\left. \begin{array} { l } { 2 \frac { 3 } { 16 } \times ( 33 \frac { 6 } { 7 } - 31 \frac { 2 } { 3 } ) + 4 \frac { 7 } { 27 } \div 2 \frac { 4 } { 21 } } \\ { ( 5 \frac { 2 } { 9 } + 1 \frac { 1 } { 2 } ) \times 2 \frac { 18 } { 22 } - 5 \frac { 1 } { 2 } \div 5 \frac { 2 } { 2 } } \end{array} \right.
Sort
\frac{485}{72},\ \frac{649}{36}
Evaluate
\frac{485}{72},\ \frac{649}{36}
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sort(\frac{32+3}{16}\left(\frac{33\times 7+6}{7}-\frac{31\times 3+2}{3}\right)+\frac{\frac{4\times 27+7}{27}}{\frac{2\times 21+4}{21}},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Multiply 2 and 16 to get 32.
sort(\frac{35}{16}\left(\frac{33\times 7+6}{7}-\frac{31\times 3+2}{3}\right)+\frac{\frac{4\times 27+7}{27}}{\frac{2\times 21+4}{21}},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Add 32 and 3 to get 35.
sort(\frac{35}{16}\left(\frac{231+6}{7}-\frac{31\times 3+2}{3}\right)+\frac{\frac{4\times 27+7}{27}}{\frac{2\times 21+4}{21}},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Multiply 33 and 7 to get 231.
sort(\frac{35}{16}\left(\frac{237}{7}-\frac{31\times 3+2}{3}\right)+\frac{\frac{4\times 27+7}{27}}{\frac{2\times 21+4}{21}},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Add 231 and 6 to get 237.
sort(\frac{35}{16}\left(\frac{237}{7}-\frac{93+2}{3}\right)+\frac{\frac{4\times 27+7}{27}}{\frac{2\times 21+4}{21}},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Multiply 31 and 3 to get 93.
sort(\frac{35}{16}\left(\frac{237}{7}-\frac{95}{3}\right)+\frac{\frac{4\times 27+7}{27}}{\frac{2\times 21+4}{21}},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Add 93 and 2 to get 95.
sort(\frac{35}{16}\left(\frac{711}{21}-\frac{665}{21}\right)+\frac{\frac{4\times 27+7}{27}}{\frac{2\times 21+4}{21}},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Least common multiple of 7 and 3 is 21. Convert \frac{237}{7} and \frac{95}{3} to fractions with denominator 21.
sort(\frac{35}{16}\times \frac{711-665}{21}+\frac{\frac{4\times 27+7}{27}}{\frac{2\times 21+4}{21}},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Since \frac{711}{21} and \frac{665}{21} have the same denominator, subtract them by subtracting their numerators.
sort(\frac{35}{16}\times \frac{46}{21}+\frac{\frac{4\times 27+7}{27}}{\frac{2\times 21+4}{21}},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Subtract 665 from 711 to get 46.
sort(\frac{35\times 46}{16\times 21}+\frac{\frac{4\times 27+7}{27}}{\frac{2\times 21+4}{21}},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Multiply \frac{35}{16} times \frac{46}{21} by multiplying numerator times numerator and denominator times denominator.
sort(\frac{1610}{336}+\frac{\frac{4\times 27+7}{27}}{\frac{2\times 21+4}{21}},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Do the multiplications in the fraction \frac{35\times 46}{16\times 21}.
sort(\frac{115}{24}+\frac{\frac{4\times 27+7}{27}}{\frac{2\times 21+4}{21}},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Reduce the fraction \frac{1610}{336} to lowest terms by extracting and canceling out 14.
sort(\frac{115}{24}+\frac{\left(4\times 27+7\right)\times 21}{27\left(2\times 21+4\right)},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Divide \frac{4\times 27+7}{27} by \frac{2\times 21+4}{21} by multiplying \frac{4\times 27+7}{27} by the reciprocal of \frac{2\times 21+4}{21}.
sort(\frac{115}{24}+\frac{7\left(7+4\times 27\right)}{9\left(4+2\times 21\right)},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Cancel out 3 in both numerator and denominator.
sort(\frac{115}{24}+\frac{7\left(7+108\right)}{9\left(4+2\times 21\right)},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Multiply 4 and 27 to get 108.
sort(\frac{115}{24}+\frac{7\times 115}{9\left(4+2\times 21\right)},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Add 7 and 108 to get 115.
sort(\frac{115}{24}+\frac{805}{9\left(4+2\times 21\right)},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Multiply 7 and 115 to get 805.
