1987 AJHSME Problem 21

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^*

\text{(A)}\ 0 \qquad \text{(B)}\ 1 \qquad \text{(C)}\ 2 \qquad \text{(D)}\ 3 \qquad \text{(E)}\ 4

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.