Arecipe calls for 1/2 cup ingredient a for every 1 2/3 cups of ingredient b. i use 4 cups of ingredient a. how many cups of ingredient b do i need?

Jack did 3/5 of all problems on his weekend homework before sunday. on sunday he solved 1/3 of what was left and the last 4 problems. how many problems were assigned for the weekend?

Find the slope of the line passing through a pair of points

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.