To find a ratio that is equivalent to \( \frac{9}{78} \), we can simplify \( \frac{9}{78} \).
First, we can find the greatest common divisor (GCD) of 9 and 78, which is 9.
Now, divide both the numerator and the denominator by their GCD:
\[ \frac{9 \div 9}{78 \div 9} = \frac{1}{8.67} \]
Now let’s check the provided options against \( \frac{9}{78} \):
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\( \frac{1}{3} \) - Not equivalent
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\( \frac{1}{8} \) - Not equivalent
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\( \frac{3}{18} \)
Simplifying \( \frac{3}{18} \):
\[ \frac{3 \div 3}{18 \div 3} = \frac{1}{6} \quad \text{(Not equivalent)} \]
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\( \frac{3}{26} \)
To convert \( \frac{9}{78} \) into a common form with \( \frac{3}{26} \): We can see if:
\[ 9 \cdot 26 \quad \text{and} \quad 3 \cdot 78 \]
Simplifying out gives us equivalent terms: \[ 234 \quad \text{and} \quad 234 \quad \text{(Equivalent)} \]
Hence, \( \frac{3}{26} \) is indeed equivalent to \( \frac{9}{78} \).
So the answer is:
3/26.