To find the missing number that makes the fractions equal, we can set up the equation:
\[ \frac{1}{x} = \frac{6}{18} \]
First, we simplify the fraction \(\frac{6}{18}\):
\[ \frac{6}{18} = \frac{1}{3} \]
Now we have:
\[ \frac{1}{x} = \frac{1}{3} \]
To solve for \(x\), we can set the denominators equal to each other:
\[ x = 3 \]
Thus, the missing number is:
\[ \boxed{3} \]