It really depends who you are going to be explaining it to as to the best strategy. The really important thing, especially when teaching maths, is to have multiple strategies and to be flexible in which you use

If you have 2 pizzas and cut each one into thirds then remove one piece from each pizza. The four pieces remaining represent the number 2/3 is half of (i.e., 4/3). So each piece left represents one quarter of 4/3, i.e. 1/3.

If 2/3 is a half of a number then the number must be double 2/3, i.e. 4/3. So a quarter of that must be one third.

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