The difference of the greatest and smallest of the fractions 1/2, 8/11, 7/8, 7/9, 5/6

The correct option is 3/8.

Let us find the difference between the greatest and the smallest of the given fractions:
$\frac{1}{2}$, $\frac{8}{11}$, $\frac{7}{8}$, $\frac{7}{9}$, and $\frac{5}{6}$.

Step 1: Convert fractions to decimals to easily compare their values

We divide the numerator by the denominator for each fraction:
1. For $\frac{1}{2}$:
$1/2=0.5$
2. For $\frac{8}{11}$:
$8/11\approx 0.727$
3. For $\frac{7}{8}$:
$7/8=0.875$
4. For $\frac{7}{9}$:
$7/9\approx 0.778$
5. For $\frac{5}{6}$:
$5/6\approx 0.833$

Step 2: Identify the greatest and smallest fractions

Comparing the decimal values:
$0.5<0.727<0.778<0.833<0.875$

Therefore:
- The smallest fraction is $\frac{1}{2}$.
- The greatest fraction is $\frac{7}{8}$.

Step 3: Calculate the difference between the greatest and smallest fractions

We subtract the smallest fraction from the greatest fraction:
$\text{Difference}=\frac{7}{8}-\frac{1}{2}$

To perform the subtraction, find a common denominator, which is 8:
$\frac{1}{2}=\frac{1\times 4}{2\times 4}=\frac{4}{8}$

Now, subtract the numerators:
$\text{Difference}=\frac{7}{8}-\frac{4}{8}=\frac{7-4}{8}=\frac{3}{8}$

Thus, the difference of the greatest and smallest of the fractions is 3/8.