Improper fraction → mixed number, step by step
Core idea
Divide numerator by denominator. The quotient is the whole part; the remainder over the original denominator is the proper fractional part. Reduce the fraction if needed.
How it works
- Simplify the improper fraction first when possible.
- Compute whole = ⌊|a|/|b|⌋ and remainder = |a| mod |b|.
- Apply the original sign to the whole result; denominator stays positive.
Sanity checks
- Remainder < denominator, and remainder ≥ 0.
- If remainder = 0, the result is a whole number.
- Back‑convert: whole·den + remainder equals |numerator|.
Shortcuts
- When numerator is a multiple of denominator, answer is an integer.
- Use GCD to reduce the remainder/denominator immediately.
- Keep sign handling till the end to avoid mistakes.
Pitfalls
- Showing a negative denominator or scattering the sign.
- Leaving the fractional part unreduced.
- Converting proper fractions unnecessarily (just keep as proper).
Micro‑examples
- 7/3 → 2 1/3
- 13/4 → 3 1/4
- −22/6 → −3 2/3
Mini‑FAQ
- Should I simplify before or after? Either is fine; simplifying first can reduce arithmetic.
- Is 0 remainder allowed? Yes—then it’s just the whole part.
- Mixed number to improper? whole·den + num over den.
Action tip
Enter your improper fraction and read the step panel—the division work confirms the whole part and remainder so you can trust the final mixed form.