To represent the fractions on the number line, we first need to understand their decimal equivalents. Here is a detailed, step-by-step conversion of each fraction and their placement on a number line:
(i) [tex]\(\frac{1}{2}\)[/tex]
The fraction [tex]\(\frac{1}{2}\)[/tex] is equal to 0.5 in decimal form.
(ii) [tex]\(\frac{2}{5}\)[/tex]
The fraction [tex]\(\frac{2}{5}\)[/tex] is equal to 0.4 in decimal form.
(iii) [tex]\(\frac{1}{5}\)[/tex]
The fraction [tex]\(\frac{1}{5}\)[/tex] is equal to 0.2 in decimal form.
(iv) [tex]\(\frac{-2}{5}\)[/tex]
The fraction [tex]\(\frac{-2}{5}\)[/tex] is equal to -0.4 in decimal form.
(v) [tex]\(\frac{7}{-3}\)[/tex]
The fraction [tex]\(\frac{7}{-3}\)[/tex] is equal to -2.3333333333333335 in decimal form.
(vi) [tex]\(\frac{-5}{12}\)[/tex]
The fraction [tex]\(\frac{-5}{12}\)[/tex] is equal to -0.4166666666666667 in decimal form.
(vii) [tex]\(\frac{5}{11}\)[/tex]
The fraction [tex]\(\frac{5}{11}\)[/tex] is equal to approximately 0.45454545454545453 in decimal form.
(viii) [tex]\(\frac{5}{9}\)[/tex]
The fraction [tex]\(\frac{5}{9}\)[/tex] is equal to approximately 0.5555555555555556 in decimal form.
Now, let us place these values on a number line. Mark and label each point accordingly:
```
|----+----+----+----+----+----+----+----+----+----+-----+----+----+----+----+----+----|
-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3
-2.33333
-0.41667
-0.4
0.2
0.4
0.45455
0.5
0.55556
```
Marks:
1. [tex]\(\frac{7}{-3} = -2.3333333333333335\)[/tex]
2. [tex]\(\frac{-5}{12} = -0.4166666666666667\)[/tex]
3. [tex]\(\frac{-2}{5} = -0.4\)[/tex]
4. [tex]\(\frac{1}{5} = 0.2\)[/tex]
5. [tex]\(\frac{2}{5} = 0.4\)[/tex]
6. [tex]\(\frac{5}{11} = 0.45454545454545453\)[/tex], approximately between 0.4 and 0.5
7. [tex]\(\frac{1}{2} = 0.5\)[/tex]
8. [tex]\(\frac{5}{9} = 0.5555555555555556\)[/tex], approximately between 0.5 and 0.6
