 1/4. The calculator accepts mixed numbers directly and shows each conversion.
| Calculation | Answer | Decimal |
|---|---|---|
| 1/2 + 1/3 | 5/6 | 0.8(3) |
| 3/4 - 5/6 | -1/12 | -0.08(3) |
| 2/3 x 9/10 | 3/5 | 0.6 |
| 1/2 ÷ 3/4 | 2/3 | 0.(6) |
| 1 1/2 + 2 3/4 | 4 1/4 | 4.25 |
Simplifying fractions and the greatest common factor
A fraction is in simplest form when its numerator and denominator share no factor except 1. To simplify, divide both by their greatest common factor, found with the Euclidean algorithm: repeatedly replace the larger number with the remainder until the remainder is zero. For 18/30, 30 mod 18 = 12, 18 mod 12 = 6 and 12 mod 6 = 0, so the greatest common factor is 6 and 18/30 = 3/5. The calculator does this after every operation so answers are always reduced.
Converting between fractions, decimals and percents
To change a fraction to a decimal, divide the top by the bottom: 3/8 = 0.375. Some fractions never end. 1/3 is 0.333..., and the repeating block is shown in brackets, so 5/6 appears as 0.8(3) and 1/7 as 0.(142857). To change a decimal to a fraction, put it over a power of ten and simplify: 0.375 = 375/1000 = 3/8. To get a percent, multiply the decimal by 100. 3/4 = 0.75 = 75 percent. Typing a decimal such as 0.7 into either box is converted exactly to 7/10.
Comparing and ordering fractions
Fractions with the same denominator are compared by their numerators. With different denominators, either convert to a common denominator or to decimals. For 3/4, 5/8, 2/3 and 0.7 the order from smallest to largest is 5/8 (0.625), 2/3 (0.667), 7/10 (0.7) and 3/4 (0.75). The compare tab draws each fraction as a bar so the differences are easy to see, and lists the common denominator form beside it.
Where fractions are used in everyday life
Cooks scale recipes with fractions, such as taking 3/4 of a cup and doubling it to 1 1/2 cups. Carpenters and sewists work in sixteenths and eighths of an inch, and the closest-fraction feature turns a decimal like 0.4375 into 7/16. Pharmacists and nurses use ratios and fractions for doses, though they should always follow professional guidance. Fractions also underlie probability, discounts and sharing a bill.
Accuracy, privacy and responsible use
The calculator uses exact whole-number arithmetic for numerators and denominators up to about nine digits and rejects numbers that would overflow. Decimals are accepted up to nine places. It is an educational aid, so check high-stakes results yourself. Nothing you type leaves your browser.
Related free tools
Use these free online tools together with this one:
- Turn a fraction into a percent change or discount with the percentage calculator.
- Find the mean, median and mode of a list with the average calculator.
- See what a fraction off a price saves with the discount calculator.
- Compare prices per ounce or litre with the unit price calculator.
- Cost the ingredients once you have scaled a recipe with the recipe cost calculator.
Frequently asked questions
What is a fraction calculator?
A tool that adds, subtracts, multiplies and divides fractions and mixed numbers, simplifies the answer and shows the working. This one also converts fractions to decimals and percents and puts fractions in order.
How do I add fractions with different denominators?
Find the least common denominator, convert both fractions to it, add the numerators and simplify. For 1/2 + 1/3 the common denominator is 6, so 3/6 + 2/6 = 5/6.
How do I subtract fractions?
Use the same method as adding: common denominator first, then subtract the numerators. For 3/4 - 5/6 the denominator is 12, giving 9/12 - 10/12 = -1/12.
How do I multiply fractions?
Multiply the numerators together and the denominators together, then simplify. 2/3 x 9/10 = 18/30 = 3/5.
How do I divide fractions?
Flip the second fraction (take its reciprocal) and multiply. 1/2 divided by 3/4 equals 1/2 x 4/3 = 4/6 = 2/3.
How do I add mixed numbers?
Convert each mixed number to an improper fraction, add as usual, and convert back. 1 1/2 + 2 3/4 = 3/2 + 11/4 = 6/4 + 11/4 = 17/4 = 4 1/4.
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common factor. 18/30 has a greatest common factor of 6, so it simplifies to 3/5.
What is the least common denominator?
The smallest number that both denominators divide into evenly. For 4 and 6 it is 12. It keeps the numbers as small as possible.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. 3/8 is 0.375. Some fractions repeat, such as 5/6 = 0.8333, which the tool writes as 0.8(3).
How do I convert a decimal to a fraction?
Write the decimal over a power of ten and simplify. 0.375 = 375/1000 = 3/8. Type the decimal into the calculator and it does the steps.
How do I convert a fraction to a percent?
Divide the numerator by the denominator and multiply by 100. 3/4 = 0.75 = 75%.
How do I compare fractions?
Convert them to a common denominator or to decimals. 5/8 is 0.625 and 2/3 is 0.667, so 2/3 is larger. The compare tab sorts a list for you.
What is an improper fraction?
A fraction whose numerator is larger than or equal to its denominator, such as 17/4. It can be written as the mixed number 4 1/4.
Can I enter negative fractions and decimals?
Yes. Use a minus sign, such as -3/4 or -1 1/2, or a decimal like 0.75. Decimals up to nine places are converted exactly.
What is the closest fraction to a decimal?
The conversion tab finds the best fraction up to a denominator you choose, for example the nearest sixteenth for a ruler measurement.
Is my data stored or sent anywhere?
No. All calculations run in your browser.
Is this fraction calculator free?
Yes. It is free to use online with no sign-up.
Sources and further reading
- Khan Academy, Fraction arithmetic.
- Wolfram MathWorld, Fraction.
- Wolfram MathWorld, Euclidean algorithm.
- National Council of Teachers of Mathematics, NCTM.
Sources were consulted in October 2026. Standards and rules can change, so always check the official page for your situation.