A recipe for a cake requires 2/3 cup of sugar for every 1/2 cup of flour. If you want to make a batch using 3 cups of flour, how much sugar will you need? Additionally, if you decide to make another batch using 1/4 of the original amount of flour, how much sugar will you need for this smaller batch? Let's think step by step and output the final answer within \boxed{}.
user