`1/39 : 1/27 =` _____

Options

A. `14:1`
B. `11:4`
C. `9:13`
D. `1:5`

Answer

To solve the ratio \( \frac{1}{39} : \frac{1}{27} \), we can follow these steps:

### Step-by-Step Solution:

1. **Write the Ratio**:
We start with the ratio given in the problem:
\[ \frac{1}{39} : \frac{1}{27} \]

2. **Convert the Ratio**:
To simplify the ratio, we can express it as a division:
\[ \frac{\frac{1}{39}}{\frac{1}{27}} = \frac{1}{39} \times \frac{27}{1} = \frac{27}{39} \]

3. **Simplify the Fraction**:
Now, we simplify the fraction \( \frac{27}{39} \). We can find the greatest common divisor (GCD) of 27 and 39.
- The GCD of 27 and 39 is 3.
- Now, we divide both the numerator and the denominator by their GCD:
\[ \frac{27 \div 3}{39 \div 3} = \frac{9}{13} \]

4. **Write the Ratio**:
Therefore, the ratio \( \frac{27}{39} \) simplifies to:
\[ 9 : 13 \]

### Final Answer:
Thus, the answer to the ratio \( \frac{1}{39} : \frac{1}{27} \) is:
\[ \boxed{9 : 13} \]