Least common denominator of the numbers in the list $\frac{3}{4},\frac{5}{8},\frac{1}{12}$ is $24$. Convert numbers in the list to fractions with denominator $24$.
$$\frac{18}{24},\frac{15}{24},\frac{2}{24}$$
To sort the list, start from a single element $\frac{18}{24}$.
$$\frac{18}{24}$$
Insert $\frac{15}{24}$ to the appropriate location in the new list.
$$\frac{15}{24},\frac{18}{24}$$
Insert $\frac{2}{24}$ to the appropriate location in the new list.
$$\frac{2}{24},\frac{15}{24},\frac{18}{24}$$
Replace the obtained fractions with the initial values.
