- Separate the mixed numbers into whole number parts and fractional parts.
- Add the whole numbers: \(4 + 1 + 6 = 11\).
- Add the fractions: \(\frac{1}{2} + \frac{1}{3} + \frac{1}{3} = \frac{7}{6} = 1 \frac{1}{6}\).
- Combine the results: \(11 + 1 \frac{1}{6} = 12 \frac{1}{6}\).
- The total amount of punch is \(\boxed{12 \frac{1}{6}}\).
Explanation
- Understanding the Problem
To find the total volume of punch Peter makes, we need to add the volumes of the three individual ingredients: \(4 \frac{1}{2}\) cups of orange juice, \(1 \frac{1}{3}\) cups of ginger ale, and \(6 \frac{1}{3}\) cups of strawberry lemonade. The problem is a straightforward arithmetic operation involving the addition of mixed numbers.
- Adding the Ingredients
We express the total volume \(V_{total}\) as the sum:
\[V_{total} = 4 \frac{1}{2} + 1 \frac{1}{3} + 6 \frac{1}{3}.\]
To add these easily, we can add the whole number parts and the fractional parts separately.
The whole number parts are: \(4 + 1 + 6 = 11\).
The fractional parts are: \(\frac{1}{2} + \frac{1}{3} + \frac{1}{3}\).
Adding the fractions: \(\frac{1}{2} + (\frac{1}{3} + \frac{1}{3}) = \frac{1}{2} + \frac{2}{3}\).
To add \(\frac{1}{2} + \frac{2}{3}\), we find a common denominator, which is 6:
\[\frac{1}{2} = \frac{3}{6}, \quad \frac{2}{3} = \frac{4}{6}.\]
Summing these gives \(\frac{3}{6} + \frac{4}{6} = \frac{7}{6}\).
Since \(\frac{7}{6}\) is an improper fraction, we convert it to a mixed number: \(\frac{7}{6} = 1 \frac{1}{6}\).
- Final Calculation
Now, we combine the sum of the whole numbers and the sum of the fractional parts:
\[V_{total} = 11 + 1 \frac{1}{6} = 12 \frac{1}{6}.\]
Thus, the total amount of punch Peter makes is \(12 \frac{1}{6}\) cups. This matches the second option provided in the question.
Examples
Mixing ingredients to create drinks or recipes is a common task in cooking and catering. When you are combining multiple quantities of liquids measured in mixed numbers, the ability to convert and sum these values ensures your final product has the correct proportions. For instance, if you are preparing a large batch of punch for a party, accurately totaling your ingredients guarantees you do not exceed the capacity of your serving bowls and helps you adjust recipes for different crowd sizes.