Free · Fractions
Improper Fraction to Mixed Number with Steps
Convert a signed improper integer fraction into a whole part and a reduced fractional remainder, retaining the optional worked solution.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
Loading calculator…
How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
17/6 equals 2 and 5/6. For −17/6, the leading minus applies to the entire mixed number: −(2+5/6).
|n|=d q+r, 0≤r<d; whole=sign(n)q; reduce r/d by gcd(r,d).
Worked example
Enter these known values and leave the other values blank.
- Numerator (n₁)
- 17
- Denominator (d₁)
- 6
- Result
- Write the signed whole part and the remaining fraction. improper numerator: 17. improper denominator: 6. whole number: 2. numerator: 5. denominator: 6.
Assumptions and limitations
- Enter integer operands with |numerator| ≥ denominator > 0 and magnitudes no greater than 10^10. This is the computational scope of the retained exact Euclidean kernel.
- The whole part truncates toward zero. The fractional numerator is a nonnegative remainder, and a leading negative sign applies to the complete mixed number.
- A zero remainder is an integer result. A nonzero fractional part is simplified by the greatest common divisor. All captured result and worked-solution branches remain available.
- The original calculator is forward-only; the hidden mixed-number fields are explanatory outputs, not invented inverse controls.
Common questions
How is a negative mixed number read?
−2 5/6 means −(2+5/6), not −2+5/6. The retained negative-input explanation makes that convention explicit.
What if the numerator is a multiple of the denominator?
The remainder is zero and the result is the signed whole number. The worked solution states that no fractional part remains.
References
- OpenStax: convert improper fractions to mixed numbers
- OpenStax: fractions and mixed numbers
- Calculation definition and unit reference
Preserve signed improper-fraction conversion and all retained worked steps using bounded exact integer quotient, remainder and the existing Euclidean GCD kernel. Require integer operands of magnitude at most 10^10, a positive denominator and an improper fraction. Expand only the captured fixed three-variable note predicates into equivalent conjunctions.