To determine which of the given values is closest to \(\frac{9}{11}\), we first need to approximate \(\frac{9}{11}\).

\[
\frac{9}{11} \approx 0.818
\]

Now, let's compare this with the given values:

- \(-1 = -1.000\)
- \(-\frac{1}{2} = -0.500\)
- \(0 = 0.000\)
- \(\frac{1}{2} = 0.500\)
- \(1 = 1.000\)

Comparing \(0.818\) to these values, we calculate the absolute differences:

- \(|0.818 - (-1)| = |0.818 + 1| = 1.818\)
- \(|0.818 - (-0.5)| = |0.818 + 0.5| = 1.318\)
- \(|0.818 - 0| = 0.818\)
- \(|0.818 - 0.5| = 0.318\)
- \(|0.818 - 1| = |0.818 - 1| = 0.182\)

The smallest difference is \(|0.818 - 1| = 0.182\).

Thus, \(\frac{9}{11}\) is closest to **1**.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. How would the closest value change if the options included \(\frac{3}{4}\)?
2. What method can you use to determine the decimal representation of fractions quickly?
3. How do you determine the closest integer to any given fraction?
4. How can approximations like this be useful in everyday life?
5. What is the decimal approximation of \(\frac{7}{8}\), and how does it compare to the values above?

**Tip:** When determining which number a fraction is closest to, comparing the fraction’s decimal form to each choice is an effective approach.

Explore how to determine which integer fraction 9/11 is closest to among the given options (-1, -1/2, 0, 1/2, 1). Understand the concept of decimal approximation, absolute difference, and how to compare fractions to decimals. Ideal for students in Grades 6-8.

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