\left. \begin{array} { l } { ( 4 \times 10 ) + ( 2 \times 1 ) + ( 5 \times \frac { 1 } { 10 } ) + ( 9 \times \frac { 1 } { 100 } ) + ( 3 \times \frac { 1 } { 1,000 } ) } \\ { ( 4 \times 10 ) + ( 1 \times 1 ) + ( 6 \times \frac { 1 } { 10 } ) + ( 2 \times \frac { 1 } { 100 } ) + ( 5 \times \frac { 1 } { 1,000 } ) } \\ { ( 4 \times 10 ) + ( 2 \times 1 ) + ( 5 \times \frac { 1 } { 10 } ) + ( 3 \times \frac { 1 } { 100 } ) + ( 7 \times \frac { 1 } { 1,000 } ) } \\ { ( 4 \times 10 ) + ( 2 \times 1 ) + ( 5 \times \frac { 1 } { 10 } ) + ( 1 \times \frac { 1 } { 100 } ) + ( 9 \times \frac { 1 } { 1,000 } ) } \end{array} \right.
Sort
\frac{4559}{100},\ \frac{2331}{50},\ \frac{4953}{100},\ \frac{5151}{100}
Evaluate
\frac{4559}{100},\ \frac{2331}{50},\ \frac{4953}{100},\ \frac{5151}{100}
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sort(4\times 10+2\times 1+5\times \frac{1}{10}+9\times \frac{1}{100}+3\times 1;4\times 10+1\times 1+6\times \frac{1}{10}+2\times \frac{1}{100}+5\times \frac{1}{1};4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times \frac{1}{1};4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times \frac{1}{1})
Divide 1 by 1 to get 1.
sort(4\times 10+2\times 1+5\times \frac{1}{10}+9\times \frac{1}{100}+3\times 1;4\times 10+1\times 1+6\times \frac{1}{10}+2\times \frac{1}{100}+5\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times \frac{1}{1};4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times \frac{1}{1})
Divide 1 by 1 to get 1.
sort(4\times 10+2\times 1+5\times \frac{1}{10}+9\times \frac{1}{100}+3\times 1;4\times 10+1\times 1+6\times \frac{1}{10}+2\times \frac{1}{100}+5\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times \frac{1}{1})
Divide 1 by 1 to get 1.
sort(4\times 10+2\times 1+5\times \frac{1}{10}+9\times \frac{1}{100}+3\times 1;4\times 10+1\times 1+6\times \frac{1}{10}+2\times \frac{1}{100}+5\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Divide 1 by 1 to get 1.
sort(40+2+5\times \frac{1}{10}+9\times \frac{1}{100}+3;4\times 10+1\times 1+6\times \frac{1}{10}+2\times \frac{1}{100}+5\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Multiply 4 and 10 to get 40. Multiply 2 and 1 to get 2. Multiply 3 and 1 to get 3.
sort(42+5\times \frac{1}{10}+9\times \frac{1}{100}+3;4\times 10+1\times 1+6\times \frac{1}{10}+2\times \frac{1}{100}+5\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Add 40 and 2 to get 42.
sort(42+\frac{5}{10}+9\times \frac{1}{100}+3;4\times 10+1\times 1+6\times \frac{1}{10}+2\times \frac{1}{100}+5\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Multiply 5 and \frac{1}{10} to get \frac{5}{10}.
sort(42+\frac{1}{2}+9\times \frac{1}{100}+3;4\times 10+1\times 1+6\times \frac{1}{10}+2\times \frac{1}{100}+5\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.
sort(\frac{84}{2}+\frac{1}{2}+9\times \frac{1}{100}+3;4\times 10+1\times 1+6\times \frac{1}{10}+2\times \frac{1}{100}+5\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Convert 42 to fraction \frac{84}{2}.
sort(\frac{84+1}{2}+9\times \frac{1}{100}+3;4\times 10+1\times 1+6\times \frac{1}{10}+2\times \frac{1}{100}+5\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Since \frac{84}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.
sort(\frac{85}{2}+9\times \frac{1}{100}+3;4\times 10+1\times 1+6\times \frac{1}{10}+2\times \frac{1}{100}+5\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Add 84 and 1 to get 85.
sort(\frac{85}{2}+\frac{9}{100}+3;4\times 10+1\times 1+6\times \frac{1}{10}+2\times \frac{1}{100}+5\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Multiply 9 and \frac{1}{100} to get \frac{9}{100}.
sort(\frac{4250}{100}+\frac{9}{100}+3;4\times 10+1\times 1+6\times \frac{1}{10}+2\times \frac{1}{100}+5\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Least common multiple of 2 and 100 is 100. Convert \frac{85}{2} and \frac{9}{100} to fractions with denominator 100.
