1. **State the problem:** Jessica used a total of $4 \frac{3}{4}$ gallons of gas. Each hour she drove, she used $\frac{5}{6}$ gallons. We need to find the total number of hours she was driving. 2. **Write the formula:** Total gallons used = (Gallons per hour) $\times$ (Number of hours) Let the number of hours be $h$. Then: $$4 \frac{3}{4} = \frac{5}{6} \times h$$ 3. **Convert mixed number to improper fraction:** $$4 \frac{3}{4} = \frac{4 \times 4 + 3}{4} = \frac{19}{4}$$ 4. **Set up the equation:** $$\frac{19}{4} = \frac{5}{6} h$$ 5. **Solve for $h$ by dividing both sides by $\frac{5}{6}$:** $$h = \frac{19}{4} \div \frac{5}{6}$$ 6. **Division of fractions means multiplying by the reciprocal:** $$h = \frac{19}{4} \times \frac{6}{5}$$ 7. **Multiply numerators and denominators:** $$h = \frac{19 \times 6}{4 \times 5} = \frac{114}{20}$$ 8. **Simplify the fraction by dividing numerator and denominator by 2:** $$h = \frac{\cancel{114}^ {57}}{\cancel{20}^{10}}$$ 9. **Convert improper fraction to mixed number:** $$57 \div 10 = 5 \text{ remainder } 7$$ So, $$h = 5 \frac{7}{10}$$ **Final answer:** Jessica was driving for $5 \frac{7}{10}$ hours.