I heard someone on television the other day say that something was going to be "bisected in two." If you are going to bisect something, it's hard to bisect it into three pieces. On the other hand, we frequently use the expression "the larger half", as in when you are splitting a piece of meat and your companion says, "You take the larger half." If it is half, it's the same as the other half. Half is just half. 50% = 50%.