Question

which equation is shown by the number line?

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 $\frac{5}{6}$, and it moves left (subtraction) to $\frac{1}{6}$. The distance between $\frac{5}{6}$ and $\frac{1}{6}$ is calculated by subtracting the smaller from the larger, but here we see the movement from $\frac{5}{6}$ to $\frac{1}{6}$, so we check the difference. The number of units moved: from $\frac{5}{6}$ to $\frac{1}{6}$, the difference is $\frac{5}{6}-\frac{4}{6}=\frac{1}{6}$? Wait, no, let's count the intervals. From $\frac{5}{6}$ to $\frac{1}{6}$, how many steps? Each step is $\frac{1}{6}$. From $\frac{5}{6}$ to $\frac{4}{6}$ is 1 step, $\frac{4}{6}$ to $\frac{3}{6}$ 2, $\frac{3}{6}$ to $\frac{2}{6}$ 3, $\frac{2}{6}$ to $\frac{1}{6}$ 4? Wait, no, the arrow is from $\frac{5}{6}$ to $\frac{1}{6}$, but the options: let's check each option.

Option D: $\frac{5}{6}-\frac{4}{6}=\frac{1}{6}$. Wait, $\frac{5}{6}$ minus $\frac{4}{6}$ is $\frac{1}{6}$. Let's see the number line: start at $\frac{5}{6}$, move left by 4 units? No, wait the labels are $\frac{1}{6}, \frac{2}{6}, \frac{3}{6}, \frac{4}{6}, \frac{5}{6}$. The start is $\frac{5}{6}$, end at $\frac{1}{6}$. The difference between $\frac{5}{6}$ and $\frac{1}{6}$ is $\frac{4}{6}$, but that's not. Wait, maybe I misread. Wait the arrow is from $\frac{5}{6}$ to $\frac{1}{6}$, but the options: D is $\frac{5}{6}-\frac{4}{6}=\frac{1}{6}$. Wait, $\frac{5}{6}$ minus $\frac{4}{6}$ is $\frac{1}{6}$, which is the end point? Wait the end point is $\frac{1}{6}$, start at $\frac{5}{6}$. So the equation should be start - amount moved = end. So $\frac{5}{6} - x = \frac{1}{6}$, so $x = \frac{4}{6}$, so the equation is $\frac{5}{6}-\frac{4}{6}=\frac{1}{6}$, which is option D.

Step2: Verify each option

• Option A: $\frac{1}{6}+\frac{5}{6}=1$, but the number line starts at $\frac{5}{6}$, not adds, so A is wrong.
• Option B: $\frac{3}{6}+\frac{2}{6}=\frac{5}{6}$, starts at $\frac{3}{6}$? No, start at $\frac{5}{6}$, so B wrong.
• Option C: $\frac{4}{6}-\frac{1}{6}=\frac{3}{6}$, starts at $\frac{4}{6}$? No, start at $\frac{5}{6}$, so C wrong.
• Option D: $\frac{5}{6}-\frac{4}{6}=\frac{1}{6}$, starts at $\frac{5}{6}$, subtracts $\frac{4}{6}$ (4 units of $\frac{1}{6}$) to get to $\frac{1}{6}$, which matches the number line.

Answer:

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