1. The problem is to multiply the mixed number $9 \frac{1}{12}$ by 9. 2. First, convert the mixed number to an improper fraction. The mixed number $9 \frac{1}{12}$ means $9 + \frac{1}{12}$. 3. Convert 9 to a fraction with denominator 12: $9 = \frac{9 \times 12}{12} = \frac{108}{12}$. 4. Add the fractions: $\frac{108}{12} + \frac{1}{12} = \frac{108 + 1}{12} = \frac{109}{12}$. 5. Now multiply this improper fraction by 9: $\frac{109}{12} \times 9 = \frac{109 \times 9}{12} = \frac{981}{12}$. 6. Simplify the fraction $\frac{981}{12}$. Divide numerator and denominator by 3: $\frac{981 \div 3}{12 \div 3} = \frac{327}{4}$. 7. Convert $\frac{327}{4}$ back to a mixed number by dividing 327 by 4: $327 \div 4 = 81$ remainder $3$. 8. So, $\frac{327}{4} = 81 \frac{3}{4}$. Final answer: $81 \frac{3}{4}$.