If the fractions `(19)/(21), ( 21)/( 25), ( 25)/( 29) , ( 29)/( 31)` and `( 31)/( 37)` are arranged in ascending order of their values, then which one will be the 2nd ?

Options

A. a. `(19)/( 21) `
B. b. `( 21)/( 25)`
C. c. `( 25)/( 29)`
D. d. `( 29)/( 31)`

Answer

To find the second fraction in ascending order from the given fractions \(\frac{19}{21}, \frac{21}{25}, \frac{25}{29}, \frac{29}{31}, \frac{31}{37}\), we will first convert each fraction to its decimal form and then arrange them in ascending order.

### Step-by-Step Solution:

1. **Convert each fraction to decimal:**
- \(\frac{19}{21} = 0.90476\) (approximately)
- \(\frac{21}{25} = 0.84\)
- \(\frac{25}{29} = 0.86207\) (approximately)
- \(\frac{29}{31} = 0.93548\) (approximately)
- \(\frac{31}{37} = 0.83784\) (approximately)

2. **List the decimal values:**
- \(\frac{19}{21} \approx 0.90476\)
- \(\frac{21}{25} = 0.84\)
- \(\frac{25}{29} \approx 0.86207\)
- \(\frac{29}{31} \approx 0.93548\)
- \(\frac{31}{37} \approx 0.83784\)

3. **Arrange the decimal values in ascending order:**
- \(0.83784\) (from \(\frac{31}{37}\))
- \(0.84\) (from \(\frac{21}{25}\))
- \(0.86207\) (from \(\frac{25}{29}\))
- \(0.90476\) (from \(\frac{19}{21}\))
- \(0.93548\) (from \(\frac{29}{31}\))

4. **Identify the second fraction:**
- The first value is \(0.83784\) (which corresponds to \(\frac{31}{37}\)).
- The second value is \(0.84\) (which corresponds to \(\frac{21}{25}\)).

### Conclusion:
The second fraction in ascending order is \(\frac{21}{25}\).