Question

Peter mixes 4 1/3
cups of orange juice, 2 1/3
cups of ginger ale, and 6 1/2
cups of strawberry lemonade to make some punch. What is the total number of cups of punch that Peter makes?

Answer 1

To find the total number of cups of punch that Peter makes, we need to add the three quantities together:

1. **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:
\[
6 \frac{1}{2} = \frac{6 \times 2 + 1}{2} = \frac{12 + 1}{2} = \frac{13}{2}
\]

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.

3. **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:
\[
\frac{13}{2} = \frac{13 \times 3}{2 \times 3} = \frac{39}{6}
\]

4. **Now add all the fractions:**
\[
\frac{26}{6} + \frac{14}{6} + \frac{39}{6} = \frac{26 + 14 + 39}{6} = \frac{79}{6}
\]

5. **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 \(\boxed{13 \frac{1}{6}}\).