Mixed Numbers — the 80/20
A mixed number is a whole part plus a proper fraction. Convert to improper fractions to calculate cleanly, then convert back and simplify.
How it works
- Mixed → improper: a b/c → (a×c + b)/c.
- Add/Subtract: find LCD, combine numerators, simplify.
- Multiply: multiply numerators and denominators, simplify.
- Divide: multiply by the reciprocal, simplify.
Sanity checks
- 2 1/3 ≈ 2.333; results should be near that scale.
- Whole-only inputs behave like integers.
- Negative signs apply to the whole value, not just the fraction.
Shortcuts
- Add/Subtract: add whole parts separately if denominators match.
- Prefer improper form to avoid borrowing mistakes.
- Simplify early when multiplying/dividing.
Pitfalls
- Forgetting to find a common denominator for +/−.
- Borrowing incorrectly in subtraction.
- Leaving answers unsimplified or with negative denominator.
Micro‑examples
- 2 1/3 + 1 1/4 → 7/3 + 5/4 = 28/12 + 15/12 = 43/12 = 3 7/12.
- 3 1/4 − 1 2/3 → 13/4 − 5/3 = 39/12 − 20/12 = 19/12 = 1 7/12.
- 1 1/2 × 2 2/3 → 3/2 × 8/3 = 4.
Mini‑FAQ
- Keep as improper or convert back? Either works; mixed is often clearer.
- Can results be whole numbers? Yes—fractions can cancel.
- How to handle negatives? Apply the sign to the improper fraction, then convert back.
Action tip
Enter two mixed numbers, pick an operation, and the tool converts, computes, simplifies, and shows a mixed-number result with steps.