To find the total number of cups of punch that Peter makes, we need to add the three quantities together:
-
Convert the mixed numbers to improper fractions:
- For orange juice: \[ 4 \frac{1}{3} = \frac{4 \times 3 + 1}{3} = \frac{12 + 1}{3} = \frac{13}{3} \]
- For ginger ale: \[ 2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3} \]
- For strawberry lemonade: \[ 6 \frac{1}{2} = \frac{6 \times 2 + 1}{2} = \frac{12 + 1}{2} = \frac{13}{2} \]
-
Now add the improper fractions:
- First, we find a common denominator. The denominators are 3 and 2. The least common multiple (LCM) of 3 and 2 is 6.
-
Convert each fraction to have a denominator of 6:
- For orange juice: \[ \frac{13}{3} = \frac{13 \times 2}{3 \times 2} = \frac{26}{6} \]
- For ginger ale: \[ \frac{7}{3} = \frac{7 \times 2}{3 \times 2} = \frac{14}{6} \]
- For strawberry lemonade: \[ \frac{13}{2} = \frac{13 \times 3}{2 \times 3} = \frac{39}{6} \]
-
Now add all the fractions: \[ \frac{26}{6} + \frac{14}{6} + \frac{39}{6} = \frac{26 + 14 + 39}{6} = \frac{79}{6} \]
-
Convert the improper fraction back to a mixed number:
- Divide 79 by 6, which gives us 13 with a remainder of 1. \[ 79 \div 6 = 13 \quad \text{(remainder 1)} \]
- So, \(\frac{79}{6} = 13 \frac{1}{6}\).
Therefore, the total number of cups of punch that Peter makes is \(\boxed{13 \frac{1}{6}}\).