1. **State the problem:** Find the number $x$ such that when added to $1\frac{1}{3}$, the result is 2. 2. **Write the equation:** $$x + 1\frac{1}{3} = 2$$ 3. **Convert the mixed number to an improper fraction:** $$1\frac{1}{3} = \frac{4}{3}$$ 4. **Rewrite the equation:** $$x + \frac{4}{3} = 2$$ 5. **Isolate $x$ by subtracting $\frac{4}{3}$ from both sides:** $$x = 2 - \frac{4}{3}$$ 6. **Convert 2 to a fraction with denominator 3:** $$2 = \frac{6}{3}$$ 7. **Subtract the fractions:** $$x = \frac{6}{3} - \frac{4}{3} = \frac{6 - 4}{3} = \frac{2}{3}$$ **Final answer:** $$x = \frac{2}{3}$$