To find which ratio is equivalent to \( \frac{9}{78} \), we can simplify \( \frac{9}{78} \) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 9.
\[ \frac{9 \div 9}{78 \div 9} = \frac{1}{8.6667} \text{ (approximately)} \]
Let's check the choices to see if any can be simplified to an equivalent fraction:
- \( \frac{1}{3} \)
- \( \frac{1}{8} \)
- \( \frac{3}{26} \)
- \( \frac{3}{18} \)
Now let's check \( \frac{3}{26} \):
We can simplify \( \frac{3}{26} \) as follows:
The GCD of 3 and 26 is 1, so \( \frac{3}{26} \) is already in simplest form.
Now let's check \( \frac{3}{18} \):
Now we simplify \( \frac{3}{18} \):
\[ \frac{3 \div 3}{18 \div 3} = \frac{1}{6} \]
Now, let's see if any are equivalent:
If we now compare each with the simplified form of \( \frac{9}{78} = \frac{1}{8.6667} \)
The only fraction that approximates \( \frac{1}{8.6667} \) within rationale fractions choices when checked:
None of the others match except re-evaluating for numerical conversion.
Conclusion:
The equivalent fraction for \( \frac{9}{78} \) among given responses goes toward \( \frac{3}{26} \).
So:
The answer is thus: \( \frac{3}{26} \)