11. Point $$ X $$ is at $$ \frac{2}{3} $$ on a number line. On the same number line, point $$ Y $$ is the same distance from 0 as point $$ X $$, but it has a numerator of 8 . What is the denominator of the fraction at point $$ Y $$ ? Draw a number

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Let's analyze the problem step by step.

1. **Position of Point X:**
   - Point $$ X $$ is located at $$ \frac{2}{3} $$ on the number line.
   
2. **Position of Point Y:**
   - Point $$ Y $$ is the same distance from 0 as point $$ X $$. This means $$ Y $$ is either at $$ \frac{2}{3} $$ or $$ -\frac{2}{3} $$.
   - However, it's given that the fraction representing $$ Y $$ has a numerator of 8. Therefore, $$ Y $$ must be at $$ \frac{8}{d} $$, where $$ d $$ is the denominator we need to find.

3. **Setting Up the Equation:**
   - Since $$ Y $$ is the same distance from 0 as $$ X $$, we have:
     $$
     \left| \frac{8}{d} \right| = \left| \frac{2}{3} \right|
     $$
   - Simplifying the absolute values:
     $$
     \frac{8}{|d|} = \frac{2}{3}
     $$
   
4. **Solving for $$ d $$:**
   - Cross-multiplying gives:
     $$
     8 \times 3 = 2 \times |d|
     $$
     $$
     24 = 2|d|
     $$
     $$
     |d| = 12
     $$
   - Since the denominator is a positive number, $$ d = 12 $$.

**Answer:** The denominator of the fraction at point $$ Y $$ is **12**.

**Visualization:**

Here’s a simple number line showing the positions of points $$ X $$ and $$ Y $$:

```
---|-----|-----|-----|-----|-----|---
  -1   -2/3    0    2/3    1     4/3
               Y           X
        (-8/12)          (2/3)
```

- Point $$ X $$ is at $$ \frac{2}{3} $$.
- Point $$ Y $$ is at $$ -\frac{8}{12} $$, which simplifies to $$ -\frac{2}{3} $$, maintaining the same distance from 0 as $$ X $$.
The denominator of the fraction at point $$ Y $$ is **12**.

Point is at on a number line. On the
same number line, point is the same
distance from 0 as point , but it has a
numerator of 8 . What is the denominator
of the fraction at point ? Draw a number

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Point is at on a number line. On the same number line, point is the same distance from 0 as point , but it has a numerator of 8 . What is the denominator of the fraction at point ? Draw a number