sort(\frac{4250+9}{100}+3;4\times 10+1\times 1+6\times \frac{1}{10}+2\times \frac{1}{100}+5\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Since \frac{4250}{100} and \frac{9}{100} have the same denominator, add them by adding their numerators.
sort(\frac{4259}{100}+3;4\times 10+1\times 1+6\times \frac{1}{10}+2\times \frac{1}{100}+5\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Add 4250 and 9 to get 4259.
sort(\frac{4259}{100}+\frac{300}{100};4\times 10+1\times 1+6\times \frac{1}{10}+2\times \frac{1}{100}+5\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Convert 3 to fraction \frac{300}{100}.
sort(\frac{4259+300}{100};4\times 10+1\times 1+6\times \frac{1}{10}+2\times \frac{1}{100}+5\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Since \frac{4259}{100} and \frac{300}{100} have the same denominator, add them by adding their numerators.
sort(\frac{4559}{100};4\times 10+1\times 1+6\times \frac{1}{10}+2\times \frac{1}{100}+5\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Add 4259 and 300 to get 4559.
sort(\frac{4559}{100};40+1+6\times \frac{1}{10}+2\times \frac{1}{100}+5;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Multiply 4 and 10 to get 40. Multiply 1 and 1 to get 1. Multiply 5 and 1 to get 5.
sort(\frac{4559}{100};41+6\times \frac{1}{10}+2\times \frac{1}{100}+5;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Add 40 and 1 to get 41.
sort(\frac{4559}{100};41+\frac{6}{10}+2\times \frac{1}{100}+5;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Multiply 6 and \frac{1}{10} to get \frac{6}{10}.
sort(\frac{4559}{100};41+\frac{3}{5}+2\times \frac{1}{100}+5;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.
sort(\frac{4559}{100};\frac{205}{5}+\frac{3}{5}+2\times \frac{1}{100}+5;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Convert 41 to fraction \frac{205}{5}.
sort(\frac{4559}{100};\frac{205+3}{5}+2\times \frac{1}{100}+5;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Since \frac{205}{5} and \frac{3}{5} have the same denominator, add them by adding their numerators.
sort(\frac{4559}{100};\frac{208}{5}+2\times \frac{1}{100}+5;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Add 205 and 3 to get 208.
sort(\frac{4559}{100};\frac{208}{5}+\frac{2}{100}+5;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Multiply 2 and \frac{1}{100} to get \frac{2}{100}.
sort(\frac{4559}{100};\frac{208}{5}+\frac{1}{50}+5;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Reduce the fraction \frac{2}{100} to lowest terms by extracting and canceling out 2.
sort(\frac{4559}{100};\frac{2080}{50}+\frac{1}{50}+5;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Least common multiple of 5 and 50 is 50. Convert \frac{208}{5} and \frac{1}{50} to fractions with denominator 50.
sort(\frac{4559}{100};\frac{2080+1}{50}+5;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Since \frac{2080}{50} and \frac{1}{50} have the same denominator, add them by adding their numerators.
sort(\frac{4559}{100};\frac{2081}{50}+5;4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Add 2080 and 1 to get 2081.
sort(\frac{4559}{100};\frac{2081}{50}+\frac{250}{50};4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Convert 5 to fraction \frac{250}{50}.
sort(\frac{4559}{100};\frac{2081+250}{50};4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Since \frac{2081}{50} and \frac{250}{50} have the same denominator, add them by adding their numerators.
sort(\frac{4559}{100};\frac{2331}{50};4\times 10+2\times 1+5\times \frac{1}{10}+3\times \frac{1}{100}+7\times 1;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Add 2081 and 250 to get 2331.
sort(\frac{4559}{100};\frac{2331}{50};40+2+5\times \frac{1}{10}+3\times \frac{1}{100}+7;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Multiply 4 and 10 to get 40. Multiply 2 and 1 to get 2. Multiply 7 and 1 to get 7.
sort(\frac{4559}{100};\frac{2331}{50};42+5\times \frac{1}{10}+3\times \frac{1}{100}+7;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Add 40 and 2 to get 42.
sort(\frac{4559}{100};\frac{2331}{50};42+\frac{5}{10}+3\times \frac{1}{100}+7;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Multiply 5 and \frac{1}{10} to get \frac{5}{10}.
sort(\frac{4559}{100};\frac{2331}{50};42+\frac{1}{2}+3\times \frac{1}{100}+7;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.
sort(\frac{4559}{100};\frac{2331}{50};\frac{84}{2}+\frac{1}{2}+3\times \frac{1}{100}+7;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Convert 42 to fraction \frac{84}{2}.
sort(\frac{4559}{100};\frac{2331}{50};\frac{84+1}{2}+3\times \frac{1}{100}+7;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Since \frac{84}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.
