Fraction Calculator

How to use this calculator

Every calculator on this page follows the same three-step pattern, so moving between them takes no relearning.

1. Pick a calculator. Scroll to the Fraction Calculator, Mixed Numbers Calculator, Simplify Fractions Calculator, Decimal to Fraction Calculator, Fraction to Decimal Calculator, or Big Number Fraction Calculator, depending on what you need to calculate or convert.
2. Enter your numbers. Type a numerator and denominator, a decimal, or a whole number with a numerator and denominator for a mixed number, depending on which calculator you are using.
3. Press Calculate. The result panel above the inputs shows the answer as a simplified fraction, a decimal, or a mixed number; nothing computes until you press Calculate, and Clear resets that calculator back to its defaults.
4. Scroll to another calculator to try a different mode. Every calculator on the page keeps working the same way, so you can move between operations, simplifying, and decimal conversion without leaving the page.

Adding, subtracting, multiplying and dividing fractions

Adding and subtracting fractions calculator style requires a common denominator first. To add 1/2 and 1/3, rewrite both over the same denominator (here, 6): 1/2 becomes 3/6 and 1/3 becomes 2/6, and the numerators simply add: 3/6 + 2/6 = 5/6. The Fraction Calculator reaches the same answer by cross-multiplying: (1 x 3 + 1 x 2) / (2 x 3) = 5/6, without writing out a common denominator by hand. Subtracting fractions works the same way, with the numerators subtracted instead of added.

Multiplying and dividing fractions with different denominators need no common denominator at all, which trips people up precisely because adding and subtracting do need one. To multiply, multiply the numerators together and the denominators together: 3/4 x 2/3 = (3 x 2) / (4 x 3) = 6/12, which simplifies to 1/2. To divide, multiply by the second fraction flipped upside down (its reciprocal): 1/2 ÷ 1/4 is the same as 1/2 x 4/1, giving 4/2, which simplifies to 2. A fraction whose numerator is zero cannot be used as a divisor, since flipping it upside down would put a zero in the denominator.

Simplifying a fraction to its lowest terms

Every result on this calculator is reduced to lowest terms automatically, and the Simplify Fractions Calculator does the same for any fraction you type in, once you press Calculate. Reducing means dividing both the numerator and denominator by their greatest common divisor (GCD), the largest number that goes evenly into both. For 18/24, the GCD is 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4, so 18/24 simplifies to 3/4, which has a GCD of 1 with its own denominator and so cannot be written any more simply.

Mixed numbers: converting to and from an improper fraction

A mixed number, like 2 and 3/4, combines a whole number with a proper fraction. To convert it to an improper fraction, multiply the whole number by the denominator, add the numerator, and keep the same denominator: 2 and 3/4 becomes (2 x 4 + 3)/4 = 11/4. Converting back reverses the process: divide 11 by 4 to get a whole number of 2 with a remainder of 3, so 11/4 becomes 2 and 3/4 again. The Mixed Numbers Calculator applies all four operations directly to two mixed numbers, converting each to an improper fraction first: 2 and 3/4 plus 1 and 1/2 becomes 11/4 + 3/2, which works out to 17/4, or 4 and 1/4 as a mixed number.

Converting between decimals and fractions

Turning a fraction into a decimal is ordinary division: the numerator divided by the denominator. 5/8 divides evenly to 0.625, an exact, terminating decimal, since 8’s only prime factor is 2. A fraction such as 2/3 instead produces 0.6666..., a decimal that repeats forever, because 3 remains after removing every factor of 2 and 5 from the denominator; the Fraction to Decimal Calculator shows a case like that to 10 digits and marks it as repeating rather than implying it stops.

Going the other way, converting a decimal to a fraction, works from place value: the digits after the decimal point become the numerator, and a power of 10 with one zero per digit becomes the denominator. 1.375 has three digits after the point, so it becomes 1375/1000, and since the GCD of 1375 and 1000 is 125, that simplifies to 11/8. The Decimal to Fraction Calculator handles any plain, finite decimal this way; a repeating decimal has no fixed number of digits to convert from, so that case is out of scope for an exact conversion.

Comparing and ordering fractions

Comparing two fractions directly, without converting either to a decimal first, uses the same cross-multiplication idea the Fraction Calculator already relies on for adding and subtracting. To compare a/b and c/d, cross-multiply: check whether a × d is greater than, less than, or equal to c × b. Whichever side of that comparison is larger tells you which fraction is larger, since both cross-products represent the same two fractions rewritten over the identical common denominator, b × d, with that shared denominator left out of the comparison because it is positive and equal on both sides.

Worked example. Compare 3/5 and 5/8. Cross-multiplying gives 3 × 8 = 24 against 5 × 5 = 25. Since 25 is larger than 24, 5/8 is the larger fraction, which matches a direct decimal check: 3/5 is 0.6 and 5/8 is 0.625. Comparing three or more fractions at once is usually faster on the Fraction to Decimal Calculator instead, converting each one in turn, since cross-multiplication only compares a single pair at a time.

Ordering a longer list from smallest to largest works the same way in either direction: convert every fraction to a decimal and sort by that, or rewrite the whole list over one shared common denominator (the least common multiple of every denominator involved) and compare the resulting numerators directly. A shared denominator is the cleaner method when the ordered list still needs to be added or subtracted afterward, since it keeps every value in exact fraction form; converting to decimals first is usually quicker when the list only needs ranking.

Working with very large numbers (Big Number Fraction Calculator)

Ordinary numbers in a browser, and in most calculators, lose exact precision above 9,007,199,254,740,991. Type a 20-digit numerator like 33434421132232234333 into a calculator that uses ordinary floating-point arithmetic and it silently rounds to 33434421132232233000 before any addition, subtraction, multiplication or division even runs, an error of more than a thousand. The Big Number Fraction Calculator parses both fractions with JavaScript’s BigInt type instead, which represents whole numbers of any length exactly, so every numerator and denominator you enter here, however long, is combined without that silent rounding.

Common mistakes to avoid

A handful of mix-ups account for most wrong answers people get by hand. Writing a fraction slash as a decimal point, treating 3/4 as though it meant 3.4, is one of the most common, and the two are not close: 3/4 is 0.75. Placing the negative sign in the wrong spot on a mixed number is another: for a negative value, the sign belongs on the whole number (-2 for “negative 2 and 3/4”), or on the numerator only when the whole number is 0. Comparing two fractions without a common denominator first, or without converting both to decimals, is a third: 3/5 looks smaller than 5/8 at a glance, but 3/5 is 0.6 and 5/8 is 0.625, so 5/8 is actually larger. Forgetting to simplify a final answer will not make it wrong, but 8/16 and 1/2 are the same value, and lowest terms is the form most teachers and most other calculators expect.