# Fraction Calculator - Add, Subtract, Multiply, Divide, Simplify and Convert

Page: https://hirantha.me/tools/fraction-calculator
Part of: Hirantha Sandaruwan Lakshan free tools (https://hirantha.me/tools)
Updated: 2026-10-13

Add, subtract, multiply and divide fractions and mixed numbers, with the working shown, the answer in lowest terms and as a decimal.

This is a free tool that runs in the browser: open the page to use it. File tools process files on the visitor's own device; files are never uploaded or stored. No account, sign-up, payment or watermark.

Enter two fractions or mixed numbers, pick add, subtract, multiply or divide, and get the answer in lowest terms, as a mixed number and as a decimal, with every step written out. You can also simplify a single fraction or turn a decimal such as 0.375 into a fraction. The arithmetic is exact, so big numerators and denominators never lose a digit, and nothing leaves your browser.

To add or subtract fractions, first give them the same denominator. The calculator uses the least common multiple of the two denominators, rewrites each fraction over it, then adds or subtracts the numerators and keeps the denominator. For 1/2 + 1/3 the common denominator is 6, so you add 3/6 and 2/6 to get 5/6. A mixed number such as 2 1/2 is first turned into an improper fraction: (2 × 2 + 1) / 2 = 5/2.

To multiply, multiply the numerators together and the denominators together. To divide, flip the second fraction and multiply: 5/6 ÷ 2/3 = 5/6 × 3/2 = 15/12. You cannot divide by a fraction that equals zero, such as 0/5, and a denominator can never be zero, so the calculator stops and says why instead of showing a wrong answer.

Every answer is reduced to lowest terms by dividing the top and bottom by their greatest common divisor, found with Euclid's algorithm. For example 63/462 reduces to 3/22 because the greatest common divisor is 21. If the result is larger than 1 it is also shown as a mixed number: 13/4 is 3 1/4 because 13 ÷ 4 is 3 remainder 1.

A fraction in lowest terms has a decimal that ends only when its denominator has no prime factors except 2 and 5, like 3/8 = 0.375. Otherwise the decimal repeats, and the repeating digits are shown in brackets: 1/3 = 0.(3) and 1/6 = 0.1(6). The same brackets work in the decimal to fraction box, and the conversion is exact: 0.(9) comes out as exactly 1. Numerators and denominators are whole numbers of any size up to 200 digits, because the maths uses exact integer arithmetic and not floating point.

Common fractions as decimals (digits in brackets repeat for ever):
| Fraction | Decimal | Type |
| --- | --- | --- |
| 1/2 | 0.5 | Ends |
| 1/3 | 0.(3) | Repeats |
| 1/4 | 0.25 | Ends |
| 1/5 | 0.2 | Ends |
| 1/6 | 0.1(6) | Repeats |
| 1/7 | 0.(142857) | Repeats, 6-digit block |
| 1/8 | 0.125 | Ends |
| 1/9 | 0.(1) | Repeats |
| 1/10 | 0.1 | Ends |
| 1/11 | 0.(09) | Repeats |
| 1/12 | 0.08(3) | Repeats |
| 2/3 | 0.(6) | Repeats |
| 3/4 | 0.75 | Ends |
| 3/8 | 0.375 | Ends |
| 5/8 | 0.625 | Ends |
| 7/8 | 0.875 | Ends |

Q: How do you add fractions with different denominators?
A: Find a common denominator, usually the least common multiple of the two denominators, and rewrite each fraction over it. Then add the numerators and keep the denominator. For 1/2 + 1/3 the common denominator is 6, so you add 3/6 and 2/6 to get 5/6.

Q: How do you add or subtract mixed numbers?
A: Turn each mixed number into an improper fraction (whole number times denominator, plus numerator, over the denominator), do the sum, then turn the answer back into a mixed number. For 3 2/3 + 1 3/4 that is 11/3 + 7/4 = 44/12 + 21/12 = 65/12, which is 5 5/12.

Q: How do you divide one fraction by another?
A: Flip the second fraction and multiply. 5/6 ÷ 2/3 is 5/6 × 3/2 = 15/12, which simplifies to 5/4 or 1 1/4. You cannot divide by a fraction that equals zero, so the calculator shows a message instead of an answer.

Q: How do I change an improper fraction to a mixed number?
A: Divide the numerator by the denominator. The quotient is the whole part and the remainder is the new numerator over the same denominator. For 13/4, 13 ÷ 4 is 3 remainder 1, so it is 3 1/4.

Q: What does the bracket in 0.1(6) mean?
A: The digits in brackets repeat for ever, so 0.1(6) is 0.1666... and equals 1/6. Every decimal that ends or repeats is a fraction, and the box turns it into an exact one. Decimals that never end and never repeat, like pi, are not fractions and cannot be typed here.

Q: How do I enter a negative fraction or mixed number?
A: Put the minus sign on the numerator for an ordinary fraction, for example -3/4, or on the whole part of a mixed number: -2 and 1/2 means minus two and a half, which is -5/2. A minus sign on both is refused because it would be unclear what you meant.

Q: Is 0.999... really equal to 1?
A: Yes. Type 0.(9) into the decimal to fraction box and the answer is exactly 1. The method that turns 0.(3) into 1/3 gives 9/9 for 0.(9), and 9/9 is 1.

Q: Why is the answer different from my calculator's decimal?
A: Many calculators round to about 10 digits, so 1/3 shows as 0.3333333333. This page keeps the exact fraction and shows the true repeating decimal 0.(3) with a rounded version beside it.

Sources: Fraction (mathematics) - Wikipedia: arithmetic, mixed numbers and lowest terms (https://en.wikipedia.org/wiki/Fraction); Repeating decimal - Wikipedia: converting to and from fractions (https://en.wikipedia.org/wiki/Repeating_decimal); Euclid's Elements, Book VII, Proposition 2: the greatest common measure (https://mathcs.clarku.edu/~djoyce/elements/bookVII/propVII2.html)

Related tools:

- [GCD and LCM calculator](https://hirantha.me/tools/gcd-lcm-calculator.md): Find the greatest common divisor and least common multiple of two or more whole numbers, with the Euclidean steps and prime factors shown.
- [Ratio calculator](https://hirantha.me/tools/ratio-calculator.md): Simplify a ratio, scale it to a new value, divide an amount in a ratio such as Rs. 10,000 in 3:2, or turn a ratio into percentages.
- [Percentage calculator](https://hirantha.me/tools/percentage-calculator.md): Find X% of a number, what percent one number is of another, the whole from a part, or add and subtract a percentage, with the working shown.
- [Prime number checker](https://hirantha.me/tools/prime-number-checker.md): Check whether a number is prime, up to 2^64, see its prime factors and the previous and next prime, and list every prime up to 100,000.