Which of the following represents a correct proportion?

Options

A. 12 : 9 = 16 : 12
B. 13 : 11 = 5 : 4
C. 30 : 45 = 13 : 24
D. 3 : 5 = 2 : 5

Answer

To determine which of the given options represents a correct proportion, we need to check if the ratios in each option are equivalent. A proportion states that two ratios are equal, which can be expressed as \( \frac{a}{b} = \frac{c}{d} \).

### Step-by-Step Solution:

1. **Identify the Options**: We have four options to evaluate:
- Option 1: \( \frac{12}{9} = \frac{16}{12} \)
- Option 2: \( \frac{13}{11} = \frac{5}{4} \)
- Option 3: \( \frac{30}{45} = \frac{13}{24} \)
- Option 4: \( \frac{3}{5} = \frac{4}{5} \)

2. **Evaluate Option 1**:
- Calculate \( \frac{12}{9} \) and \( \frac{16}{12} \).
- Simplifying \( \frac{12}{9} \) gives \( \frac{4}{3} \) (dividing both numerator and denominator by 3).
- Simplifying \( \frac{16}{12} \) gives \( \frac{4}{3} \) (dividing both numerator and denominator by 4).
- Since \( \frac{4}{3} = \frac{4}{3} \), Option 1 is a correct proportion.

3. **Evaluate Option 2**:
- Calculate \( \frac{13}{11} \) and \( \frac{5}{4} \).
- These fractions cannot be simplified further.
- Since \( \frac{13}{11} \neq \frac{5}{4} \), Option 2 is not a correct proportion.

4. **Evaluate Option 3**:
- Calculate \( \frac{30}{45} \) and \( \frac{13}{24} \).
- Simplifying \( \frac{30}{45} \) gives \( \frac{2}{3} \) (dividing both by 15).
- The fraction \( \frac{13}{24} \) cannot be simplified further.
- Since \( \frac{2}{3} \neq \frac{13}{24} \), Option 3 is not a correct proportion.

5. **Evaluate Option 4**:
- Calculate \( \frac{3}{5} \) and \( \frac{4}{5} \).
- Since both fractions have the same denominator, we can directly compare the numerators.
- Since \( 3 \neq 4 \), Option 4 is not a correct proportion.

### Conclusion:
After evaluating all options, the only correct proportion is found in **Option 1**: \( \frac{12}{9} = \frac{16}{12} \).