How this calculator works
Addition and subtraction first use a common denominator. Multiplication combines the numerators and denominators directly. Division multiplies by the second fraction reversed. Integer arithmetic keeps the result exact, and the greatest common divisor reduces it to lowest terms with a positive denominator.
Formula
a/b ± c/d = (ad ± bc)/(bd). (a/b) × (c/d) = ac/(bd). (a/b) ÷ (c/d) = ad/(bc). Divide the result by the numerator and denominator gcd.
Worked example
1/2 + 1/3 = 3/6 + 2/6 = 5/6. Multiplying 3/4 by 2/5 gives 6/20, which reduces to 3/10. Dividing 2/3 by 4/5 gives 5/6.
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Frequently asked questions
Can a denominator be negative?
Yes. The answer moves the sign to the numerator, so 1/-2 becomes -1/2.
Why can I not divide by a zero fraction?
A fraction with a zero numerator is zero. Its reciprocal would have a zero denominator, so division by it is undefined.
Can I enter a whole number?
Yes. Put the whole number over a denominator of 1, so 3 is entered as 3 over 1.