I will start out by thinking Fawn Nguyen and her blog Finding Ways for this method. It is cool and makes a lot of sense. Look at the division problem 3/4 divided by 2/3.

Fawn uses rectangles as a way of creating the base for the problem so for 3/4 she recommends a 3 by 4 rectangle and the same 3 by 4 rectangle for 2/3. 3/4th of the squares are colored in to represent 3/4th of 1 while 2/3rds of the other rectangle is colored in to represent 2/3rds of 1.

3/4 and 2/3 are colored in. |

If you do the math you find it is correct because 3/4/2/3 is 3/4 * 3/2 or 9/8 = 1 1/8

This is one of the cooler ways I've seen to illustrate the concept for division. Most of the sites simply tell people to invert and multiply but they do not provide a conceptual drawing to help explain. I like this method and I'm going to play around with it to see if it works in a certain form. I'll report back in a while on it. Enjoy playing with this idea.