For example, if it's 4 1/3 divided by 1 1/3, multiply the denominator, 3, by the whole number. For 4 1/3, it would be 3*4 to get 12. Then add the numerator to get 13. 4 1/3 is then represented as 13/3. Do the same for 1 1/3 to get 4/3. Do the reciprocal to get 3/4. Then instead of dividing, do 13/3 times 3/4. Since the denominator of 13/3 and the numerator of 3/4 are the same, cross them out. You're left with 13/1 times 1/4. Multiply to get 13/4, or 3 1/4.
Tip: Use a website called Wolfram Alpha. Type in mixed numbers by using 4 (space) 1/3 (type times, don't put *) whatever number. wolframalpha.com