Question 21
Suppose $n^\ast$ means $\dfrac1n,$ the reciprocal of $n.$ For example, $5^\ast = \dfrac15.$ How many of the following four statements are true?
$$
\mathrm{(i)}\quad 3^\ast + 6^\ast = 9^\ast
$$
$$
\mathrm{(ii)}\quad 6^\ast - 4^\ast = 2^\ast
$$
$$
\mathrm{(iii)}\quad 2^\ast \cdot 6^\ast = 12^\ast
$$
$$
\mathrm{(iv)}\quad 10^\ast \div 2^\ast = 5^\ast
$$
$$
\mathrm{(i)}\quad 3^\ast + 6^\ast = 9^\ast
$$
$$
\mathrm{(ii)}\quad 6^\ast - 4^\ast = 2^\ast
$$
$$
\mathrm{(iii)}\quad 2^\ast \cdot 6^\ast = 12^\ast
$$
$$
\mathrm{(iv)}\quad 10^\ast \div 2^\ast = 5^\ast
$$