Final answer:
A glass that is two-thirds full holds more than a glass that is half full. The fraction 2/3 represents a greater quantity than the fraction 1/2. Comparing fractions helps to determine which of the two states of fullness contains a larger amount. The correct option is 2).
Step-by-step explanation:
The question compares two different states of fullness of a glass: half full and two-thirds full. To determine which state holds more, we compare the fractions 1/2 and 2/3. In this case, it is clear that two-thirds full refers to a larger quantity than half full because the fraction 2/3 is greater than 1/2.
Therefore, a glass that is two-thirds full contains more than a glass that is half full.
For instance, if we consider a glass with a capacity of 6 units, being half full would mean it contains 3 units (6 * 1/2), while two-thirds full means it contains 4 units (6 * 2/3). Thus, two-thirds is more than half.
Understanding fractions is critical in determining quantities, and this example with the glass illustrates the concept of comparing different fractional parts of the same whole. Thinking about this concept in familiar terms, like the amount of water in a glass, can make it easier to grasp the relationship between different fractions. Option 2) is the correct one.