What does the phrase "Three divided by one half" represent?

The phrase "Three divided by one half" can be interpreted mathematically as how many half-sized parts are contained within three whole units. To break it down, dividing by a fraction involves multiplying by its reciprocal. Therefore, dividing three by one half is equivalent to multiplying three by two, because the reciprocal of one half is two. This means that there are six halves within three wholes – confirming that the first answer choice accurately captures this relationship.

When looking at the other interpretations, it becomes evident why they do not align with the mathematical concept. The notion of how many whole numbers are in three does not apply because it addresses whole units rather than focusing on the halves, and thus it doesn’t address the division by a fraction. Similarly, the third choice regarding the amount of one half in three halves misinterprets the division as comparing halves to a different quantity rather than asking how many halves fit into three. Finally, the idea of dividing three into two equal parts does not reflect the mathematical operation of dividing by a fraction but rather implies splitting three into two distinct groups, which is unrelated to the concept of halves.