9•7 5/6

To calculate \( 9 \cdot 7 \frac{5}{6} \), first convert the mixed number \( 7 \frac{5}{6} \) into an improper fraction.

1. Convert \( 7 \frac{5}{6} \): \[ 7 \frac{5}{6} = 7 + \frac{5}{6} = \frac{7 \cdot 6}{6} + \frac{5}{6} = \frac{42}{6} + \frac{5}{6} = \frac{42 + 5}{6} = \frac{47}{6} \]

2. Now, multiply \( 9 \) by the improper fraction: \[ 9 \cdot \frac{47}{6} = \frac{9 \cdot 47}{6} = \frac{423}{6} \]

3. To convert \( \frac{423}{6} \) to a mixed number, divide \( 423 \) by \( 6 \): \[ 423 \div 6 = 70 \quad \text{remainder } 3 \] Thus, \[ 423 = 6 \cdot 70 + 3, \] which means \( \frac{423}{6} = 70 \frac{3}{6} \).

4. Simplify \( \frac{3}{6} \): \[ \frac{3}{6} = \frac{1}{2}. \] Therefore, \[ 70 \frac{3}{6} = 70 \frac{1}{2}. \]

So, the final answer is: \[ 9 \cdot 7 \frac{5}{6} = 70 \frac{1}{2}. \]