Least common multiple of $15$ and $5$ is $15$. Convert $\frac{4}{15}$ and $\frac{2}{5}$ to fractions with denominator $15$.
$$sort(\frac{4}{15}+\frac{6}{15},\frac{4}{15})$$
Since $\frac{4}{15}$ and $\frac{6}{15}$ have the same denominator, add them by adding their numerators.
$$sort(\frac{4+6}{15},\frac{4}{15})$$
Add $4$ and $6$ to get $10$.
$$sort(\frac{10}{15},\frac{4}{15})$$
Reduce the fraction $\frac{10}{15}$ to lowest terms by extracting and canceling out $5$.
$$sort(\frac{2}{3},\frac{4}{15})$$
Least common denominator of the numbers in the list $\frac{2}{3},\frac{4}{15}$ is $15$. Convert numbers in the list to fractions with denominator $15$.
$$\frac{10}{15},\frac{4}{15}$$
To sort the list, start from a single element $\frac{10}{15}$.
$$\frac{10}{15}$$
Insert $\frac{4}{15}$ to the appropriate location in the new list.
$$\frac{4}{15},\frac{10}{15}$$
Replace the obtained fractions with the initial values.
