Half of 2/3 cup is equal to 1/3 cup. Two-thirds of a cup is equal to adding two 1/3 portions. Thus, halving of two 1/3 portions leaves only 1/3.
Reducing certain measurements can be easier if they are considered in portions instead of whole amounts. Halving 1/4 cup results in 1/8 cup (which is equivalent to 2 tablespoons), and halving 1/2 cup results in 1/4 cup (which is equivalent to 2 ounces).
However, amounts such as 3/4 cup and 1/3 cup are best halved when they are considered in tablespoons. Twelve tablespoons is equivalent to 3/4 cup, and 1/3 cup is equal to 5 tablespoons plus 1 teaspoon.