This instructable is an entry to the Burning Questions Round 6.5 contest.
The fraction images were generated using this site
Step 1: Reciprocate the Second Fraction
This just means we switch the positions of the numerator(top number) and denominator (bottom number) (See second image).
Then, after reciprocating the fraction we need to change the divide sign to a multiply(See third image).
In this example using 1/2 / 1/3, we are left with 1/2 X 3/1.
Step 2: Do the Multiplication
If you don't know how to multiply fractions, then check out my other instructable called Multiplying Fractions. Remember to simplify your result if necessary. If you cross-cancel the multiplication, (again, see Multiplying Fractions) remember that you must cross cancel AFTER you convert the divide to multiply, NOT before!!!