1. **State the problem:** Add the mixed numbers $5 \frac{11}{21}$ and $3 \frac{4}{7}$. 2. **Convert mixed numbers to improper fractions:** $5 \frac{11}{21} = \frac{5 \times 21 + 11}{21} = \frac{105 + 11}{21} = \frac{116}{21}$ $3 \frac{4}{7} = \frac{3 \times 7 + 4}{7} = \frac{21 + 4}{7} = \frac{25}{7}$ 3. **Find a common denominator:** The denominators are 21 and 7. The least common denominator (LCD) is 21. 4. **Convert $\frac{25}{7}$ to denominator 21:** $\frac{25}{7} = \frac{25 \times 3}{7 \times 3} = \frac{75}{21}$ 5. **Add the fractions:** $\frac{116}{21} + \frac{75}{21} = \frac{116 + 75}{21} = \frac{191}{21}$ 6. **Convert back to a mixed number:** Divide 191 by 21: $191 \div 21 = 9$ remainder $2$, so $\frac{191}{21} = 9 \frac{2}{21}$ **Final answer:** $$9 \frac{2}{21}$$