Arectangular cake has a length of 22 1/2 inches and a width of 10 inches. how many whole, square pieces of cake with side lengths of 2 1/2 inches can be cut from the cake?

Well, we need to find the area of the cake.  22.5 times 10 is 225.  That is the area then we need to find the area of each piece of cake.  2.5 times 2.5 is 6.26.
so divide the area of the cake by the area of each piece to find how many pieces can be cut.
225/6.25=36  36 pieces of cake can be cut from the cake