Solve 2/1,3/3,4/5,5/7,frac{6}{9}

$$\frac { 2 } { 1 } , \frac { 3 } { 3 } , \frac { 4 } { 5 } , \frac { 5 } { 7 } , \frac { 6 } { 9 }$$

Sort

$$\frac{2}{3},\frac{5}{7},\frac{4}{5},1,2$$

Solution Steps

Divide 3 by 3 to get 1.

$$sort(\frac{2}{1},1,\frac{4}{5},\frac{5}{7},\frac{6}{9})$$

Anything divided by one gives itself.

$$sort(2,1,\frac{4}{5},\frac{5}{7},\frac{6}{9})$$

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

$$sort(2,1,\frac{4}{5},\frac{5}{7},\frac{2}{3})$$

Convert decimal numbers in the list 2,1,\frac{4}{5},\frac{5}{7},\frac{2}{3} to fractions.

$$2,1,\frac{4}{5},\frac{5}{7},\frac{2}{3}$$

Least common denominator of the numbers in the list 2,1,\frac{4}{5},\frac{5}{7},\frac{2}{3} is 105. Convert numbers in the list to fractions with denominator 105.

$$\frac{210}{105},\frac{105}{105},\frac{84}{105},\frac{75}{105},\frac{70}{105}$$

To sort the list, start from a single element \frac{210}{105}.

$$\frac{210}{105}$$

Insert \frac{105}{105} to the appropriate location in the new list.

$$\frac{105}{105},\frac{210}{105}$$

Insert \frac{84}{105} to the appropriate location in the new list.

$$\frac{84}{105},\frac{105}{105},\frac{210}{105}$$

Insert \frac{75}{105} to the appropriate location in the new list.

$$\frac{75}{105},\frac{84}{105},\frac{105}{105},\frac{210}{105}$$

Insert \frac{70}{105} to the appropriate location in the new list.

$$\frac{70}{105},\frac{75}{105},\frac{84}{105},\frac{105}{105},\frac{210}{105}$$

Replace the obtained fractions with the initial values.

$$\frac{2}{3},\frac{5}{7},\frac{4}{5},1,2$$

Evaluate

$$2,1,\frac{4}{5},\frac{5}{7},\frac{2}{3}$$