Is six true or false? a. \( \frac{1}{2}=\frac{2}{4}=\frac{3}{6} \) b. \( 500 \mathrm{~mm}=50 \mathrm{~cm} \) c. \( 500 \mathrm{~mm}=1 \mathrm{~m} \) d. \( \frac{1}{2} \) or \( \frac{2}{4} \) or \( \frac{3}{6} \) e. \( \frac{6}{12} \) is bigger than \( \frac{2}{4} \).

Sure, let's evaluate each statement to determine whether it's **True** or **False**: --- **a. \( \frac{1}{2} = \frac{2}{4} = \frac{3}{6} \)** **Answer:** **True** **Explanation:** All three fractions simplify to \( \frac{1}{2} \). \[ \frac{2}{4} = \frac{1}{2} \quad \text{and} \quad \frac{3}{6} = \frac{1}{2} \] --- **b. \( 500 \ \text{mm} = 50 \ \text{cm} \)** **Answer:** **True** **Explanation:** Conversion between millimeters and centimeters: \[ 1 \ \text{cm} = 10 \ \text{mm} \quad \Rightarrow \quad 500 \ \text{mm} = \frac{500}{10} \ \text{cm} = 50 \ \text{cm} \] --- **c. \( 500 \ \text{mm} = 1 \ \text{m} \)** **Answer:** **False** **Explanation:** Conversion between millimeters and meters: \[ 1 \ \text{m} = 1000 \ \text{mm} \quad \Rightarrow \quad 500 \ \text{mm} = 0.5 \ \text{m} \] Therefore, \( 500 \ \text{mm} \neq 1 \ \text{m} \). --- **d. \( \frac{1}{2} \) or \( \frac{2}{4} \) or \( \frac{3}{6} \)** **Answer:** **True** **Explanation:** All three fractions are equivalent to \( \frac{1}{2} \): \[ \frac{2}{4} = \frac{1}{2} \quad \text{and} \quad \frac{3}{6} = \frac{1}{2} \] So, at least one of them being \( \frac{1}{2} \) makes the statement true. --- **e. \( \frac{6}{12} \) is bigger than \( \frac{2}{4} \)** **Answer:** **False** **Explanation:** Simplifying both fractions: \[ \frac{6}{12} = \frac{1}{2} \quad \text{and} \quad \frac{2}{4} = \frac{1}{2} \] They are equal, so \( \frac{6}{12} \) is **not** bigger than \( \frac{2}{4} \). --- **Summary:** - **a. True** - **b. True** - **c. False** - **d. True** - **e. False**