Solve 16/6,15/21,4/22,2/3,frac{12}{9}

$$\frac { 16 } { 6 } , \frac { 15 } { 21 } , \frac { 4 } { 22 } , \frac { 2 } { 3 } , \frac { 12 } { 9 }$$

Sort

$$\frac{2}{11},\frac{2}{3},\frac{5}{7},\frac{4}{3},\frac{8}{3}$$

Solution Steps

Reduce the fraction \frac{16}{6} to lowest terms by extracting and canceling out 2.

$$sort(\frac{8}{3},\frac{15}{21},\frac{4}{22},\frac{2}{3},\frac{12}{9})$$

Reduce the fraction \frac{15}{21} to lowest terms by extracting and canceling out 3.

$$sort(\frac{8}{3},\frac{5}{7},\frac{4}{22},\frac{2}{3},\frac{12}{9})$$

Reduce the fraction \frac{4}{22} to lowest terms by extracting and canceling out 2.

$$sort(\frac{8}{3},\frac{5}{7},\frac{2}{11},\frac{2}{3},\frac{12}{9})$$

Reduce the fraction \frac{12}{9} to lowest terms by extracting and canceling out 3.

$$sort(\frac{8}{3},\frac{5}{7},\frac{2}{11},\frac{2}{3},\frac{4}{3})$$

Least common denominator of the numbers in the list \frac{8}{3},\frac{5}{7},\frac{2}{11},\frac{2}{3},\frac{4}{3} is 231. Convert numbers in the list to fractions with denominator 231.

$$\frac{616}{231},\frac{165}{231},\frac{42}{231},\frac{154}{231},\frac{308}{231}$$

To sort the list, start from a single element \frac{616}{231}.

$$\frac{616}{231}$$

Insert \frac{165}{231} to the appropriate location in the new list.

$$\frac{165}{231},\frac{616}{231}$$

Insert \frac{42}{231} to the appropriate location in the new list.

$$\frac{42}{231},\frac{165}{231},\frac{616}{231}$$

Insert \frac{154}{231} to the appropriate location in the new list.

$$\frac{42}{231},\frac{154}{231},\frac{165}{231},\frac{616}{231}$$

Insert \frac{308}{231} to the appropriate location in the new list.

$$\frac{42}{231},\frac{154}{231},\frac{165}{231},\frac{308}{231},\frac{616}{231}$$

Replace the obtained fractions with the initial values.

$$\frac{2}{11},\frac{2}{3},\frac{5}{7},\frac{4}{3},\frac{8}{3}$$

Evaluate

$$\frac{8}{3},\frac{5}{7},\frac{2}{11},\frac{2}{3},\frac{4}{3}$$