Which of the following is a false statement?

Options

A. `1/7 lt 3/14`
B. `5/8=15/24`
C. `3/4=6/16`
D. `5/12 gt 2/6`

Answer

To determine which of the following statements is false, we will evaluate each statement one by one using the cross multiplication method for comparing fractions.

### Step-by-Step Solution:

1. **Evaluate the first statement:**
- Statement: \( \frac{1}{7} < \frac{3}{14} \)
- Cross multiplication:
- Multiply the numerator of the first fraction by the denominator of the second: \( 1 \times 14 = 14 \)
- Multiply the numerator of the second fraction by the denominator of the first: \( 3 \times 7 = 21 \)
- Comparison: \( 14 < 21 \) is true.
- Conclusion: The first statement is **true**.

2. **Evaluate the second statement:**
- Statement: \( \frac{5}{8} = \frac{15}{24} \)
- Cross multiplication:
- Multiply the numerator of the first fraction by the denominator of the second: \( 5 \times 24 = 120 \)
- Multiply the numerator of the second fraction by the denominator of the first: \( 15 \times 8 = 120 \)
- Comparison: \( 120 = 120 \) is true.
- Conclusion: The second statement is **true**.

3. **Evaluate the third statement:**
- Statement: \( \frac{3}{4} = \frac{6}{16} \)
- Cross multiplication:
- Multiply the numerator of the first fraction by the denominator of the second: \( 3 \times 16 = 48 \)
- Multiply the numerator of the second fraction by the denominator of the first: \( 6 \times 4 = 24 \)
- Comparison: \( 48 > 24 \) is true, but the statement claims they are equal.
- Conclusion: The third statement is **false**.

4. **Evaluate the fourth statement:**
- Statement: \( \frac{5}{12} > \frac{2}{6} \)
- Cross multiplication:
- Multiply the numerator of the first fraction by the denominator of the second: \( 5 \times 6 = 30 \)
- Multiply the numerator of the second fraction by the denominator of the first: \( 2 \times 12 = 24 \)
- Comparison: \( 30 > 24 \) is true.
- Conclusion: The fourth statement is **true**.

### Final Conclusion:
The false statement among the options is the **third statement: \( \frac{3}{4} = \frac{6}{16} \)**.