Let’s address each part of the question step-by-step.
### Part A: Arrange in Ascending Order
For the fractions:
- [tex]\(-\frac{7}{3}\)[/tex]
- [tex]\(-\frac{25}{8}\)[/tex]
- [tex]\(-\frac{5}{2}\)[/tex]
- [tex]\(-\frac{9}{4}\)[/tex]
We need to arrange them in ascending order. The calculations give us the approximate decimal values of these fractions:
- [tex]\(-\frac{7}{3} \approx -2.3333\)[/tex]
- [tex]\(-\frac{25}{8} \approx -3.125\)[/tex]
- [tex]\(-\frac{5}{2} = -2.5\)[/tex]
- [tex]\(-\frac{9}{4} = -2.25\)[/tex]
Comparing these values from smallest to largest:
- [tex]\(-3.125\)[/tex] (i.e., [tex]\(-\frac{25}{8}\)[/tex])
- [tex]\(-2.5\)[/tex] (i.e., [tex]\(-\frac{5}{2}\)[/tex])
- [tex]\(-2.3333\)[/tex] (i.e., [tex]\(-\frac{7}{3}\)[/tex])
- [tex]\(-2.25\)[/tex] (i.e., [tex]\(-\frac{9}{4}\)[/tex])
Thus, the fractions in ascending order are:
[tex]\[ -\frac{25}{8}, \quad -\frac{5}{2}, \quad -\frac{7}{3}, \quad -\frac{9}{4} \][/tex]
### Part B: Compare Fractions
To compare [tex]\( \frac{5}{4} \)[/tex] and [tex]\( \frac{7}{6} \)[/tex], we consider their approximate decimal values:
- [tex]\( \frac{5}{4} = 1.25 \)[/tex]
- [tex]\( \frac{7}{6} \approx 1.1667 \)[/tex]
Since [tex]\( 1.25 \)[/tex] is greater than [tex]\( 1.1667 \)[/tex], we can conclude that:
[tex]\[ \frac{5}{4} > \frac{7}{6} \][/tex]
Therefore, the results for both parts are:
1. Part A:
[tex]\[ -\frac{25}{8}, \quad -\frac{5}{2}, \quad -\frac{7}{3}, \quad -\frac{9}{4} \][/tex]
2. Part B:
[tex]\[ \frac{5}{4} > \frac{7}{6} \][/tex]
