The division equation \( 9 \div \frac{1}{6} \) can be rewritten as a multiplication equation using the reciprocal of \( \frac{1}{6} \).
The reciprocal of \( \frac{1}{6} \) is \( 6 \). Therefore, the multiplication equation equivalent to \( 9 \div \frac{1}{6} \) is:
\[ 9 \times 6 \]
So, \( 9 \div \frac{1}{6} = 9 \times 6 \).