Solve 37/10,24/5,31/4,23/10,3frac{3}{4}

$$3 \frac { 7 } { 10 } , 2 \frac { 4 } { 5 } , 3 \frac { 1 } { 4 } , 2 \frac { 3 } { 10 } , 3 \frac { 3 } { 4 }$$

Sort

$$\frac{23}{10},\frac{14}{5},\frac{13}{4},\frac{37}{10},\frac{15}{4}$$

Solution Steps

Multiply 3 and 10 to get 30.

$$sort(\frac{30+7}{10},\frac{2\times 5+4}{5},\frac{3\times 4+1}{4},\frac{2\times 10+3}{10},\frac{3\times 4+3}{4})$$

Add 30 and 7 to get 37.

$$sort(\frac{37}{10},\frac{2\times 5+4}{5},\frac{3\times 4+1}{4},\frac{2\times 10+3}{10},\frac{3\times 4+3}{4})$$

Multiply 2 and 5 to get 10.

$$sort(\frac{37}{10},\frac{10+4}{5},\frac{3\times 4+1}{4},\frac{2\times 10+3}{10},\frac{3\times 4+3}{4})$$

Add 10 and 4 to get 14.

$$sort(\frac{37}{10},\frac{14}{5},\frac{3\times 4+1}{4},\frac{2\times 10+3}{10},\frac{3\times 4+3}{4})$$

Multiply 3 and 4 to get 12.

$$sort(\frac{37}{10},\frac{14}{5},\frac{12+1}{4},\frac{2\times 10+3}{10},\frac{3\times 4+3}{4})$$

Add 12 and 1 to get 13.

$$sort(\frac{37}{10},\frac{14}{5},\frac{13}{4},\frac{2\times 10+3}{10},\frac{3\times 4+3}{4})$$

Multiply 2 and 10 to get 20.

$$sort(\frac{37}{10},\frac{14}{5},\frac{13}{4},\frac{20+3}{10},\frac{3\times 4+3}{4})$$

Add 20 and 3 to get 23.

$$sort(\frac{37}{10},\frac{14}{5},\frac{13}{4},\frac{23}{10},\frac{3\times 4+3}{4})$$

Multiply 3 and 4 to get 12.

$$sort(\frac{37}{10},\frac{14}{5},\frac{13}{4},\frac{23}{10},\frac{12+3}{4})$$

Add 12 and 3 to get 15.

$$sort(\frac{37}{10},\frac{14}{5},\frac{13}{4},\frac{23}{10},\frac{15}{4})$$

Least common denominator of the numbers in the list \frac{37}{10},\frac{14}{5},\frac{13}{4},\frac{23}{10},\frac{15}{4} is 20. Convert numbers in the list to fractions with denominator 20.

$$\frac{74}{20},\frac{56}{20},\frac{65}{20},\frac{46}{20},\frac{75}{20}$$

To sort the list, start from a single element \frac{74}{20}.

$$\frac{74}{20}$$

Insert \frac{56}{20} to the appropriate location in the new list.

$$\frac{56}{20},\frac{74}{20}$$

Insert \frac{65}{20} to the appropriate location in the new list.

$$\frac{56}{20},\frac{65}{20},\frac{74}{20}$$

Insert \frac{46}{20} to the appropriate location in the new list.

$$\frac{46}{20},\frac{56}{20},\frac{65}{20},\frac{74}{20}$$

Insert \frac{75}{20} to the appropriate location in the new list.

$$\frac{46}{20},\frac{56}{20},\frac{65}{20},\frac{74}{20},\frac{75}{20}$$

Replace the obtained fractions with the initial values.

$$\frac{23}{10},\frac{14}{5},\frac{13}{4},\frac{37}{10},\frac{15}{4}$$

Evaluate

$$\frac{37}{10},\frac{14}{5},\frac{13}{4},\frac{23}{10},\frac{15}{4}$$