sort(\frac{115}{24}+\frac{805}{9\left(4+42\right)},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Multiply 2 and 21 to get 42.
sort(\frac{115}{24}+\frac{805}{9\times 46},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Add 4 and 42 to get 46.
sort(\frac{115}{24}+\frac{805}{414},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Multiply 9 and 46 to get 414.
sort(\frac{115}{24}+\frac{35}{18},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Reduce the fraction \frac{805}{414} to lowest terms by extracting and canceling out 23.
sort(\frac{345}{72}+\frac{140}{72},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Least common multiple of 24 and 18 is 72. Convert \frac{115}{24} and \frac{35}{18} to fractions with denominator 72.
sort(\frac{345+140}{72},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Since \frac{345}{72} and \frac{140}{72} have the same denominator, add them by adding their numerators.
sort(\frac{485}{72},\left(\frac{5\times 9+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Add 345 and 140 to get 485.
sort(\frac{485}{72},\left(\frac{45+2}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Multiply 5 and 9 to get 45.
sort(\frac{485}{72},\left(\frac{47}{9}+\frac{1\times 2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Add 45 and 2 to get 47.
sort(\frac{485}{72},\left(\frac{47}{9}+\frac{2+1}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Multiply 1 and 2 to get 2.
sort(\frac{485}{72},\left(\frac{47}{9}+\frac{3}{2}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Add 2 and 1 to get 3.
sort(\frac{485}{72},\left(\frac{94}{18}+\frac{27}{18}\right)\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Least common multiple of 9 and 2 is 18. Convert \frac{47}{9} and \frac{3}{2} to fractions with denominator 18.
sort(\frac{485}{72},\frac{94+27}{18}\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Since \frac{94}{18} and \frac{27}{18} have the same denominator, add them by adding their numerators.
sort(\frac{485}{72},\frac{121}{18}\times \frac{2\times 22+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Add 94 and 27 to get 121.
sort(\frac{485}{72},\frac{121}{18}\times \frac{44+18}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Multiply 2 and 22 to get 44.
sort(\frac{485}{72},\frac{121}{18}\times \frac{62}{22}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Add 44 and 18 to get 62.
sort(\frac{485}{72},\frac{121}{18}\times \frac{31}{11}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Reduce the fraction \frac{62}{22} to lowest terms by extracting and canceling out 2.
sort(\frac{485}{72},\frac{121\times 31}{18\times 11}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Multiply \frac{121}{18} times \frac{31}{11} by multiplying numerator times numerator and denominator times denominator.
sort(\frac{485}{72},\frac{3751}{198}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Do the multiplications in the fraction \frac{121\times 31}{18\times 11}.
sort(\frac{485}{72},\frac{341}{18}-\frac{\frac{5\times 2+1}{2}}{\frac{5\times 2+2}{2}})
Reduce the fraction \frac{3751}{198} to lowest terms by extracting and canceling out 11.
sort(\frac{485}{72},\frac{341}{18}-\frac{\left(5\times 2+1\right)\times 2}{2\left(5\times 2+2\right)})
Divide \frac{5\times 2+1}{2} by \frac{5\times 2+2}{2} by multiplying \frac{5\times 2+1}{2} by the reciprocal of \frac{5\times 2+2}{2}.
sort(\frac{485}{72},\frac{341}{18}-\frac{1+2\times 5}{2+2\times 5})
Cancel out 2 in both numerator and denominator.
sort(\frac{485}{72},\frac{341}{18}-\frac{1+10}{2+2\times 5})
Multiply 2 and 5 to get 10.
sort(\frac{485}{72},\frac{341}{18}-\frac{11}{2+2\times 5})
Add 1 and 10 to get 11.
sort(\frac{485}{72},\frac{341}{18}-\frac{11}{2+10})
Multiply 2 and 5 to get 10.
sort(\frac{485}{72},\frac{341}{18}-\frac{11}{12})
Add 2 and 10 to get 12.
sort(\frac{485}{72},\frac{682}{36}-\frac{33}{36})
Least common multiple of 18 and 12 is 36. Convert \frac{341}{18} and \frac{11}{12} to fractions with denominator 36.
sort(\frac{485}{72},\frac{682-33}{36})
Since \frac{682}{36} and \frac{33}{36} have the same denominator, subtract them by subtracting their numerators.
sort(\frac{485}{72},\frac{649}{36})
Subtract 33 from 682 to get 649.
\frac{485}{72},\frac{1298}{72}
Least common denominator of the numbers in the list \frac{485}{72},\frac{649}{36} is 72. Convert numbers in the list to fractions with denominator 72.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}