https://file.aiquickdraw.com/mathbot/file/1725909060419lj3o8fb9.jpg

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.

Which set below shows these numbers listed from smallest to greatest value? -5/6, -2/7, -1/11

Learn how to order negative fractions from smallest to greatest using decimal conversion. This problem covers comparing fractions and understanding the behavior of negative numbers, suitable for students in Grades 6-8.

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