Solve 2+1/2,2+1/2+frac{1{2}},2+1/2+1{2+frac{1/2}}

$$2 + \frac { 1 } { 2 } , 2 + \frac { 1 } { 2 + \frac { 1 } { 2 } } , 2 + \frac { 1 } { 2 + \frac { 1 } { 2 + \frac { 1 } { 2 } } }$$

Sort

$$\frac{12}{5},\frac{29}{12},\frac{5}{2}$$

Solution Steps

Convert 2 to fraction \frac{4}{2}.

$$sort(\frac{4}{2}+\frac{1}{2},2+\frac{1}{2+\frac{1}{2}},2+\frac{1}{2+\frac{1}{2+\frac{1}{2}}})$$

Since \frac{4}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$sort(\frac{4+1}{2},2+\frac{1}{2+\frac{1}{2}},2+\frac{1}{2+\frac{1}{2+\frac{1}{2}}})$$

Add 4 and 1 to get 5.

$$sort(\frac{5}{2},2+\frac{1}{2+\frac{1}{2}},2+\frac{1}{2+\frac{1}{2+\frac{1}{2}}})$$

Convert 2 to fraction \frac{4}{2}.

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

Since \frac{4}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

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

Add 4 and 1 to get 5.

$$sort(\frac{5}{2},2+\frac{1}{\frac{5}{2}},2+\frac{1}{2+\frac{1}{2+\frac{1}{2}}})$$

Divide 1 by \frac{5}{2} by multiplying 1 by the reciprocal of \frac{5}{2}.

$$sort(\frac{5}{2},2+1\times \frac{2}{5},2+\frac{1}{2+\frac{1}{2+\frac{1}{2}}})$$

Multiply 1 and \frac{2}{5} to get \frac{2}{5}.

$$sort(\frac{5}{2},2+\frac{2}{5},2+\frac{1}{2+\frac{1}{2+\frac{1}{2}}})$$

Convert 2 to fraction \frac{10}{5}.

$$sort(\frac{5}{2},\frac{10}{5}+\frac{2}{5},2+\frac{1}{2+\frac{1}{2+\frac{1}{2}}})$$

Since \frac{10}{5} and \frac{2}{5} have the same denominator, add them by adding their numerators.

$$sort(\frac{5}{2},\frac{10+2}{5},2+\frac{1}{2+\frac{1}{2+\frac{1}{2}}})$$

Add 10 and 2 to get 12.

$$sort(\frac{5}{2},\frac{12}{5},2+\frac{1}{2+\frac{1}{2+\frac{1}{2}}})$$

Convert 2 to fraction \frac{4}{2}.

$$sort(\frac{5}{2},\frac{12}{5},2+\frac{1}{2+\frac{1}{\frac{4}{2}+\frac{1}{2}}})$$

Since \frac{4}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$sort(\frac{5}{2},\frac{12}{5},2+\frac{1}{2+\frac{1}{\frac{4+1}{2}}})$$

Add 4 and 1 to get 5.

$$sort(\frac{5}{2},\frac{12}{5},2+\frac{1}{2+\frac{1}{\frac{5}{2}}})$$

Divide 1 by \frac{5}{2} by multiplying 1 by the reciprocal of \frac{5}{2}.

$$sort(\frac{5}{2},\frac{12}{5},2+\frac{1}{2+1\times \frac{2}{5}})$$

Multiply 1 and \frac{2}{5} to get \frac{2}{5}.

$$sort(\frac{5}{2},\frac{12}{5},2+\frac{1}{2+\frac{2}{5}})$$

Convert 2 to fraction \frac{10}{5}.

$$sort(\frac{5}{2},\frac{12}{5},2+\frac{1}{\frac{10}{5}+\frac{2}{5}})$$

Since \frac{10}{5} and \frac{2}{5} have the same denominator, add them by adding their numerators.

$$sort(\frac{5}{2},\frac{12}{5},2+\frac{1}{\frac{10+2}{5}})$$

Add 10 and 2 to get 12.

$$sort(\frac{5}{2},\frac{12}{5},2+\frac{1}{\frac{12}{5}})$$

Divide 1 by \frac{12}{5} by multiplying 1 by the reciprocal of \frac{12}{5}.

$$sort(\frac{5}{2},\frac{12}{5},2+1\times \frac{5}{12})$$

Multiply 1 and \frac{5}{12} to get \frac{5}{12}.

$$sort(\frac{5}{2},\frac{12}{5},2+\frac{5}{12})$$

Convert 2 to fraction \frac{24}{12}.

$$sort(\frac{5}{2},\frac{12}{5},\frac{24}{12}+\frac{5}{12})$$

Since \frac{24}{12} and \frac{5}{12} have the same denominator, add them by adding their numerators.

$$sort(\frac{5}{2},\frac{12}{5},\frac{24+5}{12})$$

Add 24 and 5 to get 29.

$$sort(\frac{5}{2},\frac{12}{5},\frac{29}{12})$$

Least common denominator of the numbers in the list \frac{5}{2},\frac{12}{5},\frac{29}{12} is 60. Convert numbers in the list to fractions with denominator 60.

$$\frac{150}{60},\frac{144}{60},\frac{145}{60}$$

To sort the list, start from a single element \frac{150}{60}.

$$\frac{150}{60}$$

Insert \frac{144}{60} to the appropriate location in the new list.

$$\frac{144}{60},\frac{150}{60}$$

Insert \frac{145}{60} to the appropriate location in the new list.

$$\frac{144}{60},\frac{145}{60},\frac{150}{60}$$

Replace the obtained fractions with the initial values.

$$\frac{12}{5},\frac{29}{12},\frac{5}{2}$$

Evaluate

$$\frac{5}{2},\frac{12}{5},\frac{29}{12}$$