To determine if the ratios \( \frac{6}{14} \) and \( \frac{10}{23} \) are equivalent, we can simplify \( \frac{6}{14} \) and compare it to \( \frac{10}{23} \).
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Simplifying \( \frac{6}{14} \):
- The greatest common divisor (GCD) of 6 and 14 is 2.
- Dividing both the numerator and the denominator by 2: \[ \frac{6 \div 2}{14 \div 2} = \frac{3}{7} \]
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Comparing \( \frac{3}{7} \) and \( \frac{10}{23} \):
- To compare \( \frac{3}{7} \) and \( \frac{10}{23} \), we can cross-multiply: \[ 3 \times 23 = 69 \] \[ 10 \times 7 = 70 \]
- Since \( 69 \neq 70 \), the ratios are not equivalent.
Therefore, the ratios \( \frac{6}{14} \) and \( \frac{10}{23} \) are not equivalent.