Problem 21 (1987 AJHSME)

Suppose $n^*$ means $\frac{1}{n}$, the reciprocal of $n$. For example, $5^*=\frac{1}{5}$. How many of the following statements are true? i) $3^*+6^*=9^*$ ii) $6^*-4^*=2^*$ iii) $2^* \cdot 6^*=12^*$ iv) $10^* \div 2^*=5^*$