First we study what reciprocal numbers are: two numbers are reciprocal numbers if their product is one. Then I show the shortcut for fraction division: flip the second fraction, and multiply.
I intend this video for 5th grade - it is fairly short and to the point, and doesn't fully explain why this all works. A longer version of this video that goes into all that is here (for 6th grade).
Fraction video lessons, part 2: multiplication and division
Math Mammoth Grade 5 curriculum