\left. \begin{array} { l } { \frac { 5 } { 7 } - \frac { 1 } { 3 } } \\ { 2 \frac { 3 } { 5 } - \frac { 7 } { 8 } } \\ { 4 \frac { 1 } { 2 } \times 1 \frac { 3 } { 4 } } \\ { 2 \frac { 1 } { 3 } \div \frac { 5 } { 7 } } \end{array} \right.
Sort
\frac{8}{21},\frac{69}{40},\frac{49}{15},\frac{63}{8}
Evaluate
\frac{8}{21},\ \frac{69}{40},\ \frac{63}{8},\ \frac{49}{15}
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sort(\frac{15}{21}-\frac{7}{21},\frac{2\times 5+3}{5}-\frac{7}{8},\frac{4\times 2+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})
Least common multiple of 7 and 3 is 21. Convert \frac{5}{7} and \frac{1}{3} to fractions with denominator 21.
sort(\frac{15-7}{21},\frac{2\times 5+3}{5}-\frac{7}{8},\frac{4\times 2+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})
Since \frac{15}{21} and \frac{7}{21} have the same denominator, subtract them by subtracting their numerators.
sort(\frac{8}{21},\frac{2\times 5+3}{5}-\frac{7}{8},\frac{4\times 2+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})
Subtract 7 from 15 to get 8.
sort(\frac{8}{21},\frac{10+3}{5}-\frac{7}{8},\frac{4\times 2+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})
Multiply 2 and 5 to get 10.
sort(\frac{8}{21},\frac{13}{5}-\frac{7}{8},\frac{4\times 2+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})
Add 10 and 3 to get 13.
sort(\frac{8}{21},\frac{104}{40}-\frac{35}{40},\frac{4\times 2+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})
Least common multiple of 5 and 8 is 40. Convert \frac{13}{5} and \frac{7}{8} to fractions with denominator 40.
sort(\frac{8}{21},\frac{104-35}{40},\frac{4\times 2+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})
Since \frac{104}{40} and \frac{35}{40} have the same denominator, subtract them by subtracting their numerators.
sort(\frac{8}{21},\frac{69}{40},\frac{4\times 2+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})
Subtract 35 from 104 to get 69.
sort(\frac{8}{21},\frac{69}{40},\frac{8+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})
Multiply 4 and 2 to get 8.
sort(\frac{8}{21},\frac{69}{40},\frac{9}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})
Add 8 and 1 to get 9.
sort(\frac{8}{21},\frac{69}{40},\frac{9}{2}\times \frac{4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})
Multiply 1 and 4 to get 4.
sort(\frac{8}{21},\frac{69}{40},\frac{9}{2}\times \frac{7}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})
Add 4 and 3 to get 7.
sort(\frac{8}{21},\frac{69}{40},\frac{9\times 7}{2\times 4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})
Multiply \frac{9}{2} times \frac{7}{4} by multiplying numerator times numerator and denominator times denominator.
sort(\frac{8}{21},\frac{69}{40},\frac{63}{8},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})
Do the multiplications in the fraction \frac{9\times 7}{2\times 4}.
sort(\frac{8}{21},\frac{69}{40},\frac{63}{8},\frac{\left(2\times 3+1\right)\times 7}{3\times 5})
Divide \frac{2\times 3+1}{3} by \frac{5}{7} by multiplying \frac{2\times 3+1}{3} by the reciprocal of \frac{5}{7}.
sort(\frac{8}{21},\frac{69}{40},\frac{63}{8},\frac{\left(6+1\right)\times 7}{3\times 5})
Multiply 2 and 3 to get 6.
sort(\frac{8}{21},\frac{69}{40},\frac{63}{8},\frac{7\times 7}{3\times 5})
Add 6 and 1 to get 7.
sort(\frac{8}{21},\frac{69}{40},\frac{63}{8},\frac{49}{3\times 5})
Multiply 7 and 7 to get 49.
sort(\frac{8}{21},\frac{69}{40},\frac{63}{8},\frac{49}{15})
Multiply 3 and 5 to get 15.
\frac{320}{840},\frac{1449}{840},\frac{6615}{840},\frac{2744}{840}
Least common denominator of the numbers in the list \frac{8}{21},\frac{69}{40},\frac{63}{8},\frac{49}{15} is 840. Convert numbers in the list to fractions with denominator 840.
\frac{320}{840}
To sort the list, start from a single element \frac{320}{840}.
\frac{320}{840},\frac{1449}{840}
Insert \frac{1449}{840} to the appropriate location in the new list.
\frac{320}{840},\frac{1449}{840},\frac{6615}{840}
Insert \frac{6615}{840} to the appropriate location in the new list.
\frac{320}{840},\frac{1449}{840},\frac{2744}{840},\frac{6615}{840}
Insert \frac{2744}{840} to the appropriate location in the new list.
\frac{8}{21},\frac{69}{40},\frac{49}{15},\frac{63}{8}
Replace the obtained fractions with the initial values.
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}