The ratio $\dfrac{1}{8} : \dfrac{1}{12}$ converted to the simplest form is

1. 12 : 8
2. 3 : 2
3. 2 : 5
4. 8 : 20

Given:

Ratio: $\dfrac{1}{8} : \dfrac{1}{12}$

Let us find the L.C.M. of denominators 8 and 12:

$\begin{array}{l|rr} 2 & 8, & 12 \ \hline 2 & 4, & 6 \ \hline 2 & 2, & 3 \ \hline 3 & 1, & 3 \ \hline & 1, & 1 \end{array}$

L.C.M. = 2 x 2 x 2 x 3 = 24

Multiply both terms by 24:

$\Big(\dfrac{1}{8} \times 24\Big) : \Big(\dfrac{1}{12} \times 24\Big) = 3 : 2$

Hence, option 2 is the correct option.