Solve {c}{(57/36-41/18+11/72)36}{75-1/2}

$$\left. \begin{array} { c } { ( 5 \frac { 7 } { 36 } - 4 \frac { 1 } { 18 } + 1 \frac { 1 } { 72 } ) 36 } \\ { 75 - \frac { 1 } { 2 } } \end{array} \right.$$

Sort

$$\frac{149}{2},\frac{155}{2}$$

Solution Steps

Multiply 5 and 36 to get 180.

$$sort(\left(\frac{180+7}{36}-\frac{4\times 18+1}{18}+\frac{1\times 72+1}{72}\right)\times 36,75-\frac{1}{2})$$

Add 180 and 7 to get 187.

$$sort(\left(\frac{187}{36}-\frac{4\times 18+1}{18}+\frac{1\times 72+1}{72}\right)\times 36,75-\frac{1}{2})$$

Multiply 4 and 18 to get 72.

$$sort(\left(\frac{187}{36}-\frac{72+1}{18}+\frac{1\times 72+1}{72}\right)\times 36,75-\frac{1}{2})$$

Add 72 and 1 to get 73.

$$sort(\left(\frac{187}{36}-\frac{73}{18}+\frac{1\times 72+1}{72}\right)\times 36,75-\frac{1}{2})$$

Least common multiple of 36 and 18 is 36. Convert \frac{187}{36} and \frac{73}{18} to fractions with denominator 36.

$$sort(\left(\frac{187}{36}-\frac{146}{36}+\frac{1\times 72+1}{72}\right)\times 36,75-\frac{1}{2})$$

Since \frac{187}{36} and \frac{146}{36} have the same denominator, subtract them by subtracting their numerators.

$$sort(\left(\frac{187-146}{36}+\frac{1\times 72+1}{72}\right)\times 36,75-\frac{1}{2})$$

Subtract 146 from 187 to get 41.

$$sort(\left(\frac{41}{36}+\frac{1\times 72+1}{72}\right)\times 36,75-\frac{1}{2})$$

Multiply 1 and 72 to get 72.

$$sort(\left(\frac{41}{36}+\frac{72+1}{72}\right)\times 36,75-\frac{1}{2})$$

Add 72 and 1 to get 73.

$$sort(\left(\frac{41}{36}+\frac{73}{72}\right)\times 36,75-\frac{1}{2})$$

Least common multiple of 36 and 72 is 72. Convert \frac{41}{36} and \frac{73}{72} to fractions with denominator 72.

$$sort(\left(\frac{82}{72}+\frac{73}{72}\right)\times 36,75-\frac{1}{2})$$

Since \frac{82}{72} and \frac{73}{72} have the same denominator, add them by adding their numerators.

$$sort(\frac{82+73}{72}\times 36,75-\frac{1}{2})$$

Add 82 and 73 to get 155.

$$sort(\frac{155}{72}\times 36,75-\frac{1}{2})$$

Express \frac{155}{72}\times 36 as a single fraction.

$$sort(\frac{155\times 36}{72},75-\frac{1}{2})$$

Multiply 155 and 36 to get 5580.

$$sort(\frac{5580}{72},75-\frac{1}{2})$$

Reduce the fraction \frac{5580}{72} to lowest terms by extracting and canceling out 36.

$$sort(\frac{155}{2},75-\frac{1}{2})$$

Convert 75 to fraction \frac{150}{2}.

$$sort(\frac{155}{2},\frac{150}{2}-\frac{1}{2})$$

Since \frac{150}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{155}{2},\frac{150-1}{2})$$

Subtract 1 from 150 to get 149.

$$sort(\frac{155}{2},\frac{149}{2})$$

To sort the list, start from a single element \frac{155}{2}.

$$\frac{155}{2}$$

Insert \frac{149}{2} to the appropriate location in the new list.

$$\frac{149}{2},\frac{155}{2}$$

Evaluate

$$\frac{155}{2},\ \frac{149}{2}$$