Solve {l}{1/2}{3/4}{5/6}{5/8}{9}

$$\left. \begin{array} { l } { \frac { 1 } { 2 } } \\ { \frac { 3 } { 4 } } \\ { \frac { 5 } { 6 } } \\ { \frac { 5 } { 8 } } \\ { 9 } \end{array} \right.$$

Sort

$$\frac{1}{2},\frac{5}{8},\frac{3}{4},\frac{5}{6},9$$

Solution Steps

Convert decimal numbers in the list \frac{1}{2},\frac{3}{4},\frac{5}{6},\frac{5}{8},9 to fractions.

$$\frac{1}{2},\frac{3}{4},\frac{5}{6},\frac{5}{8},9$$

Least common denominator of the numbers in the list \frac{1}{2},\frac{3}{4},\frac{5}{6},\frac{5}{8},9 is 24. Convert numbers in the list to fractions with denominator 24.

$$\frac{12}{24},\frac{18}{24},\frac{20}{24},\frac{15}{24},\frac{216}{24}$$

To sort the list, start from a single element \frac{12}{24}.

$$\frac{12}{24}$$

Insert \frac{18}{24} to the appropriate location in the new list.

$$\frac{12}{24},\frac{18}{24}$$

Insert \frac{20}{24} to the appropriate location in the new list.

$$\frac{12}{24},\frac{18}{24},\frac{20}{24}$$

Insert \frac{15}{24} to the appropriate location in the new list.

$$\frac{12}{24},\frac{15}{24},\frac{18}{24},\frac{20}{24}$$

Insert \frac{216}{24} to the appropriate location in the new list.

$$\frac{12}{24},\frac{15}{24},\frac{18}{24},\frac{20}{24},\frac{216}{24}$$

Replace the obtained fractions with the initial values.

$$\frac{1}{2},\frac{5}{8},\frac{3}{4},\frac{5}{6},9$$

Evaluate

$$\frac{1}{2},\ \frac{3}{4},\ \frac{5}{6},\ \frac{5}{8},\ 9$$