1. **State the problem:** Solve the expression $$\left(\frac{2}{7} + \frac{1}{3}\right) + \frac{2}{3}$$ using properties and mental math. 2. **Recall the formula and rules:** To add fractions, find a common denominator, then add the numerators. 3. **Find common denominator for the first parentheses:** $$\text{LCM of }7 \text{ and } 3 = 21$$ 4. **Convert fractions:** $$\frac{2}{7} = \frac{2 \times 3}{7 \times 3} = \frac{6}{21}$$ $$\frac{1}{3} = \frac{1 \times 7}{3 \times 7} = \frac{7}{21}$$ 5. **Add inside parentheses:** $$\frac{6}{21} + \frac{7}{21} = \frac{6+7}{21} = \frac{13}{21}$$ 6. **Add the remaining fraction:** $$\frac{13}{21} + \frac{2}{3}$$ 7. **Find common denominator for $$\frac{13}{21}$$ and $$\frac{2}{3}$$:** $$\text{LCM of }21 \text{ and } 3 = 21$$ 8. **Convert $$\frac{2}{3}$$:** $$\frac{2}{3} = \frac{2 \times 7}{3 \times 7} = \frac{14}{21}$$ 9. **Add the fractions:** $$\frac{13}{21} + \frac{14}{21} = \frac{13+14}{21} = \frac{27}{21}$$ 10. **Simplify the fraction:** $$\frac{27}{21} = \frac{\cancel{3} \times 9}{\cancel{3} \times 7} = \frac{9}{7}$$ 11. **Final answer:** $$\boxed{\frac{9}{7}}$$ This is an improper fraction and can also be written as $$1 \frac{2}{7}$$.