Solve {l}{3:54}{6:35}{7:26}{8:15}{6:36}{7:21}{6:27}{8:35}{5:12}{3:57}

$$\left. \begin{array} { l } { 3 : 54 } \\ { 6 : 35 } \\ { 7 : 26 } \\ { 8 : 15 } \\ { 6 : 36 } \\ { 7 : 21 } \\ { 6 : 27 } \\ { 8 : 35 } \\ { 5 : 12 } \\ { 3 : 57 } \end{array} \right.$$

Sort

$$\frac{1}{19},\frac{1}{18},\frac{1}{6},\frac{6}{35},\frac{2}{9},\frac{8}{35},\frac{7}{26},\frac{1}{3},\frac{5}{12},\frac{8}{15}$$

Solution Steps

Reduce the fraction \frac{3}{54} to lowest terms by extracting and canceling out 3.

$$sort(\frac{1}{18},\frac{6}{35},\frac{7}{26},\frac{8}{15},\frac{6}{36},\frac{7}{21},\frac{6}{27},\frac{8}{35},\frac{5}{12},\frac{3}{57})$$

Reduce the fraction \frac{6}{36} to lowest terms by extracting and canceling out 6.

$$sort(\frac{1}{18},\frac{6}{35},\frac{7}{26},\frac{8}{15},\frac{1}{6},\frac{7}{21},\frac{6}{27},\frac{8}{35},\frac{5}{12},\frac{3}{57})$$

Reduce the fraction \frac{7}{21} to lowest terms by extracting and canceling out 7.

$$sort(\frac{1}{18},\frac{6}{35},\frac{7}{26},\frac{8}{15},\frac{1}{6},\frac{1}{3},\frac{6}{27},\frac{8}{35},\frac{5}{12},\frac{3}{57})$$

Reduce the fraction \frac{6}{27} to lowest terms by extracting and canceling out 3.

$$sort(\frac{1}{18},\frac{6}{35},\frac{7}{26},\frac{8}{15},\frac{1}{6},\frac{1}{3},\frac{2}{9},\frac{8}{35},\frac{5}{12},\frac{3}{57})$$

Reduce the fraction \frac{3}{57} to lowest terms by extracting and canceling out 3.

$$sort(\frac{1}{18},\frac{6}{35},\frac{7}{26},\frac{8}{15},\frac{1}{6},\frac{1}{3},\frac{2}{9},\frac{8}{35},\frac{5}{12},\frac{1}{19})$$

Least common denominator of the numbers in the list \frac{1}{18},\frac{6}{35},\frac{7}{26},\frac{8}{15},\frac{1}{6},\frac{1}{3},\frac{2}{9},\frac{8}{35},\frac{5}{12},\frac{1}{19} is 311220. Convert numbers in the list to fractions with denominator 311220.

$$\frac{17290}{311220},\frac{53352}{311220},\frac{83790}{311220},\frac{165984}{311220},\frac{51870}{311220},\frac{103740}{311220},\frac{69160}{311220},\frac{71136}{311220},\frac{129675}{311220},\frac{16380}{311220}$$

To sort the list, start from a single element \frac{17290}{311220}.

$$\frac{17290}{311220}$$

Insert \frac{53352}{311220} to the appropriate location in the new list.

$$\frac{17290}{311220},\frac{53352}{311220}$$

Insert \frac{83790}{311220} to the appropriate location in the new list.

$$\frac{17290}{311220},\frac{53352}{311220},\frac{83790}{311220}$$

Insert \frac{165984}{311220} to the appropriate location in the new list.

$$\frac{17290}{311220},\frac{53352}{311220},\frac{83790}{311220},\frac{165984}{311220}$$

Insert \frac{51870}{311220} to the appropriate location in the new list.

$$\frac{17290}{311220},\frac{51870}{311220},\frac{53352}{311220},\frac{83790}{311220},\frac{165984}{311220}$$

Insert \frac{103740}{311220} to the appropriate location in the new list.

$$\frac{17290}{311220},\frac{51870}{311220},\frac{53352}{311220},\frac{83790}{311220},\frac{103740}{311220},\frac{165984}{311220}$$

Insert \frac{69160}{311220} to the appropriate location in the new list.

$$\frac{17290}{311220},\frac{51870}{311220},\frac{53352}{311220},\frac{69160}{311220},\frac{83790}{311220},\frac{103740}{311220},\frac{165984}{311220}$$

Insert \frac{71136}{311220} to the appropriate location in the new list.

$$\frac{17290}{311220},\frac{51870}{311220},\frac{53352}{311220},\frac{69160}{311220},\frac{71136}{311220},\frac{83790}{311220},\frac{103740}{311220},\frac{165984}{311220}$$

Insert \frac{129675}{311220} to the appropriate location in the new list.

$$\frac{17290}{311220},\frac{51870}{311220},\frac{53352}{311220},\frac{69160}{311220},\frac{71136}{311220},\frac{83790}{311220},\frac{103740}{311220},\frac{129675}{311220},\frac{165984}{311220}$$

Insert \frac{16380}{311220} to the appropriate location in the new list.

$$\frac{16380}{311220},\frac{17290}{311220},\frac{51870}{311220},\frac{53352}{311220},\frac{69160}{311220},\frac{71136}{311220},\frac{83790}{311220},\frac{103740}{311220},\frac{129675}{311220},\frac{165984}{311220}$$

Replace the obtained fractions with the initial values.

$$\frac{1}{19},\frac{1}{18},\frac{1}{6},\frac{6}{35},\frac{2}{9},\frac{8}{35},\frac{7}{26},\frac{1}{3},\frac{5}{12},\frac{8}{15}$$

Evaluate

$$\frac{1}{18},\ \frac{6}{35},\ \frac{7}{26},\ \frac{8}{15},\ \frac{1}{6},\ \frac{1}{3},\ \frac{2}{9},\ \frac{8}{35},\ \frac{5}{12},\ \frac{1}{19}$$