1. **State the problem:** We need to divide the mixed number $5 \frac{8}{1}$ by the mixed number $4 \frac{3}{8}$. 2. **Convert mixed numbers to improper fractions:** $5 \frac{8}{1} = 5 + \frac{8}{1} = \frac{5 \times 1}{1} + \frac{8}{1} = \frac{5}{1} + \frac{8}{1} = \frac{13}{1}$ $4 \frac{3}{8} = \frac{4 \times 8 + 3}{8} = \frac{32 + 3}{8} = \frac{35}{8}$ 3. **Division of fractions rule:** Dividing by a fraction is the same as multiplying by its reciprocal. $$ \frac{13}{1} \div \frac{35}{8} = \frac{13}{1} \times \frac{8}{35} $$ 4. **Multiply the numerators and denominators:** $$ \frac{13 \times 8}{1 \times 35} = \frac{104}{35} $$ 5. **Simplify the fraction if possible:** Both 104 and 35 have no common factors other than 1, so the fraction is already in simplest form. 6. **Convert improper fraction to mixed number:** Divide 104 by 35: $$ 104 \div 35 = 2 \text{ remainder } 34 $$ So, $$ \frac{104}{35} = 2 \frac{34}{35} $$ **Final answer:** $$ 5 \frac{8}{1} \div 4 \frac{3}{8} = 2 \frac{34}{35} $$