1. **State the problem:** Grace drove 44 1/2 miles using 1 1/4 gallons of gasoline. We need to find the unit rate in miles per gallon. 2. **Formula:** The unit rate (miles per gallon) is calculated by dividing the total miles driven by the total gallons used: $$\text{Unit rate} = \frac{\text{miles}}{\text{gallons}}$$ 3. **Convert mixed numbers to improper fractions:** - 44 1/2 miles = $$44 + \frac{1}{2} = \frac{88}{2} + \frac{1}{2} = \frac{89}{2}$$ miles - 1 1/4 gallons = $$1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4}$$ gallons 4. **Calculate the unit rate:** $$\frac{89/2}{5/4} = \frac{89}{2} \times \frac{4}{5} = \frac{89 \times 4}{2 \times 5} = \frac{356}{10}$$ 5. **Simplify the fraction:** $$\frac{356}{10} = \frac{178}{5}$$ 6. **Convert to mixed number:** $$178 \div 5 = 35 \text{ remainder } 3$$ So, $$\frac{178}{5} = 35 \frac{3}{5}$$ **Final answer:** The unit rate is $35 \frac{3}{5}$ miles per gallon.