Yes calculators can divide fractions. For simple non-algebraic fractions, a basic calculator with addition, subtraction, multiplication, division and parantheses functions are usually enough.
For algebraic fractions, a more advanced calculator is needed because you will use variables such as x, y and z and you might also need brackets in addition to parantheses. Texas Instruments (TI) has several of these kind of calculators, but can cost anywhere from $89 -$260 depending on the type and extra functionality needed.