1. **State the problem:** Solve the rational number operation $-1 \frac{1}{3} - 2 \frac{4}{5}$. 2. **Convert mixed numbers to improper fractions:** $-1 \frac{1}{3} = -\left(1 + \frac{1}{3}\right) = -\frac{4}{3}$ $2 \frac{4}{5} = 2 + \frac{4}{5} = \frac{10}{5} + \frac{4}{5} = \frac{14}{5}$ 3. **Find the lowest common denominator (LCD):** Denominators are 3 and 5. LCD is 15. 4. **Convert fractions to equivalent fractions with denominator 15:** $-\frac{4}{3} = -\frac{4 \times 5}{3 \times 5} = -\frac{20}{15}$ $\frac{14}{5} = \frac{14 \times 3}{5 \times 3} = \frac{42}{15}$ 5. **Perform the subtraction:** $$-\frac{20}{15} - \frac{42}{15} = \frac{-20 - 42}{15} = \frac{-62}{15}$$ 6. **Simplify the fraction if possible:** $62$ and $15$ have no common factors other than 1, so fraction is in simplest form. 7. **Convert back to mixed number:** $\frac{62}{15} = 4 \text{ remainder } 2$, so $$-\frac{62}{15} = -4 \frac{2}{15}$$ **Final answer:** $-4 \frac{2}{15}$