Solve {l}{(1/2-1/3*1/4+1/5)divfrac{1}{6}}{(frac{1}{2}+frac{1}{3}-frac{1}{6})^3+frac{2}{3}*frac{4}{5}}

$$\left. \begin{array} { l } { ( \frac { 1 } { 2 } - \frac { 1 } { 3 } \times \frac { 1 } { 4 } + \frac { 1 } { 5 } ) \div \frac { 1 } { 6 } } \\ { ( \frac { 1 } { 2 } + \frac { 1 } { 3 } - \frac { 1 } { 6 } ) ^ { 3 } + \frac { 2 } { 3 } \times \frac { 4 } { 5 } } \end{array} \right.$$

Sort

$$\frac{112}{135},\frac{37}{10}$$

Solution Steps

Multiply \frac{1}{3} and \frac{1}{4} to get \frac{1}{12}.

$$sort(\frac{\frac{1}{2}-\frac{1}{12}+\frac{1}{5}}{\frac{1}{6}},\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{6}\right)^{3}+\frac{2}{3}\times \frac{4}{5})$$

Subtract \frac{1}{12} from \frac{1}{2} to get \frac{5}{12}.

$$sort(\frac{\frac{5}{12}+\frac{1}{5}}{\frac{1}{6}},\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{6}\right)^{3}+\frac{2}{3}\times \frac{4}{5})$$

Add \frac{5}{12} and \frac{1}{5} to get \frac{37}{60}.

$$sort(\frac{\frac{37}{60}}{\frac{1}{6}},\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{6}\right)^{3}+\frac{2}{3}\times \frac{4}{5})$$

Divide \frac{37}{60} by \frac{1}{6} by multiplying \frac{37}{60} by the reciprocal of \frac{1}{6}.

$$sort(\frac{37}{60}\times 6,\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{6}\right)^{3}+\frac{2}{3}\times \frac{4}{5})$$

Multiply \frac{37}{60} and 6 to get \frac{37}{10}.

$$sort(\frac{37}{10},\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{6}\right)^{3}+\frac{2}{3}\times \frac{4}{5})$$

Add \frac{1}{2} and \frac{1}{3} to get \frac{5}{6}.

$$sort(\frac{37}{10},\left(\frac{5}{6}-\frac{1}{6}\right)^{3}+\frac{2}{3}\times \frac{4}{5})$$

Subtract \frac{1}{6} from \frac{5}{6} to get \frac{2}{3}.

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

Calculate \frac{2}{3} to the power of 3 and get \frac{8}{27}.

$$sort(\frac{37}{10},\frac{8}{27}+\frac{2}{3}\times \frac{4}{5})$$

Multiply \frac{2}{3} and \frac{4}{5} to get \frac{8}{15}.

$$sort(\frac{37}{10},\frac{8}{27}+\frac{8}{15})$$

Add \frac{8}{27} and \frac{8}{15} to get \frac{112}{135}.

$$sort(\frac{37}{10},\frac{112}{135})$$

Least common denominator of the numbers in the list \frac{37}{10},\frac{112}{135} is 270. Convert numbers in the list to fractions with denominator 270.

$$\frac{999}{270},\frac{224}{270}$$

To sort the list, start from a single element \frac{999}{270}.

$$\frac{999}{270}$$

Insert \frac{224}{270} to the appropriate location in the new list.

$$\frac{224}{270},\frac{999}{270}$$

Replace the obtained fractions with the initial values.

$$\frac{112}{135},\frac{37}{10}$$

Evaluate

$$\frac{37}{10},\ \frac{112}{135}$$