This problem asks us to find the total distance walked by adding two fractions: $\frac{1}{3}$ and $\frac{5}{8}$. The result should be expressed as a fraction in simplest form.

Step 1: Find a common denominator

The denominators are 3 and 8. The least common denominator (LCD) of 3 and 8 is 24.

Step 2: Rewrite fractions with the common denominator

$\frac{1}{3} = \frac{8}{24}, \quad \frac{5}{8} = \frac{15}{24}$

Step 3: Add the fractions

$\frac{8}{24} + \frac{15}{24} = \frac{23}{24}$

Step 4: Simplify the fraction (if needed)

The fraction $\frac{23}{24}$ is already in its simplest form since 23 is a prime number and does not share any factors with 24 other than 1.

Final Answer:

You walked $\frac{23}{24}$ miles in all.

Would you like me to break this down further or help with a related question?

5 Related Questions:

1. What is the process to find the least common denominator (LCD) of two fractions?
2. How do you convert improper fractions to mixed numbers?
3. Can you explain how to simplify a fraction step by step?
4. How can you add three fractions instead of two? (e.g., $\frac{1}{3} + \frac{5}{8} + \frac{2}{5}$)
5. What are some strategies to determine whether a fraction is already in simplest form?

Tip:

When adding fractions, always simplify the final result to avoid errors in further calculations!