Which of the fractions given below is not equal to `4/11`

Options

A. `32/88`
B. `84/209`
C. `64/176`
D. `20/55`

Answer

To determine which of the fractions given is not equal to \( \frac{4}{11} \), we will evaluate each option step by step.

### Step-by-Step Solution:

1. **Evaluate the first option: \( \frac{32}{88} \)**
- Simplify \( \frac{32}{88} \) by dividing both the numerator and denominator by 8:
\[ \frac{32 \div 8}{88 \div 8} = \frac{4}{11} \]
- This fraction is equal to \( \frac{4}{11} \).

2. **Evaluate the second option: \( \frac{84}{209} \)**
- We will check if \( \frac{84}{209} \) can be simplified to \( \frac{4}{11} \).
- Calculate \( 84 \div 21 = 4 \) and \( 209 \div 21 \).
- Since \( 209 \div 21 \approx 9.95 \), it does not simplify to \( 11 \).
- Therefore, \( \frac{84}{209} \) is **not equal** to \( \frac{4}{11} \).

3. **Evaluate the third option: \( \frac{64}{176} \)**
- Simplify \( \frac{64}{176} \) by dividing both the numerator and denominator by 16:
\[ \frac{64 \div 16}{176 \div 16} = \frac{4}{11} \]
- This fraction is equal to \( \frac{4}{11} \).

4. **Evaluate the fourth option: \( \frac{20}{55} \)**
- Simplify \( \frac{20}{55} \) by dividing both the numerator and denominator by 5:
\[ \frac{20 \div 5}{55 \div 5} = \frac{4}{11} \]
- This fraction is equal to \( \frac{4}{11} \).

### Conclusion:
After evaluating all the options, we find that the second option, \( \frac{84}{209} \), is not equal to \( \frac{4}{11} \).

### Final Answer:
The fraction that is not equal to \( \frac{4}{11} \) is \( \frac{84}{209} \).