Work with fractions: fast, exact, and clear
Core idea
Fractions are ratios. This tool performs +, −, ×, ÷; reduces to lowest terms; and shows mixed, decimal, and step‑by‑step views without changing your inputs.
How it works
- Add/Subtract: use common denominators (LCM) or cross‑multiply.
- Multiply/Divide: multiply across; for ÷, multiply by the reciprocal.
- Simplify: divide numerator and denominator by their GCD.
Sanity checks
- Denominators ≠ 0 and end positive.
- Result is in simplest form; mixed and improper are consistent.
- Decimal rendering matches the fraction within display rounding.
Shortcuts
- Reduce early only when numbers explode; otherwise reduce at the end.
- Use known families: halves, thirds, quarters, fifths, eighths.
- Convert mixed to improper before × or ÷ to avoid mistakes.
Pitfalls
- Adding denominators (wrong) instead of aligning parts.
- Forgetting to flip the second fraction when dividing.
- Placing the negative sign on the denominator.
Micro‑examples
- 3/4 + 1/2 → LCD 4 → 3/4 + 2/4 = 5/4 = 1 1/4
- (2/3) × (3/5) = 6/15 = 2/5
- 5/4 ÷ 1/2 = 5/4 × 2/1 = 10/4 = 5/2 = 2 1/2
Mini‑FAQ
- Is the simplest form unique? Yes, with a positive denominator.
- Mixed vs improper—are they equivalent? Yes, same value, different form.
- Do you round? Only for displayed decimals, never the fraction math.
Action tip
Estimate first (a/b ≈ a÷b). If the decimal view is far off your estimate, recheck inputs or the operation selected.