1. **State the problem:** Find the sum of the mixed numbers $-3 \frac{1}{3}$ and $1 \frac{1}{3}$. 2. **Convert mixed numbers to improper fractions:** $-3 \frac{1}{3} = -\left(3 + \frac{1}{3}\right) = -\frac{10}{3}$ $1 \frac{1}{3} = 1 + \frac{1}{3} = \frac{4}{3}$ 3. **Add the fractions:** $$-\frac{10}{3} + \frac{4}{3} = \frac{-10 + 4}{3} = \frac{-6}{3}$$ 4. **Simplify the fraction:** $$\frac{-6}{3} = -2$$ 5. **Final answer:** $$-3 \frac{1}{3} + 1 \frac{1}{3} = -2$$