1. **State the problem:** Ashe drove 250 miles using 5 \frac{1}{4} gallons of gasoline. We need to find how many miles per gallon (mpg) her vehicle gets. 2. **Formula:** Miles per gallon is calculated by dividing the total miles driven by the total gallons used: $$\text{mpg} = \frac{\text{miles}}{\text{gallons}}$$ 3. **Convert mixed number to improper fraction:** $$5 \frac{1}{4} = \frac{21}{4}$$ 4. **Calculate mpg:** $$\text{mpg} = \frac{250}{\frac{21}{4}}$$ 5. **Divide by a fraction by multiplying by its reciprocal:** $$\text{mpg} = 250 \times \frac{4}{21}$$ 6. **Multiply numerator and denominator:** $$\text{mpg} = \frac{250 \times 4}{21} = \frac{1000}{21}$$ 7. **Simplify fraction if possible:** 1000 and 21 have no common factors other than 1, so fraction stays as is. 8. **Convert improper fraction to mixed number:** $$\frac{1000}{21} = 47 \frac{13}{21}$$ 9. **Convert fraction to decimal for clarity:** $$\frac{13}{21} \approx 0.619$$ So, $$\text{mpg} \approx 47.62$$ **Final answer:** Ashe's vehicle gets approximately **47 \frac{13}{21}** miles per gallon.