1. **State the problem:** Calculate $\frac{16}{31} \div 8$. 2. **Recall the division of fractions rule:** Dividing by a number is the same as multiplying by its reciprocal. 3. **Rewrite the division as multiplication:** $$\frac{16}{31} \div 8 = \frac{16}{31} \times \frac{1}{8}$$ 4. **Multiply the numerators and denominators:** $$\frac{16 \times 1}{31 \times 8} = \frac{16}{248}$$ 5. **Simplify the fraction:** Both numerator and denominator are divisible by 8. $$\frac{\cancel{16}^{2 \times 8}}{\cancel{248}^{31 \times 8}} = \frac{2}{31}$$ 6. **Final answer:** $$\frac{16}{31} \div 8 = \frac{2}{31}$$