Question

what fraction is represented by point c on the number line? a \\(\frac{2}{3}\\) b \\(\frac{2}{4}\\) c \\(\frac{2}{5}\\) d \\(\frac{3}{4}\\)

Explanation:

Step1: Count intervals on number line

The number line from 0 to 1 has points A (0), B, C, D, E (1). So there are 4 intervals between 0 and 1? Wait, no: A is 0, E is 1. Let's count the segments. From 0 (A) to B: 1 segment, B to C: 2nd, C to D: 3rd, D to E: 4th? Wait, no, the points are A(0), B, C, D, E(1). So the number of equal parts between 0 and 1 is 4? Wait, no, let's see: the distance from 0 to 1 is divided into how many parts? Let's check the positions. Point B: 1st mark after 0, C: 2nd, D: 3rd, E: 4th (at 1). Wait, no, if E is at 1, then the number of segments is 4? Wait, no, the number of intervals between 0 and 1 is 4? Wait, no, the number of parts is 4? Wait, no, let's count the number of spaces between the points. From A(0) to B: 1 space, B to C: 2nd, C to D: 3rd, D to E: 4th. So total spaces: 4, so each space is $\frac{1}{4}$? Wait, no, wait the points: A(0), B, C, D, E(1). So the number of divisions is 4 (since from 0 to 1, there are 4 intervals? Wait, no, the number of parts is 4? Wait, no, if you have 5 points (A, B, C, D, E), the number of intervals between them is 4. So each interval is $\frac{1}{4}$? Wait, no, wait point B: 1st interval, so B is at $\frac{1}{4}$? No, wait maybe I miscounted. Wait, let's look at the options. Option B is $\frac{2}{4}$, option C is $\frac{2}{5}$? Wait, no, the options: A is $\frac{2}{3}$, B is $\frac{2}{4}$, C is $\frac{2}{5}$, D is $\frac{3}{4}$. Wait, maybe the number of parts is 4? Wait, no, let's check the number of segments. From 0 to 1, the points are A(0), B, C, D, E(1). So the number of equal parts is 4? Wait, no, the number of divisions is 4, so each part is $\frac{1}{4}$. Then point B is at 1 part: $\frac{1}{4}$, point C is at 2 parts: $\frac{2}{4}$, point D at 3 parts: $\frac{3}{4}$, E at 4 parts: 1. So point C is at $\frac{2}{4}$. Wait, but let's confirm. Wait, the number of intervals between 0 and 1: from A(0) to E(1), there are 4 intervals (A-B, B-C, C-D, D-E). So each interval is $\frac{1}{4}$. So point B is at 1 interval: $\frac{1}{4}$, point C at 2 intervals: $\frac{2}{4}$, point D at 3 intervals: $\frac{3}{4}$, E at 4 intervals: 1. So point C is at $\frac{2}{4}$. Wait, but let's check the options. Option B is $\frac{2}{4}$, so that's the answer. Wait, but let's re-examine. Wait, maybe the number of parts is 4? So each part is $\frac{1}{4}$. So point C is at the 2nd part, so $\frac{2}{4}$. So the correct option is B.

Step2: Identify point C's position

Point C is the second mark after 0 (since A is 0, B is first, C is second) in a number line divided into 4 equal parts (since E is at 1, with 4 intervals). So the fraction for C is $\frac{2}{4}$.

Answer:

B. $\frac{2}{4}$