Point x is at 2/3 on the 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 line to model the problem?
The correct answer and explanation is:
Correct Answer:
The denominator line to model the problem is 12.
Explanation (300 words):
We are given that:
- Point x is located at 2/3 on the number line.
- Point y is the same distance from 0 as point x, meaning its absolute value is also 2/3, but it has a numerator of 8.
- We are to find the denominator that would make 8/n = 2/3, where
nis what we are solving for.
Step-by-step Reasoning:
- Understand the position of point x:
- Point x is at 2/3, which is a positive fraction 2 units away from 0, on a scale where the whole is divided into 3 parts.
- Equal Distance from 0:
- Point y is the same distance from 0 as point x, so y must also be 2/3, but the fraction is expressed with a numerator of 8.
- Write an equation using the information: 8d=23\frac{8}{d} = \frac{2}{3} Here, we are solving for the denominator d that would make this statement true.
- Solve for d: 8d=23\frac{8}{d} = \frac{2}{3} Cross-multiply: 8⋅3=2⋅d24=2d8 \cdot 3 = 2 \cdot d \\ 24 = 2d Divide both sides by 2: d=12d = 12
Conclusion:
To represent a fraction that is equivalent to 2/3 but has a numerator of 8, you need a denominator of 12, because: 812=23\frac{8}{12} = \frac{2}{3}
So, a denominator line of 12 divisions on the number line will correctly model both points x and y.