Question

which equation is shown by the number line?
options:
a. $\frac{1}{6} + \frac{5}{6} = 1$
b. $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$
c. $\frac{4}{6} - \frac{1}{6} = \frac{3}{6}$
d. $\frac{5}{6} - \frac{4}{6} = \frac{1}{6}$

Explanation:

Step1: Analyze the number line

The start point is at $\frac{5}{6}$ (wait, looking at the number line labels, the start is at the position labeled $\frac{5}{6}$? Wait, no, the labels are 0, $\frac{1}{6}$, $\frac{2}{6}$, $\frac{3}{6}$, $\frac{4}{6}$, $\frac{5}{6}$... Wait, the arrow is going from the position (let's check the marks) – the start is at the mark that should be $\frac{5}{6}$? Wait, no, the labels: 0, then $\frac{1}{6}$, $\frac{2}{6}$, $\frac{3}{6}$, $\frac{4}{6}$, $\frac{5}{6}$ (the "Start" is at $\frac{5}{6}$? Wait, no, the arrow is going left from the "Start" (which is at the $\frac{5}{6}$ mark? Wait, no, the labels: 0, $\frac{1}{6}$, $\frac{2}{6}$, $\frac{3}{6}$, $\frac{4}{6}$, $\frac{5}{6}$ – the start is at the $\frac{5}{6}$ mark, and the end is at $\frac{1}{6}$? Wait, no, the arrow is from the right (start) to the left (end) at $\frac{1}{6}$? Wait, no, the marks: 0, then a mark at $\frac{1}{6}$, $\frac{2}{6}$, $\frac{3}{6}$, $\frac{4}{6}$, $\frac{5}{6}$. The start is at $\frac{5}{6}$, and the arrow goes left to $\frac{1}{6}$? Wait, no, the distance between $\frac{5}{6}$ and $\frac{1}{6}$: the difference is $\frac{5}{6} - \frac{4}{6} = \frac{1}{6}$? Wait, no, let's check the options. Option D: $\frac{5}{6} - \frac{4}{6} = \frac{1}{6}$? Wait, no, $\frac{5}{6} - \frac{4}{6} = \frac{1}{6}$? Wait, the start is at $\frac{5}{6}$, and the end is at $\frac{1}{6}$? Wait, no, the number line has marks at 0, $\frac{1}{6}$, $\frac{2}{6}$, $\frac{3}{6}$, $\frac{4}{6}$, $\frac{5}{6}$. The arrow starts at $\frac{5}{6}$ (labeled "Start") and moves left to $\frac{1}{6}$? Wait, no, the difference between $\frac{5}{6}$ and $\frac{1}{6}$ is $\frac{4}{6}$? Wait, no, maybe I misread. Wait, the labels: 0, then $\frac{1}{6}$, $\frac{2}{6}$, $\frac{3}{6}$, $\frac{4}{6}$, $\frac{5}{6}$. The start is at $\frac{5}{6}$, and the arrow goes left to $\frac{1}{6}$? Wait, no, the number of intervals: from $\frac{5}{6}$ to $\frac{1}{6}$: how many steps? $\frac{5}{6} - \frac{4}{6} = \frac{1}{6}$? Wait, no, let's check the options. Option D: $\frac{5}{6} - \frac{4}{6} = \frac{1}{6}$? Wait, no, $\frac{5}{6} - \frac{4}{6} = \frac{1}{6}$? Wait, the start is at $\frac{5}{6}$, and the end is at $\frac{1}{6}$? Wait, no, the mark at $\frac{1}{6}$: so the start is at $\frac{5}{6}$, and the arrow goes left by $\frac{4}{6}$? No, that can't be. Wait, maybe the start is at $\frac{5}{6}$, and the end is at $\frac{1}{6}$, so the subtraction is $\frac{5}{6} - \frac{4}{6} = \frac{1}{6}$? Wait, no, $\frac{5}{6} - \frac{4}{6} = \frac{1}{6}$? Wait, the difference between $\frac{5}{6}$ and $\frac{1}{6}$ is $\frac{4}{6}$, but option D is $\frac{5}{6} - \frac{4}{6} = \frac{1}{6}$. Wait, maybe the start is at $\frac{5}{6}$, and we move left by $\frac{4}{6}$? No, that doesn't match. Wait, let's check each option:

Option A: $\frac{1}{6} + \frac{5}{6} = 1$ – addition, but the arrow is going left (subtraction), so A is out.

Option B: $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$ – addition, arrow is left (subtraction), so B is out.

Option C: $\frac{4}{6} - \frac{1}{6} = \frac{3}{6}$ – start at $\frac{4}{6}$, move left $\frac{1}{6}$ to $\frac{3}{6}$? No, the start is at $\frac{5}{6}$.

Option D: $\frac{5}{6} - \frac{4}{6} = \frac{1}{6}$ – start at $\frac{5}{6}$, move left $\frac{4}{6}$? Wait, no, $\frac{5}{6} - \frac{4}{6} = \frac{1}{6}$. The start is at $\frac{5}{6}$, end at $\frac{1}{6}$. The difference between $\frac{5}{6}$ and $\frac{1}{6}$ is $\frac{4}{6}$, but $\frac{5}{6} - \frac{4}{6} = \frac{1}{6}$. Wait, maybe the number line has the start at $\frac{5}{6}$, and the arrow goes left 4 units (each unit is $\frac{1}{6}$), so $5/6 - 4/6 = 1/6$. Yes, that matches option D.

Step2: Verify each option

- Option A: $\frac{1}{6} + \frac{5}{6} = 1$ – addition, arrow is left (subtraction), so wrong.
- Option B: $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$ – addition, arrow is left, wrong.
- Option C: $\frac{4}{6} - \frac{1}{6} = \frac{3}{6}$ – start at $\frac{4}{6}$, not $\frac{5}{6}$, wrong.
- Option D: $\frac{5}{6} - \frac{4}{6} = \frac{1}{6}$ – start at $\frac{5}{6}$, subtract $\frac{4}{6}$ (4 units of $\frac{1}{6}$) to get to $\frac{1}{6}$, which matches the number line.

Answer:

D. $\frac{5}{6} - \frac{4}{6} = \frac{1}{6}$