What is the descending order of `11/17,7/11,8/15,5/9`?

Options

A. `11/17gt7/11gt5/9gt8/15`
B. `11/17gt8/15gt7/11gt5/9`
C. `11/17gt5/9gt7/11gt8/15`
D. `11/17gt7/11gt8/15gt5/9`

Answer

To find the descending order of the fractions \( \frac{11}{17}, \frac{7}{11}, \frac{8}{15}, \frac{5}{9} \), we will compare their values by converting them into decimal form or finding a common denominator. Here’s the step-by-step solution:

### Step 1: Convert each fraction to decimal form
1. **Calculate \( \frac{11}{17} \)**:
\[ \frac{11}{17} \approx 0.6471 \]

2. **Calculate \( \frac{7}{11} \)**:
\[ \frac{7}{11} \approx 0.6364 \]

3. **Calculate \( \frac{8}{15} \)**:
\[ \frac{8}{15} \approx 0.5333 \]

4. **Calculate \( \frac{5}{9} \)**:
\[ \frac{5}{9} \approx 0.5556 \]

### Step 2: List the decimal values
- \( \frac{11}{17} \approx 0.6471 \)
- \( \frac{7}{11} \approx 0.6364 \)
- \( \frac{5}{9} \approx 0.5556 \)
- \( \frac{8}{15} \approx 0.5333 \)

### Step 3: Arrange the decimal values in descending order
From the decimal values calculated:
- \( 0.6471 \) (which is \( \frac{11}{17} \))
- \( 0.6364 \) (which is \( \frac{7}{11} \))
- \( 0.5556 \) (which is \( \frac{5}{9} \))
- \( 0.5333 \) (which is \( \frac{8}{15} \))

### Step 4: Write the fractions in descending order
Thus, the descending order of the fractions is:
\[ \frac{11}{17}, \frac{7}{11}, \frac{5}{9}, \frac{8}{15} \]

### Final Answer:
The descending order of \( \frac{11}{17}, \frac{7}{11}, \frac{8}{15}, \frac{5}{9} \) is:
\[ \frac{11}{17} > \frac{7}{11} > \frac{5}{9} > \frac{8}{15} \]