Nehemiah wrote that 4 + 4 = 8. Then he wrote that 4 + 4 – k = 8 – k. Select the phrases that make the statement true. The equations
are or are not
balanced because Nehemiah
added k to or subtracted k from
each side of the original equation.

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.