Fraction $\frac{-5}{9}$ can be rewritten as $-\frac{5}{9}$ by extracting the negative sign.
$$sort(1.5,\frac{2}{3}-\frac{5}{9}+\frac{7}{6})$$
Least common multiple of $3$ and $9$ is $9$. Convert $\frac{2}{3}$ and $\frac{5}{9}$ to fractions with denominator $9$.
$$sort(1.5,\frac{6}{9}-\frac{5}{9}+\frac{7}{6})$$
Since $\frac{6}{9}$ and $\frac{5}{9}$ have the same denominator, subtract them by subtracting their numerators.
$$sort(1.5,\frac{6-5}{9}+\frac{7}{6})$$
Subtract $5$ from $6$ to get $1$.
$$sort(1.5,\frac{1}{9}+\frac{7}{6})$$
Least common multiple of $9$ and $6$ is $18$. Convert $\frac{1}{9}$ and $\frac{7}{6}$ to fractions with denominator $18$.
$$sort(1.5,\frac{2}{18}+\frac{21}{18})$$
Since $\frac{2}{18}$ and $\frac{21}{18}$ have the same denominator, add them by adding their numerators.
$$sort(1.5,\frac{2+21}{18})$$
Add $2$ and $21$ to get $23$.
$$sort(1.5,\frac{23}{18})$$
Convert decimal numbers in the list $1.5,\frac{23}{18}$ to fractions.
$$\frac{3}{2},\frac{23}{18}$$
Least common denominator of the numbers in the list $\frac{3}{2},\frac{23}{18}$ is $18$. Convert numbers in the list to fractions with denominator $18$.
$$\frac{27}{18},\frac{23}{18}$$
To sort the list, start from a single element $\frac{27}{18}$.
$$\frac{27}{18}$$
Insert $\frac{23}{18}$ to the appropriate location in the new list.
$$\frac{23}{18},\frac{27}{18}$$
Replace the obtained fractions with the initial values.
