Fraction Calculator - Add, Subtract, Multiply, Divide, Simplify and Convert
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.
Maintained by Hirantha Sandaruwan Lakshan. Updated 13 October 2026.
About this tool
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.
How it works
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.
Worked examples
Adding mixed numbers: 3 2/3 + 1 3/4
3 2/3 is 11/3 and 1 3/4 is 7/4. The common denominator is 12, so 11/3 = 44/12 and 7/4 = 21/12. The sum is 65/12, which is 5 5/12, or 5.41(6) as a decimal.
Subtracting: 7/12 - 3/8
The least common multiple of 12 and 8 is 24. 7/12 = 14/24 and 3/8 = 9/24, so the difference is 5/24, which is 0.208(3) as a decimal.
Multiplying and dividing: 2 1/2 × 3/4 and 5/6 ÷ 2/3
2 1/2 is 5/2, and 5/2 × 3/4 = 15/8, which is 1 7/8 or 1.875. For the division, 5/6 ÷ 2/3 = 5/6 × 3/2 = 15/12, which simplifies to 5/4, or 1 1/4.
Decimals to fractions: 0.375 and 0.1(6)
0.375 has three digits after the point, so it is 375/1000, which simplifies to 3/8. For 0.1(6), where the 6 repeats, the calculator subtracts 10 times the number from 100 times the number to get 90x = 15, so x = 15/90 = 1/6.
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 |
Frequently asked questions
How do you add fractions with different denominators?
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.
How do you add or subtract mixed numbers?
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.
How do you divide one fraction by another?
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.
How do I change an improper fraction to a mixed number?
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.
What does the bracket in 0.1(6) mean?
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.
How do I enter a negative fraction or mixed number?
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.
Is 0.999... really equal to 1?
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.
Why is the answer different from my calculator's decimal?
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 & references
Updated Oct 13, 2026