将下列分数按从大到小的顺序排列。 $\frac{9}{11} \text{ , } \frac{6}{7} \text{ , } \frac{5}{12}$ $\text{greatest} \qquad\qquad\qquad\qquad \text{smallest}$

1. Identify the smallest fraction using the benchmark of $\frac{1}{2}$

$\frac{5}{12} < \frac{6}{12} = \frac{1}{2}$
$\frac{9}{11} > \frac{1}{2}$ and $\frac{6}{7} > \frac{1}{2}$
Therefore, $\frac{5}{12}$ is the smallest fraction.

2. Compare the remaining two fractions by looking at their difference from 1

$1 - \frac{9}{11} = \frac{2}{11}$
$1 - \frac{6}{7} = \frac{1}{7} = \frac{2}{14}$
Since $\frac{2}{14} < \frac{2}{11}$, $\frac{6}{7}$ is closer to $1$ than $\frac{9}{11}$.
Thus, $\frac{6}{7} > \frac{9}{11}$.

3. Arrange the fractions from greatest to smallest

The order from greatest to smallest is $\frac{6}{7}$, $\frac{9}{11}$, $\frac{5}{12}$.