Out of the fractions , `(3)/(11), (2)/(9) , (5)/(13) , (7)/(17) ` and `(8)/(19)` which is the second highest fraction ?

Options

A. `(3)/(11)`
B. `(2)/(9)`
C. `(5)/(13)`
D. `(7)/(17)`

Answer

To find the second highest fraction among the given fractions \( \frac{3}{11}, \frac{2}{9}, \frac{5}{13}, \frac{7}{17}, \) and \( \frac{8}{19} \), we can convert each fraction to its decimal form and then compare the values.

### Step-by-Step Solution:

1. **Convert \( \frac{3}{11} \) to decimal:**
- Divide 3 by 11.
- \( 3 \div 11 = 0.2727... \) (approximately 0.27).

2. **Convert \( \frac{2}{9} \) to decimal:**
- Divide 2 by 9.
- \( 2 \div 9 = 0.2222... \) (approximately 0.22).

3. **Convert \( \frac{5}{13} \) to decimal:**
- Divide 5 by 13.
- \( 5 \div 13 = 0.3846... \) (approximately 0.38).

4. **Convert \( \frac{7}{17} \) to decimal:**
- Divide 7 by 17.
- \( 7 \div 17 = 0.4117... \) (approximately 0.41).

5. **Convert \( \frac{8}{19} \) to decimal:**
- Divide 8 by 19.
- \( 8 \div 19 = 0.4210... \) (approximately 0.42).

6. **List the decimal values:**
- \( \frac{3}{11} \approx 0.27 \)
- \( \frac{2}{9} \approx 0.22 \)
- \( \frac{5}{13} \approx 0.38 \)
- \( \frac{7}{17} \approx 0.41 \)
- \( \frac{8}{19} \approx 0.42 \)

7. **Order the fractions from highest to lowest:**
- \( \frac{8}{19} \approx 0.42 \) (highest)
- \( \frac{7}{17} \approx 0.41 \) (second highest)
- \( \frac{5}{13} \approx 0.38 \)
- \( \frac{3}{11} \approx 0.27 \)
- \( \frac{2}{9} \approx 0.22 \) (lowest)

8. **Identify the second highest fraction:**
- The second highest fraction is \( \frac{7}{17} \).

### Final Answer:
The second highest fraction is \( \frac{7}{17} \).

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