Answer :

To arrange the monthly test scores of a student in ascending and descending order, let's first convert all the given scores into decimal form for easier comparison.

The scores given are:
1. [tex]\(\frac{10}{15}\)[/tex]
2. [tex]\(\frac{12}{25}\)[/tex]
3. [tex]\(0.5\)[/tex]
4. [tex]\(75\%\)[/tex]

Let's convert these scores to their decimal equivalents:
1. [tex]\(\frac{10}{15} \approx 0.6667\)[/tex]
2. [tex]\(\frac{12}{25} = 0.48\)[/tex]
3. [tex]\(0.5\)[/tex] (already in decimal form)
4. [tex]\(75\% = 0.75\)[/tex]

Now, let's list these decimal scores:

- 0.6667
- 0.48
- 0.5
- 0.75

Next, we will arrange these scores in ascending order:

1. 0.48
2. 0.5
3. 0.6667
4. 0.75

So, the scores in ascending order are:
[tex]\[ [0.48, 0.5, 0.6667, 0.75] \][/tex]

Now, we will arrange these scores in descending order:

1. 0.75
2. 0.6667
3. 0.5
4. 0.48

So, the scores in descending order are:
[tex]\[ [0.75, 0.6667, 0.5, 0.48] \][/tex]

Hence, the monthly test scores arranged in ascending and descending order are:
- Ascending order: [tex]\([0.48, 0.5, 0.6667, 0.75]\)[/tex]
- Descending order: [tex]\([0.75, 0.6667, 0.5, 0.48]\)[/tex]