To find the difference between the largest and smallest of the given fractions, we must first compare them. The fractions are $\frac{1}{2}$, $\frac{8}{11}$, $\frac{7}{8}$, $\frac{7}{9}$, and $\frac{5}{6}$. For easier comparison, we can convert each fraction to a common denominator or their decimal equivalents.
Converting each fraction to its decimal form:
Comparing these decimal values allows us to identify the smallest and greatest fractions:
The next step is to calculate the difference between the greatest and smallest fractions.
Difference = $\frac{7}{8} - \frac{1}{2}$
To perform the subtraction, we find a common denominator, which is 8:
$\frac{1}{2}$ is equivalent to $\frac{4}{8}$
Thus, $\frac{7}{8} - \frac{4}{8} = \frac{3}{8}$
Consequently, the difference between the greatest and smallest fractions is $\frac{3}{8}$.