Free Fraction Calculator
Add, subtract, multiply, or divide two fractions or mixed numbers, with the result automatically simplified to lowest terms. Every calculation shows its working, step by step, so you can check your homework or learn the method.
How Fraction Operations Work
- Adding/subtracting: find a common denominator, then add or subtract the numerators
- Multiplying: multiply the numerators together and the denominators together
- Dividing: multiply by the reciprocal (flip the second fraction, then multiply)
Simplifying Fractions
Every result is automatically reduced to lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD). For example, 6/8 simplifies to 3/4 because both numbers share a common factor of 2.
Mixed Numbers
A mixed number like 2½ combines a whole number and a fraction. Enter the whole number in the small box before the fraction — leave it at 0 for a plain fraction. Results over 1 are automatically converted back to a mixed number for readability.
Frequently Asked Questions
Why do I need a common denominator to add fractions? Fractions represent parts of a whole, and you can only add "like parts" — quarters with quarters, thirds with thirds. Converting to a common denominator makes the pieces the same size before combining them.
What if my denominator is 0? Division by zero is undefined in mathematics — the calculator will flag this as an invalid input rather than showing a result.
Does this handle negative fractions? Yes — enter a negative number in the numerator or whole-number field and the calculator handles the sign correctly through every operation.
How is dividing by a fraction the same as multiplying? Dividing by a number is the same as multiplying by its reciprocal (1 divided by that number). So a/b ÷ c/d = a/b × d/c — flip the second fraction and multiply.