Evaluate
\frac{1}{6}\approx 0.166666667
Factor
\frac{1}{2 \cdot 3} = 0.16666666666666666
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\left(\frac{2}{2}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Convert 1 to fraction \frac{2}{2}.
\left(\frac{2+1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.
\left(\frac{3}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Add 2 and 1 to get 3.
\left(\frac{9}{6}+\frac{2}{6}+\frac{1}{4}+\frac{1}{5}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{1}{3} to fractions with denominator 6.
\left(\frac{9+2}{6}+\frac{1}{4}+\frac{1}{5}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Since \frac{9}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.
\left(\frac{11}{6}+\frac{1}{4}+\frac{1}{5}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Add 9 and 2 to get 11.
\left(\frac{22}{12}+\frac{3}{12}+\frac{1}{5}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Least common multiple of 6 and 4 is 12. Convert \frac{11}{6} and \frac{1}{4} to fractions with denominator 12.
\left(\frac{22+3}{12}+\frac{1}{5}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Since \frac{22}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.
\left(\frac{25}{12}+\frac{1}{5}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Add 22 and 3 to get 25.
\left(\frac{125}{60}+\frac{12}{60}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Least common multiple of 12 and 5 is 60. Convert \frac{25}{12} and \frac{1}{5} to fractions with denominator 60.
\frac{125+12}{60}\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Since \frac{125}{60} and \frac{12}{60} have the same denominator, add them by adding their numerators.
\frac{137}{60}\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Add 125 and 12 to get 137.
\frac{137}{60}\left(\frac{3}{6}+\frac{2}{6}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.
\frac{137}{60}\left(\frac{3+2}{6}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.
\frac{137}{60}\left(\frac{5}{6}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Add 3 and 2 to get 5.
\frac{137}{60}\left(\frac{10}{12}+\frac{3}{12}+\frac{1}{5}+\frac{1}{6}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Least common multiple of 6 and 4 is 12. Convert \frac{5}{6} and \frac{1}{4} to fractions with denominator 12.
\frac{137}{60}\left(\frac{10+3}{12}+\frac{1}{5}+\frac{1}{6}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Since \frac{10}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.
\frac{137}{60}\left(\frac{13}{12}+\frac{1}{5}+\frac{1}{6}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Add 10 and 3 to get 13.
\frac{137}{60}\left(\frac{65}{60}+\frac{12}{60}+\frac{1}{6}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Least common multiple of 12 and 5 is 60. Convert \frac{13}{12} and \frac{1}{5} to fractions with denominator 60.
\frac{137}{60}\left(\frac{65+12}{60}+\frac{1}{6}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Since \frac{65}{60} and \frac{12}{60} have the same denominator, add them by adding their numerators.
\frac{137}{60}\left(\frac{77}{60}+\frac{1}{6}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Add 65 and 12 to get 77.
\frac{137}{60}\left(\frac{77}{60}+\frac{10}{60}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Least common multiple of 60 and 6 is 60. Convert \frac{77}{60} and \frac{1}{6} to fractions with denominator 60.
\frac{137}{60}\times \frac{77+10}{60}-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Since \frac{77}{60} and \frac{10}{60} have the same denominator, add them by adding their numerators.
\frac{137}{60}\times \frac{87}{60}-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Add 77 and 10 to get 87.
\frac{137}{60}\times \frac{29}{20}-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Reduce the fraction \frac{87}{60} to lowest terms by extracting and canceling out 3.
\frac{137\times 29}{60\times 20}-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Multiply \frac{137}{60} times \frac{29}{20} by multiplying numerator times numerator and denominator times denominator.
\frac{3973}{1200}-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Do the multiplications in the fraction \frac{137\times 29}{60\times 20}.
\frac{3973}{1200}-\left(\frac{2}{2}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Convert 1 to fraction \frac{2}{2}.
\frac{3973}{1200}-\left(\frac{2+1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.
\frac{3973}{1200}-\left(\frac{3}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Add 2 and 1 to get 3.
\frac{3973}{1200}-\left(\frac{9}{6}+\frac{2}{6}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{1}{3} to fractions with denominator 6.
