1. **State the problem:** Evaluate the expression $$-\frac{2}{5} - \left(-\frac{1}{10} + \frac{1}{-2}\right)$$ without a calculator. 2. **Recall the rules:** - When subtracting a sum, distribute the minus sign. - Remember that dividing by a negative number changes the sign. - Combine like terms carefully. 3. **Simplify inside the parentheses first:** $$-\frac{1}{10} + \frac{1}{-2} = -\frac{1}{10} - \frac{1}{2}$$ 4. **Find a common denominator for the terms inside the parentheses:** The common denominator of 10 and 2 is 10. $$-\frac{1}{10} - \frac{1}{2} = -\frac{1}{10} - \frac{5}{10} = -\frac{1+5}{10} = -\frac{6}{10}$$ 5. **Simplify the fraction inside the parentheses:** $$-\frac{6}{10} = -\frac{3}{5}$$ 6. **Rewrite the original expression:** $$-\frac{2}{5} - \left(-\frac{3}{5}\right)$$ 7. **Subtracting a negative is adding:** $$-\frac{2}{5} + \frac{3}{5}$$ 8. **Combine the fractions:** $$\cancel{-\frac{2}{5}} + \frac{3}{5} = \frac{-2+3}{5} = \frac{1}{5}$$ **Final answer:** $$\frac{1}{5}$$