We can apply the area model for the multiplication of fractions to visualize the division of two fractions when each is less than 1. To model division with fractions, we more or less reverse the process used for multiplication. We start with an area we're looking for, and we find one of the missing factors that makes up that area. Note 3
For example, here's how we would use the model to demonstrate the problem 1/4 2/3:
What you see now is the purple (1/4) area and the size of one of the factors that made that area.
We know from the multiplication model that the product of 2/3 and another factor (the quotient) defines an area equivalent in size to 1/4. To find the quotient, we need to move the top part of the purple area so that it's the same height as the 2/3 factor.
This shows that there are 3 2, or 6, purple parts out of 8 3, or 24, parts in all. The purple area equals 1/4, and it came from the product of 2/3 multiplied by what? We can see that the other factor is 3/8.