Todd and Gavin each made a bowl of punch. Gavin used 4 7/10 times as much lemonade as Todd did. If Todd used 2 3/8 cups of lemonade, how many cups of lemonade did Gavin use?

To determine how many cups of lemonade Gavin used, we first need to multiply the amount of lemonade Todd used by the factor of 4 \( \frac{7}{10} \).

First, convert Todd's amount of lemonade from a mixed number to an improper fraction. Todd used \( 2 \frac{3}{8} \) cups of lemonade.

1. Convert \( 2 \frac{3}{8} \) to an improper fraction: \[ 2 \frac{3}{8} = \frac{2 \times 8 + 3}{8} = \frac{16 + 3}{8} = \frac{19}{8} \]

Now we need to find the amount of lemonade Gavin used: \[ \text{Gavin's lemonade} = 4 \frac{7}{10} \times 2 \frac{3}{8} \]

2. Convert \( 4 \frac{7}{10} \) to an improper fraction: \[ 4 \frac{7}{10} = \frac{4 \times 10 + 7}{10} = \frac{40 + 7}{10} = \frac{47}{10} \]

3. Now, we multiply the two improper fractions: \[ \text{Gavin's lemonade} = \frac{47}{10} \times \frac{19}{8} \]

4. Multiply the numerators and the denominators: \[ \frac{47 \times 19}{10 \times 8} = \frac{893}{80} \]

5. Convert \( \frac{893}{80} \) to a mixed number. To do this, divide 893 by 80:

   • \( 80 \) goes into \( 893 \) eleven times (since \( 80 \times 11 = 880 \)).
   • The remainder is \( 893 - 880 = 13 \).

Thus, we can express \( \frac{893}{80} \) as: \[ \frac{893}{80} = 11 \frac{13}{80} \]

The final answer is: \[ \boxed{11 \frac{13}{80}} \text{ cups} \]