A cafeteria sold \( 13 \frac{3}{6} \) gallons of soda during lunchtime. \( 5 \frac{5}{6} \) gallons were regular soda, and the rest was diet soda. How many gallons of diet soda were sold?

To find out how many gallons of diet soda were sold, we first need to convert the mixed numbers into improper fractions. The total gallons of soda sold is: \[ 13 \frac{3}{6} = \frac{13 \times 6 + 3}{6} = \frac{78 + 3}{6} = \frac{81}{6} \] The gallons of regular soda is: \[ 5 \frac{5}{6} = \frac{5 \times 6 + 5}{6} = \frac{30 + 5}{6} = \frac{35}{6} \] Now we can find the gallons of diet soda by subtracting the gallons of regular soda from the total: \[ \text{Diet soda} = \frac{81}{6} - \frac{35}{6} = \frac{81 - 35}{6} = \frac{46}{6} = 7 \frac{2}{3} \] So, the cafeteria sold \( 7 \frac{2}{3} \) gallons of diet soda.