1. **Problem statement:** Evaluate the following expressions without using a calculator. 2. **Part (a):** Evaluate $-2 - \frac{3}{5}$ and $-2 + \frac{3}{5}$. - For $-2 - \frac{3}{5}$, convert $-2$ to a fraction with denominator 5: $-2 = \frac{-10}{5}$. - Then subtract: $$\frac{-10}{5} - \frac{3}{5} = \frac{-10 - 3}{5} = \frac{-13}{5}.$$ - For $-2 + \frac{3}{5}$, similarly convert $-2$ to $\frac{-10}{5}$. - Then add: $$\frac{-10}{5} + \frac{3}{5} = \frac{-10 + 3}{5} = \frac{-7}{5}.$$ 3. **Part (b):** Evaluate $-6 \frac{1}{3} \times -1 \frac{1}{5}$. - Convert mixed numbers to improper fractions: $$-6 \frac{1}{3} = -\left(6 + \frac{1}{3}\right) = -\frac{19}{3}$$ $$-1 \frac{1}{5} = -\left(1 + \frac{1}{5}\right) = -\frac{6}{5}$$ - Multiply: $$-\frac{19}{3} \times -\frac{6}{5} = \frac{19 \times 6}{3 \times 5} = \frac{114}{15}.$$ - Simplify by dividing numerator and denominator by 3: $$\frac{\cancel{114}^{38}}{\cancel{15}^5} = \frac{38}{5} = 7 \frac{3}{5}.$$ 4. **Part (c):** Evaluate $\frac{1}{3} \div \left(-\frac{2}{3}\right)$. - Division of fractions is multiplication by reciprocal: $$\frac{1}{3} \times \left(-\frac{3}{2}\right) = -\frac{1 \times 3}{3 \times 2} = -\frac{3}{6}.$$ - Simplify by dividing numerator and denominator by 3: $$-\frac{\cancel{3}^1}{\cancel{6}^2} = -\frac{1}{2}.$$ **Final answers:** (a) $-\frac{13}{5}$ and $-\frac{7}{5}$ (b) $\frac{38}{5}$ or $7 \frac{3}{5}$ (c) $-\frac{1}{2}$