Question

write the rational number for the indicated point on the number line.
a = \square

Explanation:

Step1: Identify interval length

The distance between $-2$ and $-1$ is $1$, split into 4 equal parts. Each part = $\frac{1}{4}$.

Step2: Count steps from -1

Point A is 1 step left of $-1$, so value = $-1 - \frac{1}{4}$

Step3: Compute final value

$ -1 - \frac{1}{4} = -\frac{4}{4} - \frac{1}{4} = -\frac{5}{4} $
Wait correction: Re-count intervals: From -2 to -1, there are 4 ticks, so each segment is $\frac{1}{4}$. Point A is 1 tick right of -2: $-2 + \frac{1}{4} = -\frac{8}{4} + \frac{1}{4} = -\frac{7}{4}$? No, re-examine number line:
Wait correct count: Between -2 and -1, there are 4 equal spaces. Starting at -2, moving 1 space right: $-2 + \frac{1}{4} = -\frac{7}{4}$? No, looking at the number line: -2, then 4 ticks to -1. So each tick is $\frac{1}{4}$. Point A is at the 1st tick after -2: $-2 + \frac{1}{4} = -\frac{7}{4}$? No, wait -2 to -1 is 1 unit, 4 divisions, so each division is $\frac{1}{4}$. So positions:
-2, $-2+\frac{1}{4}=-\frac{7}{4}$, $-2+\frac{2}{4}=-\frac{6}{4}=-\frac{3}{2}$, $-2+\frac{3}{4}=-\frac{5}{4}$, $-1$.
Yes, Point A is at $-\frac{5}{4}$? Wait no, the number line: <point>51 181</point> is -2, <point>241 181</point> is -1. The distance between -2 and -1 is 190 units (visual), divided into 4 parts, each 47.5 units. Point A is at <point>156 165</point>, which is 105 units from -2. $105/190 = 21/38$? No, better: standard number line, between -2 and -1, 4 equal segments, so each is 0.25. Point A is 1 segment left of -1: $-1 - 0.25 = -1.25 = -\frac{5}{4}$.

Step1: Define segment size

Between $-1$ and $-2$, 4 equal segments: $\frac{1}{4}$ each.

Step2: Locate point A

A is 1 segment left of $-1$.

Step3: Calculate value

$ -1 - \frac{1}{4} = -\frac{5}{4} $

Final correction: Correct count: The number line has -2, then 4 ticks to -1. So each tick is 0.25. Point A is the 3rd tick from -2: $-2 + 3*0.25 = -2 + 0.75 = -1.25 = -\frac{5}{4}$. Yes, that matches.

Step1: Find segment length

Between $-2$ and $-1$: $1 \div 4 = \frac{1}{4}$

Step2: Count segments from -2

Point A is 3 segments right of $-2$.

Step3: Compute the value

$-2 + 3 \times \frac{1}{4} = -2 + \frac{3}{4} = -\frac{8}{4} + \frac{3}{4} = -\frac{5}{4}$

Answer:

$-\frac{3}{4}$