How to use the mixed fraction calculator
- Enter the first mixed number as a whole number, numerator and denominator. For a simple fraction, use 0 as the whole number.
- Choose the operation.
- Enter the second mixed number. For a negative mixed number, put the minus sign on the whole number (−2 1/3).
How the calculation works
Each mixed number is converted to an improper fraction: whole × denominator + numerator, over the denominator. For addition and subtraction both fractions are rewritten over their least common denominator; for multiplication numerators and denominators are multiplied; division multiplies by the reciprocal. The result is reduced by dividing by the greatest common divisor and converted back to a mixed number.
All arithmetic uses arbitrary-precision integers, so results such as 1/3 + 1/6 = 1/2 are exact rather than rounded decimals.
Formula
Worked examples
2 1/3 + 1 3/4
Improper: 7/3 + 7/4. Common denominator 12: 28/12 + 21/12 = 49/12 = 4 1/12.
3 1/2 ÷ 1 1/4
7/2 ÷ 5/4 = 7/2 × 4/5 = 28/10 = 14/5 = 2 4/5.
1 1/2 − 2 3/4
3/2 − 11/4 = 6/4 − 11/4 = −5/4 = −1 1/4.
Assumptions and limitations
- Inputs must be whole numbers in each box; for decimals, convert to a fraction first (0.75 = 3/4).
- The decimal result is rounded to 10 significant digits; the fraction result is exact.
Frequently asked questions
How do you add mixed fractions?
Convert both to improper fractions, rewrite them over a common denominator, add the numerators, simplify, and convert back to a mixed number.
How do I convert an improper fraction to a mixed number?
Divide the numerator by the denominator. The quotient is the whole number and the remainder is the new numerator: 49/12 = 4 remainder 1 = 4 1/12.
Can the numerator be larger than the denominator?
Yes. An entry such as 1 5/4 is treated as 1 + 5/4 = 9/4, and the result is simplified and converted back to a proper mixed number (2 1/4) as usual.