Fraction Calculator
Enter mixed numbers (whole + fraction) or pure fractions. Results are exact and simplified.
How the Fraction Calculator Works
The Fraction Calculator lets you add, subtract, multiply, and divide fractions and mixed numbers with exact arithmetic. Instead of converting everything to rounded decimals, it keeps every step in fraction form using BigInt so your final answer is fully simplified and mathematically precise. You can enter whole numbers plus numerators and denominators for both values A and B, choose an operation, and instantly see the result as a simplified fraction, an optional mixed number, and a decimal approximation.
From Mixed Numbers to Exact Fractions
Each input is interpreted carefully to avoid sign and simplification errors:
- You can enter A and B as mixed numbers (whole + numerator/denominator) or as pure fractions.
- Negative values are supported; the sign can be on the whole or the numerator, and the calculator normalizes it correctly.
- Internally, every mixed number is converted into a single improper fraction using BigInt for numerator and denominator.
- Denominators must be at least 1; invalid denominators are rejected with a clear error.
Operations & Simplification Logic
Once A and B are normalized, the calculator:
- Performs A + B, A − B, A × B, or A ÷ B using exact fraction arithmetic.
- For division, it multiplies by the reciprocal of B and blocks division by zero with an explicit error message.
- Simplifies the result by dividing numerator and denominator by their greatest common divisor (GCD).
- Normalizes the sign so the denominator is always positive.
This guarantees that the main result is always shown in lowest terms and is mathematically correct for even very large values.
Mixed Number & Decimal Output
To make the answer easy to read in different contexts, the calculator shows:
- A simplified fraction (the canonical exact result).
- An optional mixed number representation (e.g. 2 3/5), with correct sign handling.
- A decimal approximation using your chosen precision (0–12 decimal places).
- A snapshot of how your inputs were interpreted as improper fractions, so you can double-check your entry.
Decimal output is purely for convenience; the fraction form remains the exact authoritative result.
Practical Use Cases
This Fraction Calculator is built for:
- Homework and exam prep where exact fraction answers are required.
- Cooking, recipes, and DIY projects that use mixed-unit measurements.
- Converting between mixed numbers, improper fractions, and decimals without manual simplification.
- Teaching fraction operations with a reliable, step-consistent reference.
Scope & Limitations
To stay focused and trustworthy, this tool:
- Operates on two numbers (A and B) at a time.
- Uses BigInt-based fraction math for exactness, not floating-point shortcuts.
- Does not solve algebraic equations or show full step-by-step derivations.
- Expects valid numeric inputs; impossible configurations show clear errors instead of silent failures.
Educational Insight
Fractions are easiest to understand when you see them handled correctly and consistently every time. By converting mixed numbers to improper fractions, simplifying with GCD, and separating exact vs. decimal views, this Fraction Calculator doubles as both a fast problem-solver and a clean model of how fraction arithmetic really works.