This fraction calculator converts a signed improper fraction into a whole-number part and a reduced fractional remainder.
Math
Improper Fraction to Mixed Number Calculator
Convert a signed improper fraction to a reduced whole number and fractional remainder.
Calculator
About this calculator
Formula notes
whole = truncation by absolute division with the original sign; remainder = absolute numerator mod absolute denominator; reduce the remainder by gcd(remainder, denominator).
Worked examples
- Example: -14/6 has whole part -2 and remainder 2/6, which reduces to the mixed number -2 1/3.
- The improper fraction 355/113 becomes 3 16/113 because 355 = 3 x 113 + 16 and the remainder is already reduced.
How to use it
- Enter integer numerator and denominator values.
- Keep the denominator nonzero; either value may carry the sign.
- Read the reduced whole and fractional parts.
Frequently asked questions
What happens when the remainder is zero?
The result is displayed as an integer, so 20/5 becomes 4 rather than 4 0/1.
Can the denominator be negative?
Yes. The sign is normalized into the displayed result while the remainder denominator stays positive.
Limits and interpretation
- Inputs must be finite integers and the denominator cannot be zero; decimal approximations and symbolic expressions are outside this calculator's scope.
- A mixed-number display is a formatting change, not an approximation: extremely large integers can still exceed exact JavaScript number precision.