3. Which of the fractions is equivalent. to \( \frac{2}{3} \) ? (A) \( \frac{8}{12} \) (B) \( \frac{6}{10} \) (C) \( \frac{4}{8} \) (D) \( \frac{2}{5} \)

To determine which of the given fractions is equivalent to \( \frac{2}{3} \), we can cross-multiply each option and compare the results. The fraction \( \frac{a}{b} \) is equivalent to \( \frac{c}{d} \) if \( a \cdot d = b \cdot c \). Let's check each option: 1. **Option (A)**: \( \frac{8}{12} \) - Cross-multiply: \( 2 \cdot 12 \) and \( 3 \cdot 8 \) - Calculation: \[ 2 \cdot 12 = 24 \] \[ 3 \cdot 8 = 24 \] - Since \( 24 = 24 \), \( \frac{8}{12} \) is equivalent to \( \frac{2}{3} \). 2. **Option (B)**: \( \frac{6}{10} \) - Cross-multiply: \( 2 \cdot 10 \) and \( 3 \cdot 6 \) - Calculation: \[ 2 \cdot 10 = 20 \] \[ 3 \cdot 6 = 18 \] - Since \( 20 \neq 18 \), \( \frac{6}{10} \) is not equivalent to \( \frac{2}{3} \). 3. **Option (C)**: \( \frac{4}{8} \) - Cross-multiply: \( 2 \cdot 8 \) and \( 3 \cdot 4 \) - Calculation: \[ 2 \cdot 8 = 16 \] \[ 3 \cdot 4 = 12 \] - Since \( 16 \neq 12 \), \( \frac{4}{8} \) is not equivalent to \( \frac{2}{3} \). 4. **Option (D)**: \( \frac{2}{5} \) - Cross-multiply: \( 2 \cdot 5 \) and \( 3 \cdot 2 \) - Calculation: \[ 2 \cdot 5 = 10 \] \[ 3 \cdot 2 = 6 \] - Since \( 10 \neq 6 \), \( \frac{2}{5} \) is not equivalent to \( \frac{2}{3} \). After checking all options, the only fraction that is equivalent to \( \frac{2}{3} \) is: **(A) \( \frac{8}{12} \)**.