1. **State the problem:** Calculate $9 \times \frac{1}{12} \times 9$. 2. **Formula and rules:** Multiplication of fractions and whole numbers can be done by converting whole numbers to fractions (e.g., $9 = \frac{9}{1}$) and then multiplying numerators and denominators. 3. **Convert and multiply:** $$9 \times \frac{1}{12} \times 9 = \frac{9}{1} \times \frac{1}{12} \times \frac{9}{1}$$ 4. **Multiply numerators and denominators:** $$= \frac{9 \times 1 \times 9}{1 \times 12 \times 1} = \frac{81}{12}$$ 5. **Simplify the fraction:** Divide numerator and denominator by their greatest common divisor, which is 3: $$\frac{81 \div 3}{12 \div 3} = \frac{27}{4}$$ 6. **Convert to mixed number (optional):** $$\frac{27}{4} = 6 \frac{3}{4}$$ **Final answer:** $\frac{27}{4}$ or $6 \frac{3}{4}$.