Choose the fraction equivalent to `9/(13)`

Options

A. `13/(17)`
B. `5/(9)`
C. `27/(39)`
D. `1/(4)`

Answer

To find the fraction equivalent to \( \frac{9}{13} \), we will analyze the given options and determine which one is equivalent by simplifying them.

### Step-by-Step Solution:

1. **Identify the Given Fraction**:
We start with the fraction \( \frac{9}{13} \).

2. **List the Options**:
The options provided are:
- Option 1: \( \frac{13}{17} \)
- Option 2: \( \frac{5}{9} \)
- Option 3: \( \frac{27}{39} \)
- Option 4: \( \frac{1}{4} \)

3. **Check Each Option for Equivalence**:
We will simplify each option to see if any of them equal \( \frac{9}{13} \).

- **Option 1: \( \frac{13}{17} \)**
- This fraction cannot be simplified further.
- It is not equivalent to \( \frac{9}{13} \).

- **Option 2: \( \frac{5}{9} \)**
- This fraction is also in its simplest form.
- It is not equivalent to \( \frac{9}{13} \).

- **Option 3: \( \frac{27}{39} \)**
- We can simplify this fraction:
- Divide both the numerator and denominator by 3:
\[ \frac{27 \div 3}{39 \div 3} = \frac{9}{13} \]
- Therefore, \( \frac{27}{39} \) simplifies to \( \frac{9}{13} \), making it equivalent.

- **Option 4: \( \frac{1}{4} \)**
- This fraction is in its simplest form and does not equal \( \frac{9}{13} \).

4. **Conclusion**:
The fraction equivalent to \( \frac{9}{13} \) is \( \frac{27}{39} \). Therefore, the correct option is Option 3.