Question

which fraction is represented on the number line below
options:
\\(\frac{1}{3}\\)
\\(\frac{3}{2}\\)
\\(\frac{9}{8}\\)
\\(\frac{3}{4}\\)

Explanation:

Step1: Analyze the number line

The number line ranges from 0 to 2. Let's first find the number of intervals between 0 and 2. From the number line, we can see that from 0 to 2, there are 16 small intervals (since from 0 to 2, the total length is 2, and we can count the ticks). Wait, actually, let's check the position of the arrow. Let's see the position relative to 1. Wait, maybe a better way: Let's convert all options to decimals to compare.

• $\frac{1}{3} \approx 0.333$
• $\frac{3}{2} = 1.5$
• $\frac{9}{8} = 1.125$
• $\frac{3}{4} = 0.75$

Now, looking at the number line, the arrow is between 1 and 2? Wait, no, wait the number line: 0 on the left, 2 on the right. Wait, maybe the number of intervals from 0 to 2 is 16? Wait, no, let's count the ticks. From 0 to 2, how many spaces? Let's see, the arrow is at the 9th tick (if we count from 0). Wait, maybe the total number of intervals from 0 to 2 is 16, so each interval is $\frac{2}{16} = \frac{1}{8}$. Wait, no, that might not be right. Wait, another approach: Let's see the position of the arrow. Let's check the options. $\frac{9}{8}$ is 1.125, $\frac{3}{2}$ is 1.5. Let's see the number line: the arrow is before the midpoint between 1 and 2? Wait, no, maybe the number line has 8 intervals from 0 to 1, and 8 from 1 to 2. Wait, if from 0 to 2, there are 16 intervals, each of length $\frac{2}{16} = \frac{1}{8}$. So the position of the arrow: let's count the ticks from 0. Let's say the arrow is at the 9th tick (since 0 is tick 0, then tick 1, ..., tick 16 is 2). So tick 9: $9 \times \frac{1}{8} = \frac{9}{8} = 1.125$, which is $\frac{9}{8}$. Wait, but let's check the options. Wait, $\frac{9}{8}$ is 1.125, $\frac{3}{2}$ is 1.5. Let's see the number line: the arrow is at the 9th tick (if 0 is tick 0, 2 is tick 16). So tick 9: $9 \times \frac{1}{8} = \frac{9}{8}$. Let's verify:

• $\frac{9}{8} = 1.125$
• $\frac{3}{2} = 1.5$ (which is tick 12, since $12 \times \frac{1}{8} = 1.5$)
• $\frac{1}{3} \approx 0.333$ (tick ~2.666)
• $\frac{3}{4} = 0.75$ (tick 6, since $6 \times \frac{1}{8} = 0.75$)

So the arrow is at tick 9, which is $9 \times \frac{1}{8} = \frac{9}{8}$. So the fraction is $\frac{9}{8}$.

Wait, but let's check again. Wait, maybe the number line has 8 intervals from 0 to 1, and 8 from 1 to 2. So each interval is $\frac{1}{8}$. So from 0 to 1, 8 intervals, each $\frac{1}{8}$. Then from 1 to 2, another 8. So the arrow is at the 9th interval (0 is interval 0, 1 is interval 8, 2 is interval 16). So interval 9: $1 + \frac{1}{8} = \frac{9}{8}$. Yes, that makes sense. So the fraction is $\frac{9}{8}$.

Step2: Compare with options

Now, let's check the options:

• $\frac{1}{3} \approx 0.333$ (too low)
• $\frac{3}{2} = 1.5$ (higher than 1.125)
• $\frac{9}{8} = 1.125$ (matches the position)
• $\frac{3}{4} = 0.75$ (too low)

So the correct fraction is $\frac{9}{8}$.

Answer:

$\frac{9}{8}$ (the option with $\frac{9}{8}$)