1. **State the problem:** Mary has jogged $\frac{1}{4}$ miles, and the total distance to school is $\frac{5}{8}$ miles. We need to find how many miles she still has to jog. 2. **Formula used:** To find the remaining distance, subtract the distance already jogged from the total distance: $$\text{Remaining distance} = \text{Total distance} - \text{Distance jogged}$$ 3. **Substitute the values:** $$\text{Remaining distance} = \frac{5}{8} - \frac{1}{4}$$ 4. **Find a common denominator:** The denominators are 8 and 4. The least common denominator is 8. $$\frac{1}{4} = \frac{2}{8}$$ 5. **Rewrite the subtraction:** $$\frac{5}{8} - \frac{2}{8} = \frac{5 - 2}{8} = \frac{3}{8}$$ 6. **Convert to mixed number:** Since $\frac{3}{8}$ is less than 1, it is already in simplest form and cannot be converted to a mixed number. **Final answer:** Mary still has to jog $\frac{3}{8}$ miles.