Lucy mixed 1/2 cup of cold water and 1/3 cup of hot water. How much water did she mix in total?

To determine the total amount of water that Lucy mixed, we need to add the two fractions: 1/2 cup of cold water and 1/3 cup of hot water.

To add these fractions, it's necessary to first find a common denominator. The denominators here are 2 and 3. The least common multiple of 2 and 3 is 6, which will serve as our common denominator.

Next, we convert each fraction to have 6 as the denominator:

• For 1/2, we multiply both the numerator and denominator by 3 to get 3/6.

• For 1/3, we multiply both the numerator and denominator by 2 to get 2/6.

Now we can add the two fractions:

3/6 + 2/6 = (3 + 2)/6 = 5/6.

This result, 5/6, represents the total amount of water that Lucy mixed. Therefore, the correct answer is indeed 5/6. This can be confirmed by substituting back into the physical context of the question and verifying that 5/6 of a cup accurately represents the sum of the two original amounts of cold and hot water.