\frac{3973}{1200}-\left(\frac{9+2}{6}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Since \frac{9}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.
\frac{3973}{1200}-\left(\frac{11}{6}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Add 9 and 2 to get 11.
\frac{3973}{1200}-\left(\frac{22}{12}+\frac{3}{12}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Least common multiple of 6 and 4 is 12. Convert \frac{11}{6} and \frac{1}{4} to fractions with denominator 12.
\frac{3973}{1200}-\left(\frac{22+3}{12}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Since \frac{22}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.
\frac{3973}{1200}-\left(\frac{25}{12}+\frac{1}{5}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Add 22 and 3 to get 25.
\frac{3973}{1200}-\left(\frac{125}{60}+\frac{12}{60}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Least common multiple of 12 and 5 is 60. Convert \frac{25}{12} and \frac{1}{5} to fractions with denominator 60.
\frac{3973}{1200}-\left(\frac{125+12}{60}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Since \frac{125}{60} and \frac{12}{60} have the same denominator, add them by adding their numerators.
\frac{3973}{1200}-\left(\frac{137}{60}+\frac{1}{6}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Add 125 and 12 to get 137.
\frac{3973}{1200}-\left(\frac{137}{60}+\frac{10}{60}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Least common multiple of 60 and 6 is 60. Convert \frac{137}{60} and \frac{1}{6} to fractions with denominator 60.
\frac{3973}{1200}-\frac{137+10}{60}\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Since \frac{137}{60} and \frac{10}{60} have the same denominator, add them by adding their numerators.
\frac{3973}{1200}-\frac{147}{60}\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Add 137 and 10 to get 147.
\frac{3973}{1200}-\frac{49}{20}\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)
Reduce the fraction \frac{147}{60} to lowest terms by extracting and canceling out 3.
\frac{3973}{1200}-\frac{49}{20}\left(\frac{3}{6}+\frac{2}{6}+\frac{1}{4}+\frac{1}{5}\right)
Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.
\frac{3973}{1200}-\frac{49}{20}\left(\frac{3+2}{6}+\frac{1}{4}+\frac{1}{5}\right)
Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.
\frac{3973}{1200}-\frac{49}{20}\left(\frac{5}{6}+\frac{1}{4}+\frac{1}{5}\right)
Add 3 and 2 to get 5.
\frac{3973}{1200}-\frac{49}{20}\left(\frac{10}{12}+\frac{3}{12}+\frac{1}{5}\right)
Least common multiple of 6 and 4 is 12. Convert \frac{5}{6} and \frac{1}{4} to fractions with denominator 12.
\frac{3973}{1200}-\frac{49}{20}\left(\frac{10+3}{12}+\frac{1}{5}\right)
Since \frac{10}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.
\frac{3973}{1200}-\frac{49}{20}\left(\frac{13}{12}+\frac{1}{5}\right)
Add 10 and 3 to get 13.
\frac{3973}{1200}-\frac{49}{20}\left(\frac{65}{60}+\frac{12}{60}\right)
Least common multiple of 12 and 5 is 60. Convert \frac{13}{12} and \frac{1}{5} to fractions with denominator 60.
\frac{3973}{1200}-\frac{49}{20}\times \frac{65+12}{60}
Since \frac{65}{60} and \frac{12}{60} have the same denominator, add them by adding their numerators.
\frac{3973}{1200}-\frac{49}{20}\times \frac{77}{60}
Add 65 and 12 to get 77.
\frac{3973}{1200}-\frac{49\times 77}{20\times 60}
Multiply \frac{49}{20} times \frac{77}{60} by multiplying numerator times numerator and denominator times denominator.
\frac{3973}{1200}-\frac{3773}{1200}
Do the multiplications in the fraction \frac{49\times 77}{20\times 60}.
\frac{3973-3773}{1200}
Since \frac{3973}{1200} and \frac{3773}{1200} have the same denominator, subtract them by subtracting their numerators.
\frac{200}{1200}
Subtract 3773 from 3973 to get 200.
\frac{1}{6}
Reduce the fraction \frac{200}{1200} to lowest terms by extracting and canceling out 200.
Examples
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{ 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}