1. **State the problem:** Evaluate the expression $$\frac{1}{2} - \frac{1}{5} \div \frac{2}{3}$$ and write the answer as a fraction. 2. **Recall the division rule for fractions:** Dividing by a fraction is the same as multiplying by its reciprocal. 3. **Rewrite the division:** $$\frac{1}{5} \div \frac{2}{3} = \frac{1}{5} \times \frac{3}{2}$$ 4. **Multiply the fractions:** $$\frac{1}{5} \times \frac{3}{2} = \frac{1 \times 3}{5 \times 2} = \frac{3}{10}$$ 5. **Substitute back into the expression:** $$\frac{1}{2} - \frac{3}{10}$$ 6. **Find a common denominator:** The least common denominator of 2 and 10 is 10. 7. **Convert fractions:** $$\frac{1}{2} = \frac{5}{10}$$ 8. **Subtract the fractions:** $$\frac{5}{10} - \frac{3}{10} = \frac{5 - 3}{10} = \frac{2}{10}$$ 9. **Simplify the fraction:** $$\frac{2}{10} = \frac{\cancel{2}^1}{\cancel{10}^5} = \frac{1}{5}$$ **Final answer:** $$\frac{1}{5}$$