Fraction Calculator
Perform operations on fractions and get simplified results instantly.
What is it?
This calculator performs addition, subtraction, multiplication, and division on two fractions, automatically simplifying the result to its lowest terms.
Formula
- Add: (a/b) + (c/d) = (ad + bc) / bd
- Subtract: (a/b) − (c/d) = (ad − bc) / bd
- Multiply: (a/b) × (c/d) = ac / bd
- Divide: (a/b) ÷ (c/d) = ad / bc
Formula Explanation
Adding or subtracting fractions first requires a common denominator, which is why both fractions are cross-multiplied (bd) to create matching bottoms before combining the tops. Multiplication and division work directly on numerators and denominators without needing a common denominator first.
Example Calculation
Adding 1/2 and 1/3: (1×3 + 2×1) / (2×3) = 5/6.
How to Use
- Enter the numerator and denominator of the first fraction.
- Select the operation (add, subtract, multiply, or divide).
- Enter the numerator and denominator of the second fraction.
- View the simplified fraction, mixed number, and decimal result.
Benefits
- Handles all four basic operations in one tool, always returning a simplified result.
- Shows the result as a fraction, mixed number, and decimal simultaneously.
- Removes manual cross-multiplication and simplification errors.
Use Cases
- Homework help for fraction arithmetic.
- Cooking and recipe scaling that involves fractional measurements.
- Any calculation requiring precise fractional results rather than rounded decimals.
What Your Result Means
The simplified fraction is the exact result in lowest terms. The mixed number form is useful when the result is greater than 1 (an improper fraction), and the decimal gives a quick approximate sense of the value.
Tips
- Simplify fractions before further calculations to keep numbers smaller and easier to work with.
- Remember that dividing by a fraction is the same as multiplying by its reciprocal.
- Use the decimal result to sanity-check that your fraction answer looks reasonable.
Common Mistakes
- Adding numerators and denominators directly without finding a common denominator first.
- Forgetting to simplify the final fraction to lowest terms.
- Entering a zero denominator, which makes the fraction undefined.
FAQs
Why is the result simplified?
Simplifying (reducing to lowest terms) makes a fraction easier to read and compare, by dividing both numerator and denominator by their greatest common divisor.
What is a mixed number?
A mixed number combines a whole number and a proper fraction, like 1 1/2 — this calculator converts improper fraction results into mixed number form automatically.
What happens if I enter a zero denominator?
Division by zero is mathematically undefined, so make sure denominators are non-zero, and when dividing fractions, the second numerator (which becomes a denominator) must also be non-zero.
Can I enter negative fractions?
Yes, enter a negative sign on either the numerator or denominator, and the calculator will handle the sign correctly in the result.
Why do add and subtract use cross-multiplication?
Cross-multiplication (bd) creates a common denominator between the two fractions, which is required before their numerators can be validly combined.
Results are exact fraction arithmetic, simplified automatically to lowest terms.
Last updated: July 25, 2026