Solve {l}{(7-3)(1-6)/4(11-6)div(3-8)}{(3+9*6)div3-2+2/3*6+(4-9)-3^2+5}{(4*3^2+24)div5+9*3/2*3^2-15+3+2+27+3+12+2-3^2/5+(13-2*5)-4}

$$\left. \begin{array} { l } { \frac { ( 7 - 3 ) ( 1 - 6 ) } { 4 ( 11 - 6 ) \div ( 3 - 8 ) } } \\ { \frac { ( 3 + 9 \times 6 ) \div 3 - 2 + 2 } { 3 \times 6 + ( 4 - 9 ) - 3 ^ { 2 } + 5 } } \\ { \frac { ( 4 \times 3 ^ { 2 } + 24 ) \div 5 + 9 \times 3 } { 2 \times 3 ^ { 2 } - 15 + 3 } + \frac { 2 + 27 + 3 + 12 + 2 - 3 ^ { 2 } } { 5 + ( 13 - 2 \times 5 ) - 4 } } \end{array} \right.$$

Sort

$$\frac{19}{9},5,\frac{63}{4}$$

Solution Steps

Subtract 3 from 7 to get 4.

$$sort(\frac{4\left(1-6\right)}{\frac{4\left(11-6\right)}{3-8}},\frac{\frac{3+9\times 6}{3}-2+2}{3\times 6+4-9-3^{2}+5},\frac{\frac{4\times 3^{2}+24}{5}+9\times 3}{2\times 3^{2}-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Subtract 6 from 1 to get -5.

$$sort(\frac{4\left(-5\right)}{\frac{4\left(11-6\right)}{3-8}},\frac{\frac{3+9\times 6}{3}-2+2}{3\times 6+4-9-3^{2}+5},\frac{\frac{4\times 3^{2}+24}{5}+9\times 3}{2\times 3^{2}-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Multiply 4 and -5 to get -20.

$$sort(\frac{-20}{\frac{4\left(11-6\right)}{3-8}},\frac{\frac{3+9\times 6}{3}-2+2}{3\times 6+4-9-3^{2}+5},\frac{\frac{4\times 3^{2}+24}{5}+9\times 3}{2\times 3^{2}-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Extract the negative sign in 11-6.

$$sort(\frac{-20}{\frac{-4\left(3-8\right)}{3-8}},\frac{\frac{3+9\times 6}{3}-2+2}{3\times 6+4-9-3^{2}+5},\frac{\frac{4\times 3^{2}+24}{5}+9\times 3}{2\times 3^{2}-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Cancel out 3-8 in both numerator and denominator.

$$sort(\frac{-20}{-4},\frac{\frac{3+9\times 6}{3}-2+2}{3\times 6+4-9-3^{2}+5},\frac{\frac{4\times 3^{2}+24}{5}+9\times 3}{2\times 3^{2}-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Divide -20 by -4 to get 5.

$$sort(5,\frac{\frac{3+9\times 6}{3}-2+2}{3\times 6+4-9-3^{2}+5},\frac{\frac{4\times 3^{2}+24}{5}+9\times 3}{2\times 3^{2}-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Multiply 9 and 6 to get 54.

$$sort(5,\frac{\frac{3+54}{3}-2+2}{3\times 6+4-9-3^{2}+5},\frac{\frac{4\times 3^{2}+24}{5}+9\times 3}{2\times 3^{2}-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Add 3 and 54 to get 57.

$$sort(5,\frac{\frac{57}{3}-2+2}{3\times 6+4-9-3^{2}+5},\frac{\frac{4\times 3^{2}+24}{5}+9\times 3}{2\times 3^{2}-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Divide 57 by 3 to get 19.

$$sort(5,\frac{19-2+2}{3\times 6+4-9-3^{2}+5},\frac{\frac{4\times 3^{2}+24}{5}+9\times 3}{2\times 3^{2}-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Subtract 2 from 19 to get 17.

$$sort(5,\frac{17+2}{3\times 6+4-9-3^{2}+5},\frac{\frac{4\times 3^{2}+24}{5}+9\times 3}{2\times 3^{2}-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Add 17 and 2 to get 19.

$$sort(5,\frac{19}{3\times 6+4-9-3^{2}+5},\frac{\frac{4\times 3^{2}+24}{5}+9\times 3}{2\times 3^{2}-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Multiply 3 and 6 to get 18.

$$sort(5,\frac{19}{18+4-9-3^{2}+5},\frac{\frac{4\times 3^{2}+24}{5}+9\times 3}{2\times 3^{2}-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Add 18 and 4 to get 22.

$$sort(5,\frac{19}{22-9-3^{2}+5},\frac{\frac{4\times 3^{2}+24}{5}+9\times 3}{2\times 3^{2}-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Subtract 9 from 22 to get 13.

$$sort(5,\frac{19}{13-3^{2}+5},\frac{\frac{4\times 3^{2}+24}{5}+9\times 3}{2\times 3^{2}-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Calculate 3 to the power of 2 and get 9.

