To determine which ratio is equivalent to \( \frac{9}{78} \), we can simplify the fraction.
First, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 9 and 78 is 9.
So, we divide: \[ \frac{9 \div 9}{78 \div 9} = \frac{1}{8.67} = \frac{1}{8} \]
However, upon reviewing our initial math:
The correct intermediate step should be: \[ \frac{9}{78} = \frac{9 \div 3}{78 \div 3} = \frac{3}{26} \]
Now checking the options:
- \( \frac{3}{18} \) simplifies to \( \frac{1}{6} \), which is not equivalent.
- \( \frac{1}{3} \) is not equivalent.
- \( \frac{1}{8} \) is not equivalent.
- \( \frac{3}{26} \) is equivalent.
Thus, the ratio that is equivalent to \( \frac{9}{78} \) is: \[ \frac{3}{26} \]