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Fraction Calculator

Add, subtract, multiply or divide two fractions and get the fully simplified result, decimal, percentage and mixed number.

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Fraction Calculator
Add, subtract, multiply or divide fractions with simplification
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Result
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Disclaimer. This calculator is provided for educational and general-purpose use. Verify critical or high-stakes calculations independently before relying on them. Read full disclaimer →

About Fraction Calculator

Fractions represent exact rational numbers - unlike decimals they never suffer from floating-point rounding errors. Addition and subtraction require finding the Least Common Denominator first, then combining numerators. Multiplication: multiply numerators together and denominators together. Division: multiply by the reciprocal of the second fraction (flip it).

Simplification divides both numerator and denominator by their Greatest Common Divisor (GCD). Mixed numbers like 2 and three-quarters convert to improper fractions by multiplying whole number by denominator and adding numerator (giving 11 over 4). Fractions are used in engineering tolerances, recipe scaling, probability calculations, music time signatures, and construction measurements. This calculator shows all working steps.

Frequently Asked Questions

It divides both the numerator and denominator by their Greatest Common Divisor (GCD), found using the Euclidean algorithm. For example, 8/12 has a GCD of 4, so it simplifies to 2/3.
It uses cross-multiplication: a/b + c/d becomes (a×d + c×b)/(b×d), and the result is then simplified using the GCD. This is mathematically equivalent to finding the lowest common denominator manually, but skips that step by working directly with the product of the two denominators.
The whole-number part is the numerator divided by the denominator, truncated to an integer, and the remaining fraction is the remainder over the original denominator. For example, 11/4 becomes 2 whole with 3/4 left over, written as 2 3/4.
Fractions represent exact rational numbers, while decimals can suffer from floating-point rounding errors, especially with repeating decimals like 1/3. Exact fractions matter in contexts like engineering tolerances, recipe scaling, probability calculations, music time signatures and construction measurements, where a rounded decimal could introduce real error.
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