Solve {l}{15/10}{01/02}{08/05}{00}{10}{08}{13}{07}{11}

$$\left. \begin{array} { l } { \frac { 15 } { 10 } } \\ { \frac { 01 } { 02 } } \\ { \frac { 08 } { 05 } } \\ { 00 } \\ { 10 } \\ { 08 } \\ { 13 } \\ { 07 } \\ { 11 } \end{array} \right.$$

Sort

$$0,\frac{1}{2},\frac{3}{2},\frac{8}{5},7,8,10,11,13$$

Solution Steps

Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$sort(\frac{3}{2},\frac{1}{2},\frac{8}{5},0,10,8,13,7,11)$$

Convert decimal numbers in the list \frac{3}{2},\frac{1}{2},\frac{8}{5},0,10,8,13,7,11 to fractions.

$$\frac{3}{2},\frac{1}{2},\frac{8}{5},0,10,8,13,7,11$$

Least common denominator of the numbers in the list \frac{3}{2},\frac{1}{2},\frac{8}{5},0,10,8,13,7,11 is 10. Convert numbers in the list to fractions with denominator 10.

$$\frac{15}{10},\frac{5}{10},\frac{16}{10},0,\frac{100}{10},\frac{80}{10},\frac{130}{10},\frac{70}{10},\frac{110}{10}$$

To sort the list, start from a single element \frac{15}{10}.

$$\frac{15}{10}$$

Insert \frac{5}{10} to the appropriate location in the new list.

$$\frac{5}{10},\frac{15}{10}$$

Insert \frac{16}{10} to the appropriate location in the new list.

$$\frac{5}{10},\frac{15}{10},\frac{16}{10}$$

Insert 0 to the appropriate location in the new list.

$$0,\frac{5}{10},\frac{15}{10},\frac{16}{10}$$

Insert \frac{100}{10} to the appropriate location in the new list.

$$0,\frac{5}{10},\frac{15}{10},\frac{16}{10},\frac{100}{10}$$

Insert \frac{80}{10} to the appropriate location in the new list.

$$0,\frac{5}{10},\frac{15}{10},\frac{16}{10},\frac{80}{10},\frac{100}{10}$$

Insert \frac{130}{10} to the appropriate location in the new list.

$$0,\frac{5}{10},\frac{15}{10},\frac{16}{10},\frac{80}{10},\frac{100}{10},\frac{130}{10}$$

Insert \frac{70}{10} to the appropriate location in the new list.

$$0,\frac{5}{10},\frac{15}{10},\frac{16}{10},\frac{70}{10},\frac{80}{10},\frac{100}{10},\frac{130}{10}$$

Insert \frac{110}{10} to the appropriate location in the new list.

$$0,\frac{5}{10},\frac{15}{10},\frac{16}{10},\frac{70}{10},\frac{80}{10},\frac{100}{10},\frac{110}{10},\frac{130}{10}$$

Replace the obtained fractions with the initial values.

$$0,\frac{1}{2},\frac{3}{2},\frac{8}{5},7,8,10,11,13$$

Evaluate

$$\frac{3}{2},\ \frac{1}{2},\ \frac{8}{5},\ 0,\ 10,\ 8,\ 13,\ 7,\ 11$$