To convert the division equation \(9 \div \frac{1}{6}\) into a multiplication equation, you can multiply by the reciprocal of \(\frac{1}{6}\). The reciprocal of \(\frac{1}{6}\) is \(6\).
Thus, the equivalent multiplication equation is:
\[ 9 \times 6 \]
So, \(9 \div \frac{1}{6} = 9 \times 6\).