Find the reciprocal ratio of :

(i) 4 : 7

(ii) 3² : 4²

(iii) $\dfrac{1}{9} : 2$

(i) The reciprocal ratio of 4 : 7 is,

$= \dfrac{1}{4} : \dfrac{1}{7} \\[0.5em] = \dfrac{\dfrac{1}{4}}{\dfrac{1}{7}} \\[0.5em] = \dfrac{7}{4} \\[0.5em] = 7 : 4$

Hence, the reciprocal ratio is 7 : 4.

(ii) The reciprocal ratio of 3² : 4² is,

$= \dfrac{1}{3^2} : \dfrac{1}{4^2} \\[0.5em] = \dfrac{\dfrac{1}{9}}{\dfrac{1}{16}} \\[0.5em] = \dfrac{16}{9} \\[0.5em] = 16 : 9$

Hence, the reciprocal ratio is 16 : 9.

(iii) The reciprocal ratio of $\dfrac{1}{9} : 2$ is,

$= \dfrac{1}{\dfrac{1}{9}} : \dfrac{1}{2} \\[0.5em] = \dfrac{9}{\dfrac{1}{2}} \\[0.5em] = \dfrac{18}{1} \\[0.5em] = 18 : 1$

Hence, the reciprocal ratio is 18 : 1.