Certainly! Let's represent the fractions [tex]\(-\frac{5}{11}\)[/tex], [tex]\(\frac{7}{9}\)[/tex], and [tex]\(\frac{3}{7}\)[/tex] on different number lines. Here are the steps broken down for each fraction:
### 1. Represent [tex]\(-\frac{5}{11}\)[/tex] on a Number Line
1. Convert Fraction to Decimal: The fraction [tex]\(-\frac{5}{11}\)[/tex] is equivalent to approximately -0.4545.
2. Draw the Number Line: Draw a horizontal line and mark the center as 0. Place numbers at uniform intervals to the left (negative numbers) and to the right (positive numbers) of 0.
3. Locate the Point: Estimate and plot the point -0.4545 between -0.4 and -0.5 on the number line. It will be slightly closer to -0.5.
Here is a simplified representation:
```
-1 -0.5 0
----|-----|-----|-----|-----|-----|-----|----
-0.4545
```
### 2. Represent [tex]\(\frac{7}{9}\)[/tex] on a Number Line
1. Convert Fraction to Decimal: The fraction [tex]\(\frac{7}{9}\)[/tex] is equivalent to approximately 0.7778.
2. Draw the Number Line: Draw a horizontal line and mark the center as 0. Place numbers at uniform intervals to both sides of 0.
3. Locate the Point: Estimate and plot the point 0.7778 between 0.7 and 0.8 on the number line. It will be closer to 0.8.
Here is a simplified representation:
```
0 0.5 1
----|-----|-----|-----|-----|-----|-----
0.7778
```
### 3. Represent [tex]\(\frac{3}{7}\)[/tex] on a Number Line
1. Convert Fraction to Decimal: The fraction [tex]\(\frac{3}{7}\)[/tex] is equivalent to approximately 0.4286.
2. Draw the Number Line: Draw a horizontal line and mark the center as 0. Place numbers at uniform intervals to both sides of 0.
3. Locate the Point: Estimate and plot the point 0.4286 between 0.4 and 0.5 on the number line. It will be slightly closer to 0.4.
Here is a simplified representation:
```
0 0.5 1
----|-----|-----|-----|-----|-----|-----
0.4286
```
By following these steps:
- [tex]\(-\frac{5}{11}\)[/tex] is represented around -0.4545.
- [tex]\(\frac{7}{9}\)[/tex] is represented around 0.7778.
- [tex]\(\frac{3}{7}\)[/tex] is represented around 0.4286.
Each of these points is accurately plotted on their respective number lines taking into account their approximate decimal values.
