Arecipe for chocolate chip cookies used 3 cups flour and sticks 2 sticks of butter is the amount of butter used proportional to the number of cups of flour used.

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.