Write True (T) or False (F) against each of the following statements :
`12:18 :: 28 : 12 `

Answer

To determine whether the statement \( 12:18 :: 28:12 \) is true or false, we need to check if the ratios are equivalent.

### Step-by-Step Solution:

1. **Understand the Proportion**: The statement \( 12:18 :: 28:12 \) means that the ratio of the first two numbers (12 and 18) should be equal to the ratio of the last two numbers (28 and 12).

2. **Write the Ratios as Fractions**:
- The first ratio can be written as:
\[ \frac{12}{18} \]
- The second ratio can be written as:
\[ \frac{28}{12} \]

3. **Simplify the First Ratio**:
- To simplify \( \frac{12}{18} \), we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 6:
\[ \frac{12 \div 6}{18 \div 6} = \frac{2}{3} \]

4. **Simplify the Second Ratio**:
- To simplify \( \frac{28}{12} \), we can divide both the numerator and the denominator by their GCD, which is 4:
\[ \frac{28 \div 4}{12 \div 4} = \frac{7}{3} \]

5. **Compare the Two Ratios**:
- Now we compare the simplified ratios:
\[ \frac{2}{3} \quad \text{and} \quad \frac{7}{3} \]
- Since \( \frac{2}{3} \) is not equal to \( \frac{7}{3} \), the two ratios are not equivalent.

6. **Conclusion**: Since the two ratios are not equal, the statement \( 12:18 :: 28:12 \) is **False** (F).

### Final Answer:
**False (F)**

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