Solve {l}{text{68.}36*(1/2-1/3)^2}{-2^4div4/9*(-3/2)^2}{1frac{1}{24}-(frac{3}{8}+frac{1}{6}-frac{3}{4})*frac{3}{4}}

$$\left. \begin{array} { l } { \text { 68. } 36 \times ( \frac { 1 } { 2 } - \frac { 1 } { 3 } ) ^ { 2 } } \\ { - 2 ^ { 4 } \div \frac { 4 } { 9 } \times ( - \frac { 3 } { 2 } ) ^ { 2 } } \\ { 1 \frac { 1 } { 24 } - ( \frac { 3 } { 8 } + \frac { 1 } { 6 } - \frac { 3 } { 4 } ) \times \frac { 3 } { 4 } } \end{array} \right.$$

Sort

$$-81,\frac{115}{96},68$$

Solution Steps

Multiply 68 and 36 to get 2448.

$$sort(2448\left(\frac{1}{2}-\frac{1}{3}\right)^{2},\frac{-2^{4}}{\frac{4}{9}}\left(-\frac{3}{2}\right)^{2},\frac{1\times 24+1}{24}-\left(\frac{3}{8}+\frac{1}{6}-\frac{3}{4}\right)\times \frac{3}{4})$$

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

$$sort(2448\times \left(\frac{1}{6}\right)^{2},\frac{-2^{4}}{\frac{4}{9}}\left(-\frac{3}{2}\right)^{2},\frac{1\times 24+1}{24}-\left(\frac{3}{8}+\frac{1}{6}-\frac{3}{4}\right)\times \frac{3}{4})$$

Calculate \frac{1}{6} to the power of 2 and get \frac{1}{36}.

$$sort(2448\times \frac{1}{36},\frac{-2^{4}}{\frac{4}{9}}\left(-\frac{3}{2}\right)^{2},\frac{1\times 24+1}{24}-\left(\frac{3}{8}+\frac{1}{6}-\frac{3}{4}\right)\times \frac{3}{4})$$

Multiply 2448 and \frac{1}{36} to get 68.

$$sort(68,\frac{-2^{4}}{\frac{4}{9}}\left(-\frac{3}{2}\right)^{2},\frac{1\times 24+1}{24}-\left(\frac{3}{8}+\frac{1}{6}-\frac{3}{4}\right)\times \frac{3}{4})$$

Calculate 2 to the power of 4 and get 16.

$$sort(68,\frac{-16}{\frac{4}{9}}\left(-\frac{3}{2}\right)^{2},\frac{1\times 24+1}{24}-\left(\frac{3}{8}+\frac{1}{6}-\frac{3}{4}\right)\times \frac{3}{4})$$

Divide -16 by \frac{4}{9} by multiplying -16 by the reciprocal of \frac{4}{9}.

$$sort(68,-16\times \frac{9}{4}\left(-\frac{3}{2}\right)^{2},\frac{1\times 24+1}{24}-\left(\frac{3}{8}+\frac{1}{6}-\frac{3}{4}\right)\times \frac{3}{4})$$

Multiply -16 and \frac{9}{4} to get -36.

$$sort(68,-36\left(-\frac{3}{2}\right)^{2},\frac{1\times 24+1}{24}-\left(\frac{3}{8}+\frac{1}{6}-\frac{3}{4}\right)\times \frac{3}{4})$$

Calculate -\frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$sort(68,-36\times \frac{9}{4},\frac{1\times 24+1}{24}-\left(\frac{3}{8}+\frac{1}{6}-\frac{3}{4}\right)\times \frac{3}{4})$$

Multiply -36 and \frac{9}{4} to get -81.

$$sort(68,-81,\frac{1\times 24+1}{24}-\left(\frac{3}{8}+\frac{1}{6}-\frac{3}{4}\right)\times \frac{3}{4})$$

Multiply 1 and 24 to get 24.

$$sort(68,-81,\frac{24+1}{24}-\left(\frac{3}{8}+\frac{1}{6}-\frac{3}{4}\right)\times \frac{3}{4})$$

Add 24 and 1 to get 25.

$$sort(68,-81,\frac{25}{24}-\left(\frac{3}{8}+\frac{1}{6}-\frac{3}{4}\right)\times \frac{3}{4})$$

Add \frac{3}{8} and \frac{1}{6} to get \frac{13}{24}.

$$sort(68,-81,\frac{25}{24}-\left(\frac{13}{24}-\frac{3}{4}\right)\times \frac{3}{4})$$

Subtract \frac{3}{4} from \frac{13}{24} to get -\frac{5}{24}.

$$sort(68,-81,\frac{25}{24}-\left(-\frac{5}{24}\times \frac{3}{4}\right))$$

Multiply -\frac{5}{24} and \frac{3}{4} to get -\frac{5}{32}.

$$sort(68,-81,\frac{25}{24}-\left(-\frac{5}{32}\right))$$

The opposite of -\frac{5}{32} is \frac{5}{32}.

$$sort(68,-81,\frac{25}{24}+\frac{5}{32})$$

Add \frac{25}{24} and \frac{5}{32} to get \frac{115}{96}.

$$sort(68,-81,\frac{115}{96})$$

Convert decimal numbers in the list 68,-81,\frac{115}{96} to fractions.

$$68,-81,\frac{115}{96}$$

To sort the list, start from a single element 68.

$$68$$

Insert -81 to the appropriate location in the new list.

$$-81,68$$

Insert \frac{115}{96} to the appropriate location in the new list.

$$-81,\frac{115}{96},68$$

Evaluate

$$68,\ -81,\ \frac{115}{96}$$