A cup can be 3/4 full. Can it be 5/4 full? Explain.
The Correct Answer and Explanation is :
No, a cup cannot be 5/4 full.
A cup that is “3/4 full” means that 75% of its capacity is filled with a liquid or other substance. This is a practical measurement that stays within the limits of the cup’s total volume. When we talk about 5/4 full, we are saying that the cup would contain 125% of its volume, which exceeds its capacity.
Here’s a detailed explanation:
A fraction like “3/4” refers to the relationship between the part and the whole. If a cup is 3/4 full, three parts of the cup are filled, leaving one part empty, within the four total parts (the whole cup).
Now, if we say a cup is 5/4 full, we are suggesting the contents exceed the total volume of the cup by an additional 25%. However, a physical object such as a cup has a maximum capacity—once it’s full, it cannot hold more than 100% of its volume. Any additional liquid added would spill over because the cup’s physical space is limited. So, while 5/4 makes sense as a mathematical expression (it means 1.25 times the full volume), it does not apply to real-world scenarios where physical objects have set limits.
To help visualize this, if you filled a cup to 100%, it is full. If you continued pouring, the extra liquid wouldn’t stay in the cup; it would overflow. Thus, in practical terms, the concept of a cup being 5/4 full isn’t possible, though it works in abstract math or as a way to express overflow.