1. The problem is to find the value of $4 \frac{7}{8} \div \frac{1}{8}$. 2. First, convert the mixed number $4 \frac{7}{8}$ to an improper fraction. The formula is $a \frac{b}{c} = \frac{ac + b}{c}$. 3. Calculate the numerator: $4 \times 8 + 7 = 32 + 7 = 39$. 4. So, $4 \frac{7}{8} = \frac{39}{8}$. 5. Now, divide $\frac{39}{8}$ by $\frac{1}{8}$. Division of fractions is done by multiplying the first fraction by the reciprocal of the second. 6. Write the division as multiplication: $\frac{39}{8} \times \frac{8}{1}$. 7. Multiply the numerators and denominators: $\frac{39 \times 8}{8 \times 1} = \frac{312}{8}$. 8. Simplify the fraction by canceling the common factor 8: $$\frac{\cancel{312}}{\cancel{8}} = 39$$ 9. Therefore, the answer is $39$.