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 has a numerator of 8 . What is the denominator of the fraction at point \( Y \) ? Draw a number line to model the problem.

To find the denominator of point \( Y \), we start by determining the distance of point \( X \) from 0. Point \( X \) is at \( \frac{2}{3} \), meaning it is \( \frac{2}{3} \) units away from 0. Since point \( Y \) is the same distance from 0 as point \( X \), point \( Y \) must also be \( \frac{2}{3} \) units away from 0. Point \( Y \) has a numerator of 8, so we can express point \( Y \) as \( \frac{8}{d} \) where \( d \) is the unknown denominator. Since the distance from 0 must remain the same: \[ \frac{8}{d} = \frac{2}{3} \] To find \( d \), we cross-multiply: \[ 8 \times 3 = 2 \times d \\ 24 = 2d \\ d = \frac{24}{2} = 12 \] Therefore, the denominator for point \( Y \) is 12. So the answer is: The denominator of the fraction at point \( Y \) is 12. If you were to draw a number line, you would have a point at 0, a point at \( \frac{2}{3} \), and another point at \( \frac{8}{12} \) (which is equivalent to \( \frac{2}{3} \)), showing that both points are indeed the same distance from 0.