To use the rule "multiply by the reciprocal" for the expression \( 6 \div \frac{1}{2} \), you would rewrite the division as multiplication by the reciprocal of \( \frac{1}{2} \).
The reciprocal of \( \frac{1}{2} \) is \( 2 \).
So, \( 6 \div \frac{1}{2} \) can be expressed as: \[ 6 \times 2 \]
Among the options you provided, the correct expression that follows the rule “multiply by the reciprocal” is: 6 times 2.