Question

find the distance between points q and n.

Explanation:

Step1: Identify coordinates of Q and N

From the number line, Q is at $\frac{2}{5}$? Wait, no, let's check the marks. The marks are at $-\frac{3}{5}, -\frac{1}{5}, \frac{1}{5}, \frac{3}{5}, 1$. Wait, Q is between $\frac{1}{5}$ and $\frac{3}{5}$? Wait, no, the points: let's see, the distance between each tick? Wait, the labels: -1, $-\frac{3}{5}$, $-\frac{1}{5}$, $\frac{1}{5}$, Q, $\frac{3}{5}$, N, 1? Wait, no, the number line has ticks: let's count the intervals. From -1 to 1, how many ticks? Let's see, the labels are -1, $-\frac{3}{5}$, $-\frac{1}{5}$, $\frac{1}{5}$, then Q, then $\frac{3}{5}$, then N, then 1. Wait, maybe each tick is $\frac{1}{5}$? Wait, from -1 to 1, the total length is 2, and the number of intervals? Wait, maybe Q is at $\frac{2}{5}$? No, wait, let's look again. Wait, the points: Q is at $\frac{2}{5}$? Wait, no, the labels: $\frac{1}{5}$, then Q, then $\frac{3}{5}$. So the distance between $\frac{1}{5}$ and $\frac{3}{5}$ is $\frac{2}{5}$, so Q is at $\frac{2}{5}$? Wait, no, maybe the ticks are each $\frac{1}{5}$. So from $\frac{1}{5}$ to $\frac{3}{5}$ is two ticks, so each tick is $\frac{1}{5}$. So Q is at $\frac{2}{5}$? Wait, no, the problem: N is at 1, which is $\frac{5}{5}$. Q is at $\frac{2}{5}$? Wait, no, let's check the number line again. Wait, the labels: -1, $-\frac{3}{5}$, $-\frac{1}{5}$, $\frac{1}{5}$, Q, $\frac{3}{5}$, N, 1. So between $\frac{1}{5}$ and $\frac{3}{5}$ is Q, so Q is at $\frac{2}{5}$? And N is at 1, which is $\frac{5}{5}$. Then the distance between Q ($\frac{2}{5}$) and N ($\frac{5}{5}$) is $|\frac{5}{5} - \frac{2}{5}| = \frac{3}{5}$? Wait, no, maybe I misread. Wait, the number line: let's see the positions. Wait, the tick marks: from -1 to 1, the marks are at -1, $-\frac{3}{5}$, $-\frac{1}{5}$, $\frac{1}{5}$, then Q, then $\frac{3}{5}$, then N, then 1. So the distance between $\frac{3}{5}$ and 1 (which is $\frac{5}{5}$) is $\frac{2}{5}$, and between Q and $\frac{3}{5}$ is $\frac{1}{5}$? Wait, no, maybe Q is at $\frac{2}{5}$? Wait, no, let's count the intervals. From $\frac{1}{5}$ to $\frac{3}{5}$ is two intervals, so each interval is $\frac{1}{5}$. So Q is at $\frac{2}{5}$ (since $\frac{1}{5} + \frac{1}{5} = \frac{2}{5}$). Then N is at 1, which is $\frac{5}{5}$. So the distance between Q ($\frac{2}{5}$) and N ($\frac{5}{5}$) is $|\frac{5}{5} - \frac{2}{5}| = \frac{3}{5}$? Wait, no, maybe N is at 1, which is $\frac{5}{5}$, and Q is at $\frac{2}{5}$? Wait, no, let's check the number line again. Wait, the user's number line: the labels are -1, $-\frac{3}{5}$, $-\frac{1}{5}$, $\frac{1}{5}$, Q, $\frac{3}{5}$, N, 1. So the positions:

- $\frac{1}{5}$ is a tick, then Q, then $\frac{3}{5}$: so Q is at $\frac{2}{5}$ (since $\frac{1}{5} + \frac{1}{5} = \frac{2}{5}$)
- $\frac{3}{5}$ is a tick, then N, then 1: so N is at $\frac{4}{5}$? Wait, no, 1 is $\frac{5}{5}$, so between $\frac{3}{5}$ and 1, there are two ticks? Wait, the number line has arrows, so maybe the ticks are each $\frac{1}{5}$. So from $\frac{3}{5}$ to 1 (which is $\frac{5}{5}$) is two intervals, so N is at $\frac{4}{5}$? Wait, no, the user's image shows N at 1? Wait, the label next to N is 1. So N is at 1 (which is $\frac{5}{5}$), and Q is at $\frac{2}{5}$? Wait, no, maybe I made a mistake. Wait, let's look at the number line again. The ticks: -1, then a tick, then $-\frac{3}{5}$, then a tick, then $-\frac{1}{5}$, then a tick, then $\frac{1}{5}$, then a tick, then Q, then a tick, then $\frac{3}{5}$, then a tick, then N, then a tick, then 1. So the distance between each tick is $\frac{1}{5}$. So:

- Position of Q: after $\frac{1}{5}$, so $\frac{1}{5} + \frac{1}{5} = \frac{2}{5}$? Wait, no, $\frac{1}{5}$ to Q is one tick, Q to $\frac{3}{5}$ is one tick, so Q is at $\frac{2}{5}$.
- Position of N: after $\frac{3}{5}$, two ticks to 1? Wait, $\frac{3}{5}$ to N is two ticks? No, N is at 1, so from $\frac{3}{5}$ to 1 is $\frac{2}{5}$, which is two ticks (each $\frac{1}{5}$). So N is at 1, Q is at $\frac{2}{5}$. Then the distance is $|1 - \frac{2}{5}| = |\frac{5}{5} - \frac{2}{5}| = \frac{3}{5}$. Wait, but maybe Q is at $\frac{2}{5}$ and N is at 1, so distance is $1 - \frac{2}{5} = \frac{3}{5}$.

Wait, maybe another way: count the number of intervals between Q and N. From Q to $\frac{3}{5}$ is 1 interval, $\frac{3}{5}$ to N is 2 intervals? No, let's count the ticks. From Q to N: how many ticks? Q is at $\frac{2}{5}$, N is at 1 ($\frac{5}{5}$). The difference is $\frac{5}{5} - \frac{2}{5} = \frac{3}{5}$. So the distance is $\frac{3}{5}$.

Step1: Determine coordinates of Q and N

From the number line, Q is at $\frac{2}{5}$ (since it's between $\frac{1}{5}$ and $\frac{3}{5}$, midpoint? Wait, no, each tick is $\frac{1}{5}$. So $\frac{1}{5}$, then Q, then $\frac{3}{5}$: so Q is at $\frac{2}{5}$. N is at 1 (which is $\frac{5}{5}$).

Step2: Calculate distance

Distance between two points on a number line is the absolute difference of their coordinates. So distance = $|N - Q| = |1 - \frac{2}{5}| = |\frac{5}{5} - \frac{2}{5}| = \frac{3}{5}$.

Answer:

$\frac{3}{5}$