sort(\frac{4559}{100};\frac{2331}{50};\frac{85}{2}+3\times \frac{1}{100}+7;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Add 84 and 1 to get 85.
sort(\frac{4559}{100};\frac{2331}{50};\frac{85}{2}+\frac{3}{100}+7;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Multiply 3 and \frac{1}{100} to get \frac{3}{100}.
sort(\frac{4559}{100};\frac{2331}{50};\frac{4250}{100}+\frac{3}{100}+7;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Least common multiple of 2 and 100 is 100. Convert \frac{85}{2} and \frac{3}{100} to fractions with denominator 100.
sort(\frac{4559}{100};\frac{2331}{50};\frac{4250+3}{100}+7;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Since \frac{4250}{100} and \frac{3}{100} have the same denominator, add them by adding their numerators.
sort(\frac{4559}{100};\frac{2331}{50};\frac{4253}{100}+7;4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Add 4250 and 3 to get 4253.
sort(\frac{4559}{100};\frac{2331}{50};\frac{4253}{100}+\frac{700}{100};4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Convert 7 to fraction \frac{700}{100}.
sort(\frac{4559}{100};\frac{2331}{50};\frac{4253+700}{100};4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Since \frac{4253}{100} and \frac{700}{100} have the same denominator, add them by adding their numerators.
sort(\frac{4559}{100};\frac{2331}{50};\frac{4953}{100};4\times 10+2\times 1+5\times \frac{1}{10}+1\times \frac{1}{100}+9\times 1)
Add 4253 and 700 to get 4953.
sort(\frac{4559}{100};\frac{2331}{50};\frac{4953}{100};40+2+5\times \frac{1}{10}+1\times \frac{1}{100}+9)
Multiply 4 and 10 to get 40. Multiply 2 and 1 to get 2. Multiply 9 and 1 to get 9.
sort(\frac{4559}{100};\frac{2331}{50};\frac{4953}{100};42+5\times \frac{1}{10}+1\times \frac{1}{100}+9)
Add 40 and 2 to get 42.
sort(\frac{4559}{100};\frac{2331}{50};\frac{4953}{100};42+\frac{5}{10}+1\times \frac{1}{100}+9)
Multiply 5 and \frac{1}{10} to get \frac{5}{10}.
sort(\frac{4559}{100};\frac{2331}{50};\frac{4953}{100};42+\frac{1}{2}+1\times \frac{1}{100}+9)
Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.
sort(\frac{4559}{100};\frac{2331}{50};\frac{4953}{100};\frac{84}{2}+\frac{1}{2}+1\times \frac{1}{100}+9)
Convert 42 to fraction \frac{84}{2}.
sort(\frac{4559}{100};\frac{2331}{50};\frac{4953}{100};\frac{84+1}{2}+1\times \frac{1}{100}+9)
Since \frac{84}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.
sort(\frac{4559}{100};\frac{2331}{50};\frac{4953}{100};\frac{85}{2}+1\times \frac{1}{100}+9)
Add 84 and 1 to get 85.
sort(\frac{4559}{100};\frac{2331}{50};\frac{4953}{100};\frac{85}{2}+\frac{1}{100}+9)
Multiply 1 and \frac{1}{100} to get \frac{1}{100}.
sort(\frac{4559}{100};\frac{2331}{50};\frac{4953}{100};\frac{4250}{100}+\frac{1}{100}+9)
Least common multiple of 2 and 100 is 100. Convert \frac{85}{2} and \frac{1}{100} to fractions with denominator 100.
sort(\frac{4559}{100};\frac{2331}{50};\frac{4953}{100};\frac{4250+1}{100}+9)
Since \frac{4250}{100} and \frac{1}{100} have the same denominator, add them by adding their numerators.
sort(\frac{4559}{100};\frac{2331}{50};\frac{4953}{100};\frac{4251}{100}+9)
Add 4250 and 1 to get 4251.
sort(\frac{4559}{100};\frac{2331}{50};\frac{4953}{100};\frac{4251}{100}+\frac{900}{100})
Convert 9 to fraction \frac{900}{100}.
sort(\frac{4559}{100};\frac{2331}{50};\frac{4953}{100};\frac{4251+900}{100})
Since \frac{4251}{100} and \frac{900}{100} have the same denominator, add them by adding their numerators.
sort(\frac{4559}{100};\frac{2331}{50};\frac{4953}{100};\frac{5151}{100})
Add 4251 and 900 to get 5151.
\frac{4559}{100};\frac{4662}{100};\frac{4953}{100};\frac{5151}{100}
Least common denominator of the numbers in the list \frac{4559}{100};\frac{2331}{50};\frac{4953}{100};\frac{5151}{100} is 100. Convert numbers in the list to fractions with denominator 100.
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}