Let's analyze the problem:

You are asked to list the numbers $-\frac{5}{6}$, $-\frac{2}{7}$, and $-\frac{1}{11}$ from smallest to greatest value.

Step 1: Convert to decimals

Let's approximate each fraction:

• $-\frac{5}{6} \approx -0.8333$
• $-\frac{2}{7} \approx -0.2857$
• $-\frac{1}{11} \approx -0.0909$

Step 2: Order from smallest to greatest

From the approximations:

• The smallest value is $-0.8333$ (which is $-\frac{5}{6}$).
• The next is $-0.2857$ (which is $-\frac{2}{7}$).
• The largest value is $-0.0909$ (which is $-\frac{1}{11}$).

Conclusion:

The correct order from smallest to greatest is: $-\frac{5}{6}, -\frac{2}{7}, -\frac{1}{11}$

Thus, the correct answer is the first option: $\left\{ -\frac{5}{6}, -\frac{2}{7}, -\frac{1}{11} \right\}$

Would you like further details on the calculations or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you convert fractions to decimals manually?
2. Why is a number closer to zero larger for negative values?
3. What are other methods to compare fractions without converting to decimals?
4. Can improper fractions affect the way we order them?
5. How do negative decimals behave on the number line compared to positive ones?

Tip: To compare fractions without converting them to decimals, you can find a common denominator for an exact comparison.