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 (9) and the denominator (78).
- The GCD of 9 and 78 is 9.
- Now, we divide both the numerator and the denominator by the GCD:
\[ \frac{9 \div 9}{78 \div 9} = \frac{1}{8.67} \text{ (approximately)} \]
However, it seems that my simplification leads us away from the provided options as \( \frac{9}{78} \) should simplify to \( \frac{3}{26} \).
Let’s check that:
- \( \frac{9}{78} = \frac{9 \div 3}{78 \div 3} = \frac{3}{26} \)
Now we can compare this to the given options:
- \( \frac{1}{3} \)
- \( \frac{3}{18} \) (which simplifies to \( \frac{1}{6} \))
- \( \frac{3}{26} \)
- \( \frac{1}{8} \)
The ratio equivalent to \( \frac{9}{78} \) is:
\( \frac{3}{26} \)