Sure! Let's plot the numbers \(\frac{7}{8}\) and \(1 \frac{3}{4}\) on the number line.
### Step-by-Step Solution:
1. Interpret the fractions:
- \(\frac{7}{8}\) is a proper fraction. We place it between 0 and 1 on the number line.
- \(1 \frac{3}{4}\) is a mixed number. We convert it to an improper fraction or a decimal to place it correctly on the number line. \(1 \frac{3}{4}\) is the same as \(1 + \frac{3}{4}\), which equals \(1.75\).
2. Visualize the number line:
- Start by drawing a horizontal line segment.
- Label the whole numbers on the number line, such as 0, 1, 2, and possibly segments between these whole numbers if needed.
3. Locate \(\frac{7}{8}\):
- Since \(\frac{7}{8}\) (or 0.875) lies between 0 and 1, locate a point that is \(7/8\) of the distance from 0 to 1.
- Mark this point distinctly on the number line and denote it as \(\frac{7}{8}\).
4. Locate \(1 \frac{3}{4}\):
- Since \(1 \frac{3}{4}\) (or 1.75) lies between 1 and 2, locate a point that is \(3/4\) of the distance from 1 to 2.
- Mark this point distinctly on the number line and denote it as \(1 \frac{3}{4}\).
Here’s a visual representation:
```
0 0.5 1 1.5 2
|-------|-------|-------|-------|-------
| |
0.875 1.75
(7/8) (1 3/4)
```
This helps to clearly identify the positions of [tex]\(\frac{7}{8}\)[/tex] and [tex]\(1 \frac{3}{4}\)[/tex] on the number line.