$$sort(5,\frac{19}{13-9+5},\frac{\frac{4\times 3^{2}+24}{5}+9\times 3}{2\times 3^{2}-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Subtract 9 from 13 to get 4.

$$sort(5,\frac{19}{4+5},\frac{\frac{4\times 3^{2}+24}{5}+9\times 3}{2\times 3^{2}-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Add 4 and 5 to get 9.

$$sort(5,\frac{19}{9},\frac{\frac{4\times 3^{2}+24}{5}+9\times 3}{2\times 3^{2}-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Calculate 3 to the power of 2 and get 9.

$$sort(5,\frac{19}{9},\frac{\frac{4\times 9+24}{5}+9\times 3}{2\times 3^{2}-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Multiply 4 and 9 to get 36.

$$sort(5,\frac{19}{9},\frac{\frac{36+24}{5}+9\times 3}{2\times 3^{2}-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Add 36 and 24 to get 60.

$$sort(5,\frac{19}{9},\frac{\frac{60}{5}+9\times 3}{2\times 3^{2}-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Divide 60 by 5 to get 12.

$$sort(5,\frac{19}{9},\frac{12+9\times 3}{2\times 3^{2}-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Multiply 9 and 3 to get 27.

$$sort(5,\frac{19}{9},\frac{12+27}{2\times 3^{2}-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Add 12 and 27 to get 39.

$$sort(5,\frac{19}{9},\frac{39}{2\times 3^{2}-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Calculate 3 to the power of 2 and get 9.

$$sort(5,\frac{19}{9},\frac{39}{2\times 9-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Multiply 2 and 9 to get 18.

$$sort(5,\frac{19}{9},\frac{39}{18-15+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Subtract 15 from 18 to get 3.

$$sort(5,\frac{19}{9},\frac{39}{3+3}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Add 3 and 3 to get 6.

$$sort(5,\frac{19}{9},\frac{39}{6}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Reduce the fraction \frac{39}{6} to lowest terms by extracting and canceling out 3.

$$sort(5,\frac{19}{9},\frac{13}{2}+\frac{2+27+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Add 2 and 27 to get 29.

$$sort(5,\frac{19}{9},\frac{13}{2}+\frac{29+3+12+2-3^{2}}{5+13-2\times 5-4})$$

Add 29 and 3 to get 32.

$$sort(5,\frac{19}{9},\frac{13}{2}+\frac{32+12+2-3^{2}}{5+13-2\times 5-4})$$

Add 32 and 12 to get 44.

$$sort(5,\frac{19}{9},\frac{13}{2}+\frac{44+2-3^{2}}{5+13-2\times 5-4})$$

Add 44 and 2 to get 46.

$$sort(5,\frac{19}{9},\frac{13}{2}+\frac{46-3^{2}}{5+13-2\times 5-4})$$

Calculate 3 to the power of 2 and get 9.

$$sort(5,\frac{19}{9},\frac{13}{2}+\frac{46-9}{5+13-2\times 5-4})$$

Subtract 9 from 46 to get 37.

$$sort(5,\frac{19}{9},\frac{13}{2}+\frac{37}{5+13-2\times 5-4})$$

Multiply 2 and 5 to get 10.

$$sort(5,\frac{19}{9},\frac{13}{2}+\frac{37}{5+13-10-4})$$

Subtract 10 from 13 to get 3.

$$sort(5,\frac{19}{9},\frac{13}{2}+\frac{37}{5+3-4})$$

Add 5 and 3 to get 8.

$$sort(5,\frac{19}{9},\frac{13}{2}+\frac{37}{8-4})$$

Subtract 4 from 8 to get 4.

$$sort(5,\frac{19}{9},\frac{13}{2}+\frac{37}{4})$$

Least common multiple of 2 and 4 is 4. Convert \frac{13}{2} and \frac{37}{4} to fractions with denominator 4.

$$sort(5,\frac{19}{9},\frac{26}{4}+\frac{37}{4})$$

Since \frac{26}{4} and \frac{37}{4} have the same denominator, add them by adding their numerators.

$$sort(5,\frac{19}{9},\frac{26+37}{4})$$

Add 26 and 37 to get 63.

$$sort(5,\frac{19}{9},\frac{63}{4})$$

Convert decimal numbers in the list 5,\frac{19}{9},\frac{63}{4} to fractions.

$$5,\frac{19}{9},\frac{63}{4}$$

Least common denominator of the numbers in the list 5,\frac{19}{9},\frac{63}{4} is 36. Convert numbers in the list to fractions with denominator 36.

$$\frac{180}{36},\frac{76}{36},\frac{567}{36}$$

To sort the list, start from a single element \frac{180}{36}.

$$\frac{180}{36}$$

Insert \frac{76}{36} to the appropriate location in the new list.

$$\frac{76}{36},\frac{180}{36}$$

Insert \frac{567}{36} to the appropriate location in the new list.

$$\frac{76}{36},\frac{180}{36},\frac{567}{36}$$

Replace the obtained fractions with the initial values.

$$\frac{19}{9},5,\frac{63}{4}$$

Evaluate

$$5,\ \frac{19}{9},\ \frac{63}{4}$$