The result is divided through by gcd(numerator,denominator) and the sign is moved to the numerator. A mixed number is the whole part plus the remainder over the denominator.
Worked example
Compute 43+65.
ad+bc=3×6+4×5=38, and bd=24.
38/24 has gcd=2, so it simplifies to 19/12.
As a mixed number: 17/12. As a decimal: 1.5833.
Dividing instead: 43÷65=4×53×6=2018=109.
Common mistakes
Adding numerators and denominators separately: 1/2+1/3 is not 2/5.
Forgetting to flip the second fraction when dividing.
Leaving a negative sign in the denominator. 1/(−2) should be written −1/2.
Entering a mixed number as a single numerator. Convert 21/3 to 7/3 first.
Frequently asked questions
Why do I need a common denominator to add fractions?
You can only add pieces of the same size. 1/2 and 1/3 are different sized pieces, so both are rewritten in sixths (3/6 and 2/6) before the numerators are added.
How is the answer simplified?
The numerator and denominator are both divided by their greatest common divisor, found with Euclid's algorithm. 6/8 has a GCD of 2, so it becomes 3/4.
Why does dividing flip the second fraction?
Dividing by 1/4 asks how many quarters fit, which is the same as multiplying by 4. So a/b ÷ c/d = a/b × d/c.
Are large numbers exact?
Yes. Calculations use arbitrary-precision integers, so results are exact even when numerators and denominators have dozens of digits. The decimal shown is a floating-point approximation.