1. **State the problem:** Add the numbers $9$ and $1 \frac{2}{7}$. 2. **Convert the mixed number to an improper fraction:** $$1 \frac{2}{7} = \frac{7 \times 1 + 2}{7} = \frac{9}{7}$$ 3. **Rewrite the problem:** $$9 + \frac{9}{7}$$ 4. **Convert the whole number 9 to a fraction with denominator 7:** $$9 = \frac{9 \times 7}{7} = \frac{63}{7}$$ 5. **Add the fractions:** $$\frac{63}{7} + \frac{9}{7} = \frac{63 + 9}{7} = \frac{72}{7}$$ 6. **Convert the improper fraction back to a mixed number:** Divide 72 by 7: $$72 \div 7 = 10 \text{ remainder } 2$$ So, $$\frac{72}{7} = 10 \frac{2}{7}$$ **Final answer:** $$9 + 1 \frac{2}{7} = 10 \frac{2}{7}$$