Fraction Calculator
Add, subtract, multiply and divide fractions and mixed numbers with every step shown, simplify to lowest terms and convert between fractions and decimals.
Every convention this page applies is named in the result rather than assumed. Your numbers stay in this browser.
Results
How to read this: the verdict describes how much room your numbers leave, not a decision or an offer. Change any input to see how much the result moves.
Assumptions and formula
Each operand is read as an improper fraction in lowest terms, with a mixed number’s sign taken from its whole part. Addition, subtraction and comparison rewrite both fractions over the lowest common denominator; multiplication multiplies across; division multiplies by the reciprocal. The answer is reduced by the greatest common divisor and reported as a fraction, a mixed number and a decimal.
Inputs are limited to a million per part so every intermediate product is an exact integer. A decimal is read as typed and placed over a power of ten, so 0.1 is exactly 1/10; when you set a largest denominator, the closest fraction within it is found by continued fractions and reported with its error.
Worked example
For 1/2 + 1/3, the lowest common denominator of 2 and 3 is 6: 1/2 becomes 3/6 and 1/3 becomes 2/6, and 3 + 2 = 5 gives 5/6, already in lowest terms, which is 0.8333 as a decimal. For 3/4 ÷ 2/5, flip the divisor to 5/2 and multiply: 15/8, or 1 7/8.
Frequently asked questions
How do I add fractions with different denominators?
Rewrite both over a common denominator, then add the numerators. For 1/2 + 1/3 the lowest common denominator is 6: 1/2 becomes 3/6 and 1/3 becomes 2/6, so the sum is 5/6. Any common denominator works — 2 × 3 = 6 here anyway — but the lowest one keeps the numbers small and avoids simplifying afterwards. The steps on this page show that rewrite explicitly.
How do I divide by a fraction?
Multiply by its reciprocal, meaning the fraction turned upside down. 3/4 ÷ 2/5 is 3/4 × 5/2 = 15/8, or 1 7/8. This works because dividing by 2/5 asks how many two-fifths fit, and there are five halves in each whole. Dividing by a fraction smaller than 1 gives a larger answer than you started with, which surprises people but is correct.
How do I turn a mixed number into an improper fraction?
Multiply the whole part by the denominator, add the numerator, and keep the denominator: 2 3/4 is (2 × 4 + 3)/4 = 11/4. For a negative mixed number the sign belongs to the whole, so −2 3/4 is −11/4, not −(2) + 3/4. This page asks for the whole part separately for exactly that reason.
How do I convert a decimal to a fraction?
Write the digits after the decimal point over a power of ten, then simplify. 0.375 is 375/1000, and dividing both by 125 gives 3/8. This page reads the decimal exactly as typed, so 0.1 is 1/10 — a computer that stores 0.1 as a binary number would otherwise offer a 55-digit denominator. If you want a fraction with a small denominator, set a limit and the closest fraction that fits is reported with its error.
What is the lowest common denominator, and why not just multiply the denominators?
The lowest common denominator is the smallest number both denominators divide into — the least common multiple. For 1/4 and 1/6 it is 12, whereas multiplying gives 24. Both are valid; the lowest one produces smaller numerators and an answer that is already in lowest terms more often. Teachers usually mark for it, so it is the one shown here.
How do I turn a decimal into a fraction, and a mixed number into an improper one?
A decimal to fraction calculator writes the decimal over a power of ten and simplifies: 0.375 is 375/1000, which reduces to 3/8. A fraction to decimal calculator goes the other way by dividing: 5/8 is 0.625. A mixed number calculator converts 2½ to 5/2 before adding or multiplying, then converts the answer back. Simplifying is the last step every time: a simplify fractions calculator divides top and bottom by their greatest common factor, so 18/24 becomes 3/4. This page shows each of those steps in the working.
How do multiplying and dividing fractions differ from adding them?
An adding fractions calculator has to find a common denominator first: 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6. A multiplying fractions calculator skips that step entirely and multiplies straight across: 1/2 × 1/3 = 1/6. A dividing fractions calculator flips the second fraction and multiplies: 1/2 ÷ 1/3 = 1/2 × 3/1 = 3/2, or 1½. Subtraction follows the adding rule with a common denominator. This page shows each of those steps in the working so the method is visible, not just the answer.