1. **State the problem:** We need to calculate $8 \div 1 \frac{2}{5}$ and express the answer as a mixed number in its lowest terms. 2. **Convert the mixed number to an improper fraction:** $$1 \frac{2}{5} = \frac{5 \times 1 + 2}{5} = \frac{7}{5}$$ 3. **Rewrite the division as multiplication by the reciprocal:** $$8 \div \frac{7}{5} = 8 \times \frac{5}{7}$$ 4. **Express 8 as a fraction:** $$8 = \frac{8}{1}$$ 5. **Multiply the fractions:** $$\frac{8}{1} \times \frac{5}{7} = \frac{8 \times 5}{1 \times 7} = \frac{40}{7}$$ 6. **Convert the improper fraction to a mixed number:** Divide 40 by 7: $$40 \div 7 = 5 \text{ remainder } 5$$ So, $$\frac{40}{7} = 5 \frac{5}{7}$$ 7. **Check if the fraction can be simplified:** The fraction $\frac{5}{7}$ is already in lowest terms. **Final answer:** $$8 \div 1 \frac{2}{5} = 5 \frac{5}{7}$$