Sure! Let's walk through the step-by-step procedure to plot the point [tex]\(-\frac{5}{6}\)[/tex] on a number line.
### Step-by-Step Solution
#### Step 1: Draw a number line
First, we draw a horizontal number line and label the key points [tex]\(-1\)[/tex], [tex]\(0\)[/tex], and [tex]\(1\)[/tex].
```
-1 0 1
|---------|---------|
```
#### Step 2: Determine how to divide the number line
Since the denominator of the fraction [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(6\)[/tex], we divide the spaces between each pair of consecutive integer points into 6 equal parts.
#### Step 3: Divide the number line into sixths
Now, we mark equally spaced points between [tex]\(-1\)[/tex] and [tex]\(0\)[/tex] and between [tex]\(0\)[/tex] and [tex]\(1\)[/tex]. Each of those segments represents [tex]\(\frac{1}{6}\)[/tex].
```
-1 -5/6 -4/6 -3/6 -2/6 -1/6 0 1/6 2/6 3/6 4/6 5/6 1
|----|----|----|----|----|----|----|----|----|----|----|----|
```
#### Step 4: Use the numerator to locate the point
The fraction [tex]\(-\frac{5}{6}\)[/tex] tells us to move 5 spaces from [tex]\(0\)[/tex] towards the left on the number line because the numerator is negative. Starting from [tex]\(0\)[/tex], we count 5 of these [tex]\(\frac{1}{6}\)[/tex] increments to the left:
1. [tex]\(-\frac{1}{6}\)[/tex]
2. [tex]\(-\frac{2}{6}\)[/tex] or [tex]\(-\frac{1}{3}\)[/tex]
3. [tex]\(-\frac{3}{6}\)[/tex] or [tex]\(-\frac{1}{2}\)[/tex]
4. [tex]\(-\frac{4}{6}\)[/tex] or [tex]\(-\frac{2}{3}\)[/tex]
5. [tex]\(-\frac{5}{6}\)[/tex]
By the fifth increment, we reach the point [tex]\(-\frac{5}{6}\)[/tex], so we place a mark there.
### Final Number Line with the Marked Point
```
-1 -5/6 -4/6 -3/6 -2/6 -1/6 0 1/6 2/6 3/6 4/6 5/6 1
|----|----|----|----|----|----|----|----|----|----|----|----|
*
```
Thus, the point [tex]\(-\frac{5}{6}\)[/tex] is correctly plotted on the number line at [tex]\( -0.8333\ldots \)[/tex], which is equivalent to moving 5 out of 6 segments from 0 towards [tex]\(-1\)[/tex].
