1. **State the problem:** Rewrite the fractions $\frac{2}{7}$ and $\frac{9}{11}$ with a common denominator. 2. **Find the least common denominator (LCD):** The denominators are 7 and 11. 3. The LCD is the least common multiple (LCM) of 7 and 11. Since 7 and 11 are prime, $$\text{LCM}(7,11) = 7 \times 11 = 77.$$ 4. **Rewrite each fraction with denominator 77:** For $\frac{2}{7}$, multiply numerator and denominator by 11: $$\frac{2}{7} = \frac{2 \times 11}{7 \times 11} = \frac{22}{77}.$$ For $\frac{9}{11}$, multiply numerator and denominator by 7: $$\frac{9}{11} = \frac{9 \times 7}{11 \times 7} = \frac{63}{77}.$$ 5. **Final answer:** $$\frac{2}{7} = \frac{22}{77}, \quad \frac{9}{11} = \frac{63}{77}.$$