1. **State the problem:** Calculate $2 \frac{2}{3} - 2 \frac{2}{2}$. 2. **Convert mixed numbers to improper fractions:** $$2 \frac{2}{3} = \frac{3 \times 2 + 2}{3} = \frac{8}{3}$$ $$2 \frac{2}{2} = \frac{2 \times 2 + 2}{2} = \frac{6}{2}$$ 3. **Rewrite the subtraction:** $$\frac{8}{3} - \frac{6}{2}$$ 4. **Find common denominator:** The least common denominator of 3 and 2 is 6. $$\frac{8}{3} = \frac{8 \times 2}{3 \times 2} = \frac{16}{6}$$ $$\frac{6}{2} = \frac{6 \times 3}{2 \times 3} = \frac{18}{6}$$ 5. **Subtract the fractions:** $$\frac{16}{6} - \frac{18}{6} = \frac{16 - 18}{6} = \frac{-2}{6}$$ 6. **Simplify the fraction:** $$\frac{-2}{6} = \frac{\cancel{-2}}{\cancel{6}} = \frac{-1}{3}$$ 7. **Final answer:** $$2 \frac{2}{3} - 2 \frac{2}{2} = -\frac{1}{3}$$