Which fraction among 3/11, 4/9 and 6/11 is the smallest?

Options

A. `3//11`
B. `4//9`
C. `6//11`
D. All are equal

Answer

To determine which fraction among \( \frac{3}{11} \), \( \frac{4}{9} \), and \( \frac{6}{11} \) is the smallest, we can convert each fraction to its decimal form for easier comparison.

### Step 1: Convert each fraction to decimal form

1. **Convert \( \frac{3}{11} \)**:
- Perform the division: \( 3 \div 11 \)
- This gives approximately \( 0.2727 \) (repeating).

2. **Convert \( \frac{4}{9} \)**:
- Perform the division: \( 4 \div 9 \)
- This gives approximately \( 0.4444 \) (repeating).

3. **Convert \( \frac{6}{11} \)**:
- Perform the division: \( 6 \div 11 \)
- This gives approximately \( 0.5454 \) (repeating).

### Step 2: Compare the decimal values

Now we have the decimal equivalents:
- \( \frac{3}{11} \approx 0.2727 \)
- \( \frac{4}{9} \approx 0.4444 \)
- \( \frac{6}{11} \approx 0.5454 \)

### Step 3: Identify the smallest decimal

From the decimal values:
- \( 0.2727 \) (from \( \frac{3}{11} \))
- \( 0.4444 \) (from \( \frac{4}{9} \))
- \( 0.5454 \) (from \( \frac{6}{11} \))

The smallest value is \( 0.2727 \).

### Conclusion

Thus, the smallest fraction among \( \frac{3}{11} \), \( \frac{4}{9} \), and \( \frac{6}{11} \) is \( \frac{3}{11} \).

**Final Answer**: \( \frac{3}{11} \)

---