Let's solve this step by step:

Problem Analysis:

1. Point $X$ is at $\frac{2}{3}$ on the number line.
2. Point $Y$ is at the same distance from 0 as Point $X$, but its fraction has a numerator of 8.
3. We need to find the denominator of the fraction for Point $Y$.

Solution:

Step 1: Determine the distance of $X$ from 0

The distance of $X$ from 0 is given by the fraction $\frac{2}{3}$.

Step 2: Represent $Y$'s distance with its fraction

Point $Y$ is the same distance from 0 as Point $X$. Let the fraction at $Y$ be $\frac{8}{d}$, where $d$ is the denominator we need to find. Since the distances of $X$ and $Y$ from 0 are equal: $\frac{2}{3} = \frac{8}{d}$

Step 3: Solve for $d$

To solve $\frac{2}{3} = \frac{8}{d}$, use cross-multiplication: $2 \cdot d = 3 \cdot 8$ $2d = 24$ $d = 12$

Final Answer:

The denominator of the fraction at $Y$ is 12.

Number Line:

A simple number line can be drawn with points labeled for $0$, $\frac{2}{3}$, and $\frac{8}{12}$ (which is equivalent to $\frac{2}{3}$).

Do you need help with drawing the number line, or do you have any questions?

5 Related Questions:

1. How can we convert between fractions with different numerators while keeping the value the same?
2. What does it mean for two points on a number line to have the same distance from 0?
3. How do you simplify a fraction like $\frac{8}{12}$ back to $\frac{2}{3}$?
4. What is the general method to solve $\frac{a}{b} = \frac{c}{d}$?
5. How can you use number lines to compare fractions with different denominators?

Tip:

When working with fractions, cross-multiplication is a quick and effective method to solve equations involving two fractions.