To find which ratio is equivalent to \( \frac{9}{78} \), we can simplify \( \frac{9}{78} \) by finding the greatest common divisor (GCD) of the numerator and the denominator.
The GCD of 9 and 78 is 9. Therefore, we can simplify \( \frac{9}{78} \) as follows:
\[ \frac{9 \div 9}{78 \div 9} = \frac{1}{8.67} \approx \frac{1}{9} \]
However, that’s not exactly one of the options provided. Instead, let's check the provided options directly to find an equivalent ratio.
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Checking \( \frac{3}{18} \): \[ \frac{3}{18} = \frac{1}{6} \quad \text{(not equivalent)} \]
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Checking \( \frac{1}{3} \): \[ \frac{1}{3} \quad \text{(not equivalent)} \]
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Checking \( \frac{1}{8} \): \[ \frac{1}{8} \quad \text{(not equivalent)} \]
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Checking \( \frac{3}{26} \): To compare, we can cross-multiply: \[ 9 \times 26 = 234 \quad \text{and} \quad 3 \times 78 = 234 \quad \text{(equivalent)} \]
Thus, the ratio equivalent to \( \frac{9}{78} \) is:
\[ \boxed{\frac{3}{26}} \]