Fraction Calculator
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What Your Result Means
- Simplified Fraction: The answer reduced to lowest terms by dividing the numerator and denominator by their greatest common divisor. For example, 6/8 simplifies to 3/4.
- Mixed Number: A whole number plus a proper fraction, shown when the numerator is larger than the denominator. For example, 7/4 becomes 1 3/4.
- Decimal: The fraction expressed as a decimal number, rounded to six significant decimal places. Repeating decimals are truncated, not marked.
How This Calculator Works
You enter two fractions and pick an operation. For addition and subtraction, the tool cross-multiplies to find a common denominator: (a/b) ± (c/d) = (ad ± bc) / bd. For multiplication it multiplies straight across, and for division it flips the second fraction and multiplies. The result is then reduced using the greatest common divisor.
Quick Questions
What if my denominator is zero?
Division by zero is undefined in mathematics, so the calculator will show an error. Make sure both denominators are non-zero integers.
Can I enter negative fractions?
Yes. Enter a negative numerator (e.g., -3/4) and the calculator will handle the sign correctly through all operations and simplification.
How does simplification work?
The tool finds the greatest common divisor (GCD) of the numerator and denominator using the Euclidean algorithm, then divides both by it. For example, GCD(12, 8) = 4, so 12/8 simplifies to 3/2.
Can I enter whole numbers?
Yes — enter the whole number as the numerator and 1 as the denominator. For example, to add 3 + 1/2, enter 3/1 + 1/2.
Sources
- Wikipedia — Fraction (arithmetic rules and simplification)
- Wikipedia — Euclidean Algorithm (GCD computation method)
- Khan Academy — Fraction Arithmetic (educational reference)
Method & review
Estimate only. Results reflect your inputs and standard formulas. Double-check important decisions independently.