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Fraction Calculator
Enter the numerator and denominator of two fractions, pick an operator — the simplified result and its decimal equivalent appear instantly.
Adding, subtracting, multiplying and dividing fractions
To add or subtract two fractions a/b and c/d, the simplest approach is to use the common denominator b×d: the result is (a×d ± c×b)/(b×d). To multiply two fractions, multiply the numerators together and the denominators together: (a×c)/(b×d). To divide a/b by c/d, instead of dividing directly, flip the second fraction and multiply: (a×d)/(b×c). The result of any of these steps may not be in its simplest form, so this tool finds the greatest common divisor (GCD) of the numerator and denominator using the Euclidean algorithm and divides both by it to reach the smallest possible fraction.
A worked example
Say you want to subtract 1/6 from 3/4. Using the formula above, the result is (3×6 − 1×4)/(4×6) = 14/24. Since the GCD of 14 and 24 is 2, the simplified fraction is 7/12, which is approximately 0.5833 as a decimal. That's exactly the logic this calculator runs — just enter your own numbers.
Frequently asked questions
How do I add two fractions?
Find a common denominator — the easiest way is to multiply the two denominators together — convert both numerators to match it, then add. For example 1/2 + 1/3 = (1×3 + 1×2)/(2×3) = 5/6.
Why is the result automatically simplified?
This tool finds the greatest common divisor (GCD) of the numerator and denominator using the Euclidean algorithm and divides both by it, so the fraction is shown in its simplest form.
What happens if a denominator is zero?
A fraction's denominator can never be zero, because division by zero is undefined. In that case the tool shows an error message instead of a result.
What does dividing by a fraction mean?
Dividing by a fraction is the same as multiplying by its reciprocal — the numerator and denominator of the second fraction swap places. If the second fraction's numerator is zero, this division is impossible and the tool shows an error.