1. **State the problem:** Simplify the expression $2 \frac{2}{3} - \frac{2}{2}$. 2. **Convert mixed number to improper fraction:** $$2 \frac{2}{3} = \frac{3 \times 2 + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3}$$ 3. **Simplify the second fraction:** $$\frac{2}{2} = 1$$ 4. **Rewrite the expression:** $$\frac{8}{3} - 1$$ 5. **Convert 1 to a fraction with denominator 3:** $$1 = \frac{3}{3}$$ 6. **Subtract the fractions:** $$\frac{8}{3} - \frac{3}{3} = \frac{8 - 3}{3} = \frac{5}{3}$$ 7. **Convert the improper fraction back to a mixed number:** $$\frac{5}{3} = 1 \frac{2}{3}$$ **Final answer:** $1 \frac{2}{3}$