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LunaCalc

Math

Improper Fraction to Mixed Number Calculator

Convert a signed improper fraction to a reduced whole number and fractional remainder.

Calculator

About this calculator

This fraction calculator converts a signed improper fraction into a whole-number part and a reduced fractional remainder.

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

  1. Example: -14/6 has whole part -2 and remainder 2/6, which reduces to the mixed number -2 1/3.
  2. 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

  1. Enter integer numerator and denominator values.
  2. Keep the denominator nonzero; either value may carry the sign.
  3. 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.

References