6. Add appropriate parentheses to $1 \div 2 \div 3 \div 4 \div 5$ to form a complete expression. Then, the number of different values that can be obtained is $(\quad)$.
(A) 6
(B) 8
(C) 9
(D) 10

The denominator must be below the fraction line. By appropriately placing parentheses, the numbers $3, 4, 5$ can be placed either above or below the fraction line, resulting in $2^{3}=8$ different values.
For example, the following operations can yield:
$$
\begin{array}{l}
\{[(1 \div 2) \div 3] \div 4\} \div 5=\frac{1}{2 \times 3 \times 4 \times 5}=\frac{1}{120} . \\
1 \div\{[(2 \div 3) \div 4] \div 5\}=\frac{3 \times 4 \times 5}{2}=30 .
\end{array}
$$

From equation (1),
$$
\begin{array}{l}
{[(1 \div 2) \div 3] \div(4 \div 5)=\frac{5}{2 \times 3 \times 4}=\frac{5}{24} ;} \\
{[(1 \div 2) \div(3 \div 4)] \div 5=\frac{4}{2 \times 3 \times 5}=\frac{2}{15} ;} \\
\{[1 \div(2 \div 3)] \div 4\} \div 5=\frac{3}{2 \times 4 \times 5}=\frac{3}{40} .
\end{array}
$$

From equation (2),
$$
\begin{array}{l}
1 \div[(2 \div 3) \div(4 \div 5)]=\frac{3 \times 4}{2 \times 5}=\frac{6}{5} ; \\
1 \div\{[2 \div(3 \div 4)] \div 5\}=\frac{3 \times 5}{2 \times 4}=\frac{15}{8} ; \\
(1 \div 2) \div[(3 \div 4) \div 5]=\frac{4 \times 5}{2 \times 3}=\frac{10}{3} .
\end{array}
$$

This gives all 8 possible values, and they are all distinct.
6. B.

No matter how parentheses are added, 1 must be in the numerator, 2 must