1. The problem is to understand why $\frac{8}{5} \div 3$ equals $\frac{8}{15}$.\n\n2. When dividing fractions or numbers, remember the rule: dividing by a number is the same as multiplying by its reciprocal.\n\n3. So, $\frac{8}{5} \div 3$ can be rewritten as $\frac{8}{5} \times \frac{1}{3}$.\n\n4. Multiply the numerators: $8 \times 1 = 8$.\n\n5. Multiply the denominators: $5 \times 3 = 15$.\n\n6. So, $\frac{8}{5} \times \frac{1}{3} = \frac{8}{15}$.\n\n7. Therefore, $\frac{8}{5} \div 3 = \frac{8}{15}$ because dividing by 3 is the same as multiplying by $\frac{1}{3}$.