Peter mixes $4 \frac{1}{2}$ cups of orange juice, $1 \frac{1}{3}$ cups of ginger ale, and $6 \frac{1}{3}$ cups of strawberry lemonade to make some punch. What is the total number of cups of punch that Peter makes? $11 \frac{3}{8}$ $11 \frac{3}{5}$ $11 \frac{1}{2}$ $12 \frac{1}{6}$

Step 1 ：The question is asking for the total number of cups of punch that Peter makes. This can be found by adding together the number of cups of each ingredient.

Step 2 ：The numbers are mixed numbers, which means they have a whole number part and a fractional part. To add them together, I can add the whole numbers together and the fractions together separately. If the sum of the fractions is greater than 1, I can convert it to a mixed number and add it to the sum of the whole numbers.

Step 3 ：Peter uses \(4 \frac{1}{2}\) cups of orange juice, \(1 \frac{1}{3}\) cups of ginger ale, and \(6 \frac{1}{3}\) cups of strawberry lemonade.

Step 4 ：The total whole number of cups is \(4 + 1 + 6 = 11\).

Step 5 ：The total fractional part is \(\frac{1}{2} + \frac{1}{3} + \frac{1}{3} = \frac{1}{6}\).

Step 6 ：The total number of cups of punch that Peter makes is 12 whole cups and \(\frac{1}{6}\) fractional cups.

Step 7 ：Final Answer: The total number of cups of punch that Peter makes is \(\boxed{12 \frac{1}{6}}\).