1. **State the problem:** We need to find the total amount of orange juice in the restaurant's fridge. There are 7 \frac{1}{2} bottles, and each bottle holds 1 \frac{5}{6} quarts. 2. **Convert mixed numbers to improper fractions:** \[7 \frac{1}{2} = \frac{15}{2}, \quad 1 \frac{5}{6} = \frac{11}{6}\] 3. **Multiply the number of bottles by the amount per bottle:** \[\text{Total juice} = \frac{15}{2} \times \frac{11}{6} = \frac{15 \times 11}{2 \times 6} = \frac{165}{12}\] 4. **Simplify the fraction:** \[\frac{165}{12} = \frac{\cancel{15} \times 11}{\cancel{15} \times \frac{12}{15}} = \frac{11}{\frac{12}{15}}\] (This step shows cancellation of 15 incorrectly; correct simplification is below.) Let's simplify correctly: \[\frac{165}{12} = \frac{165 \div 3}{12 \div 3} = \frac{55}{4}\] 5. **Convert improper fraction to mixed number:** \[\frac{55}{4} = 13 \frac{3}{4}\] **Final answer:** The restaurant has \boxed{13 \frac{3}{4}} quarts of orange juice.