Final answer:
To find the denominator of the fraction at point Y (which has the same distance from 0 as point X at ⅓ and a numerator of 8), we scale up the original fraction of ⅓ by a factor of 4, resulting in the fraction ⅘ and hence a denominator of 12.
Step-by-step explanation:
The question asks us to find the denominator of a fraction located at point Y on a number line, given that point, Y is the same distance from 0 as point X, which is at ⅓ (two-thirds), and that the numerator of the fraction at point Y is 8. To determine the denominator, we need to understand that the distance from 0 is represented by the absolute value of the fraction's value, which can be identified by the ratio of the numerator to the denominator.
Since point X is at ⅓, we can assume it has a numerator of 2 and a denominator of 3. This fraction represents a certain distance from 0 on the number line. To find a fraction with the numerator 8 that is the same distance from 0, we need to scale up the fraction of ⅓ proportionally. The scaling factor is the number that when multiplied by 2 (the numerator at point X) gives us 8 (the desired numerator at point Y). This scaling factor is ⅓ because 2 multiplied by 4 gives us 8.
Knowing this, we must also multiply the denominator of ⅓ by the same scaling factor of 4 to maintain the same ratio (and hence the same distance from 0). Therefore, the denominator of point Y's fraction is 3 multiplied by 4, which equals 12. The denominator of the fraction at point Y on the number line is 12, resulting in the fraction ⅘.