Everyday Math
Fraction Calculator
Add, subtract, multiply, or divide two fractions with automatic simplification and a decimal equivalent. Free instant fraction calculator.
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Result
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Decimal Equivalent 0
What Does This Fraction Calculator Do?
This calculator adds, subtracts, multiplies, or divides two fractions. Enter the numerator and denominator for each fraction, choose an operation, and it returns the result in fully simplified form along with its decimal equivalent.
Fraction Operation Formulas
Add: a/b + c/d = (a×d + c×b) / (b×d)
Subtract: a/b − c/d = (a×d − c×b) / (b×d)
Multiply: a/b × c/d = (a×c) / (b×d)
Divide: a/b ÷ c/d = (a×d) / (b×c)
Subtract: a/b − c/d = (a×d − c×b) / (b×d)
Multiply: a/b × c/d = (a×c) / (b×d)
Divide: a/b ÷ c/d = (a×d) / (b×c)
Worked Example: 1/2 + 1/3
- (1 x 3 + 1 x 2) / (2 x 3) = (3 + 2) / 6 = 5/6
- 5/6 is already in simplest form
- Decimal equivalent: 0.8333...
How Fractions Are Simplified
After the operation, the calculator finds the greatest common divisor (GCD) of the resulting numerator and denominator using the Euclidean algorithm, then divides both by the GCD. For example, 8/16 has a GCD of 8, simplifying to 1/2.
See also the percentage calculator and GPA calculator for more everyday math tools.
Frequently Asked Questions
How do I add two fractions?
Cross-multiply to get a common denominator: (a/b) + (c/d) = (a*d + c*b) / (b*d). For example, 1/2 + 1/3 = (1*3 + 1*2) / (2*3) = 5/6.
How do I subtract two fractions?
Similar to addition but subtract the cross-products: (a/b) - (c/d) = (a*d - c*b) / (b*d). For example, 3/4 - 1/4 = (3*4 - 1*4) / (4*4) = 8/16, which simplifies to 1/2.
How do I multiply two fractions?
Multiply the numerators together and the denominators together: (a/b) x (c/d) = (a*c) / (b*d). For example, 2/3 x 3/4 = 6/12, which simplifies to 1/2.
How do I divide two fractions?
Multiply the first fraction by the reciprocal (flip) of the second: (a/b) / (c/d) = (a/b) x (d/c) = (a*d) / (b*c). For example, 1/2 / 1/4 = 1/2 x 4/1 = 4/2, which simplifies to 2.
How does this calculator simplify fractions?
It finds the greatest common divisor (GCD) of the numerator and denominator using the Euclidean algorithm, then divides both by that GCD to reduce the fraction to its simplest form.
What is a fraction's decimal equivalent?
It's simply the numerator divided by the denominator. For example, 5/6 as a decimal is approximately 0.8333.
Can I use negative numbers?
Yes, this calculator supports negative numerators and denominators, and correctly handles sign simplification (e.g. a negative denominator moves the sign to the numerator).
Related Calculators
How this is calculated: This tool uses standard, well-established formulas for everyday math calculations. Results are estimates for informational and planning purposes — always double-check figures for anything with real-world consequences (e.g. ordering materials or submitting grades).