1. **Problem:** Calculate $-1 \frac{1}{3} - 2 \frac{4}{5}$. 2. **Convert mixed numbers to improper fractions:** $-1 \frac{1}{3} = -\frac{4}{3}$ because $1 \times 3 + 1 = 4$. $2 \frac{4}{5} = \frac{14}{5}$ because $2 \times 5 + 4 = 14$. 3. **Rewrite the expression:** $$-\frac{4}{3} - \frac{14}{5}$$ 4. **Find the least common denominator (LCD):** LCD of 3 and 5 is 15. 5. **Convert fractions to equivalent fractions with denominator 15:** $$-\frac{4}{3} = -\frac{4 \times 5}{3 \times 5} = -\frac{20}{15}$$ $$\frac{14}{5} = \frac{14 \times 3}{5 \times 3} = \frac{42}{15}$$ 6. **Rewrite the subtraction:** $$-\frac{20}{15} - \frac{42}{15}$$ 7. **Combine the numerators:** $$\frac{-20 - 42}{15} = \frac{-62}{15}$$ 8. **Simplify if possible:** $62$ and $15$ have no common factors other than 1, so fraction is simplified. 9. **Convert back to mixed number:** $\frac{62}{15} = 4 \frac{2}{15}$, so answer is $-4 \frac{2}{15}$. **Final answer:** $$-1 \frac{1}{3} - 2 \frac{4}{5} = -4 \frac{2}{15}$$