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

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

• A. 5/6
• B. 3/4
• C. 2/5
• D. 7/8

Answer: (A)

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.

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.