Solve {l}{25}{25}{35}{30}{80}{5/10}{5/50}{50/75}

$$\left. \begin{array} { l } { 25 } \\ { 25 } \\ { 35 } \\ { 30 } \\ { 80 } \\ { \frac { 5 } { 10 } } \\ { \frac { 5 } { 50 } } \\ { \frac { 50 } { 75 } } \end{array} \right.$$

Sort

$$\frac{1}{10},\frac{1}{2},\frac{2}{3},25,25,30,35,80$$

Solution Steps

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

$$sort(25,25,35,30,80,\frac{1}{2},\frac{5}{50},\frac{50}{75})$$

Reduce the fraction \frac{5}{50} to lowest terms by extracting and canceling out 5.

$$sort(25,25,35,30,80,\frac{1}{2},\frac{1}{10},\frac{50}{75})$$

Reduce the fraction \frac{50}{75} to lowest terms by extracting and canceling out 25.

$$sort(25,25,35,30,80,\frac{1}{2},\frac{1}{10},\frac{2}{3})$$

Convert decimal numbers in the list 25,25,35,30,80,\frac{1}{2},\frac{1}{10},\frac{2}{3} to fractions.

$$25,25,35,30,80,\frac{1}{2},\frac{1}{10},\frac{2}{3}$$

Least common denominator of the numbers in the list 25,25,35,30,80,\frac{1}{2},\frac{1}{10},\frac{2}{3} is 30. Convert numbers in the list to fractions with denominator 30.

$$\frac{750}{30},\frac{750}{30},\frac{1050}{30},\frac{900}{30},\frac{2400}{30},\frac{15}{30},\frac{3}{30},\frac{20}{30}$$

To sort the list, start from a single element \frac{750}{30}.

$$\frac{750}{30}$$

Insert \frac{750}{30} to the appropriate location in the new list.

$$\frac{750}{30},\frac{750}{30}$$

Insert \frac{1050}{30} to the appropriate location in the new list.

$$\frac{750}{30},\frac{750}{30},\frac{1050}{30}$$

Insert \frac{900}{30} to the appropriate location in the new list.

$$\frac{750}{30},\frac{750}{30},\frac{900}{30},\frac{1050}{30}$$

Insert \frac{2400}{30} to the appropriate location in the new list.

$$\frac{750}{30},\frac{750}{30},\frac{900}{30},\frac{1050}{30},\frac{2400}{30}$$

Insert \frac{15}{30} to the appropriate location in the new list.

$$\frac{15}{30},\frac{750}{30},\frac{750}{30},\frac{900}{30},\frac{1050}{30},\frac{2400}{30}$$

Insert \frac{3}{30} to the appropriate location in the new list.

$$\frac{3}{30},\frac{15}{30},\frac{750}{30},\frac{750}{30},\frac{900}{30},\frac{1050}{30},\frac{2400}{30}$$

Insert \frac{20}{30} to the appropriate location in the new list.

$$\frac{3}{30},\frac{15}{30},\frac{20}{30},\frac{750}{30},\frac{750}{30},\frac{900}{30},\frac{1050}{30},\frac{2400}{30}$$

Replace the obtained fractions with the initial values.

$$\frac{1}{10},\frac{1}{2},\frac{2}{3},25,25,30,35,80$$

Evaluate

$$25,\ 25,\ 35,\ 30,\ 80,\ \frac{1}{2},\ \frac{1}{10},\ \frac{2}{3}$$