Which ratio is equivalent to 9:78 ?

To determine which ratio is equivalent to \( 9:78 \), we can simplify the ratio first.

1. Find the greatest common divisor (GCD) of 9 and 78. The GCD is 9.
2. Divide both numbers by their GCD:

\[ \frac{9 \div 9}{78 \div 9} = \frac{1}{8} \]

So, the ratio \( 9:78 \) simplifies to \( 1:8 \).

Now, let's compare this with the given options:

1. \( 18 \) - not a ratio.
2. \( \frac{1}{8} \) - this is equivalent to the simplified ratio \( 1:8 \).
3. \( \frac{3}{26} \) - equivalent to approximately \( 0.115 \), not equal to \( \frac{1}{8} \) (or \( 0.125 \)).
4. \( \frac{3}{18} \) - simplifies to \( \frac{1}{6} \), not equal to \( \frac{1}{8} \).
5. \( 13 \) - not a ratio.

The equivalent ratio to \( 9:78 \) is:

\(\frac{1}{8}\)