Evaluate
365
Factor
5\times 73
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365\left(\frac{35}{91}-\frac{39}{91}\right)+\frac{\frac{4}{9}-\frac{5}{13}}{\frac{1}{365}}+\left(\frac{5}{9}+\frac{3}{7}\right)\times 365
Least common multiple of 13 and 7 is 91. Convert \frac{5}{13} and \frac{3}{7} to fractions with denominator 91.
365\times \frac{35-39}{91}+\frac{\frac{4}{9}-\frac{5}{13}}{\frac{1}{365}}+\left(\frac{5}{9}+\frac{3}{7}\right)\times 365
Since \frac{35}{91} and \frac{39}{91} have the same denominator, subtract them by subtracting their numerators.
365\left(-\frac{4}{91}\right)+\frac{\frac{4}{9}-\frac{5}{13}}{\frac{1}{365}}+\left(\frac{5}{9}+\frac{3}{7}\right)\times 365
Subtract 39 from 35 to get -4.
\frac{365\left(-4\right)}{91}+\frac{\frac{4}{9}-\frac{5}{13}}{\frac{1}{365}}+\left(\frac{5}{9}+\frac{3}{7}\right)\times 365
Express 365\left(-\frac{4}{91}\right) as a single fraction.
\frac{-1460}{91}+\frac{\frac{4}{9}-\frac{5}{13}}{\frac{1}{365}}+\left(\frac{5}{9}+\frac{3}{7}\right)\times 365
Multiply 365 and -4 to get -1460.
-\frac{1460}{91}+\frac{\frac{4}{9}-\frac{5}{13}}{\frac{1}{365}}+\left(\frac{5}{9}+\frac{3}{7}\right)\times 365
Fraction \frac{-1460}{91} can be rewritten as -\frac{1460}{91} by extracting the negative sign.
-\frac{1460}{91}+\frac{\frac{52}{117}-\frac{45}{117}}{\frac{1}{365}}+\left(\frac{5}{9}+\frac{3}{7}\right)\times 365
Least common multiple of 9 and 13 is 117. Convert \frac{4}{9} and \frac{5}{13} to fractions with denominator 117.
-\frac{1460}{91}+\frac{\frac{52-45}{117}}{\frac{1}{365}}+\left(\frac{5}{9}+\frac{3}{7}\right)\times 365
Since \frac{52}{117} and \frac{45}{117} have the same denominator, subtract them by subtracting their numerators.
-\frac{1460}{91}+\frac{\frac{7}{117}}{\frac{1}{365}}+\left(\frac{5}{9}+\frac{3}{7}\right)\times 365
Subtract 45 from 52 to get 7.
-\frac{1460}{91}+\frac{7}{117}\times 365+\left(\frac{5}{9}+\frac{3}{7}\right)\times 365
Divide \frac{7}{117} by \frac{1}{365} by multiplying \frac{7}{117} by the reciprocal of \frac{1}{365}.
-\frac{1460}{91}+\frac{7\times 365}{117}+\left(\frac{5}{9}+\frac{3}{7}\right)\times 365
Express \frac{7}{117}\times 365 as a single fraction.
-\frac{1460}{91}+\frac{2555}{117}+\left(\frac{5}{9}+\frac{3}{7}\right)\times 365
Multiply 7 and 365 to get 2555.
-\frac{13140}{819}+\frac{17885}{819}+\left(\frac{5}{9}+\frac{3}{7}\right)\times 365
Least common multiple of 91 and 117 is 819. Convert -\frac{1460}{91} and \frac{2555}{117} to fractions with denominator 819.
\frac{-13140+17885}{819}+\left(\frac{5}{9}+\frac{3}{7}\right)\times 365
Since -\frac{13140}{819} and \frac{17885}{819} have the same denominator, add them by adding their numerators.
\frac{4745}{819}+\left(\frac{5}{9}+\frac{3}{7}\right)\times 365
Add -13140 and 17885 to get 4745.
\frac{365}{63}+\left(\frac{5}{9}+\frac{3}{7}\right)\times 365
Reduce the fraction \frac{4745}{819} to lowest terms by extracting and canceling out 13.
\frac{365}{63}+\left(\frac{35}{63}+\frac{27}{63}\right)\times 365
Least common multiple of 9 and 7 is 63. Convert \frac{5}{9} and \frac{3}{7} to fractions with denominator 63.
\frac{365}{63}+\frac{35+27}{63}\times 365
Since \frac{35}{63} and \frac{27}{63} have the same denominator, add them by adding their numerators.
\frac{365}{63}+\frac{62}{63}\times 365
Add 35 and 27 to get 62.
\frac{365}{63}+\frac{62\times 365}{63}
Express \frac{62}{63}\times 365 as a single fraction.
\frac{365}{63}+\frac{22630}{63}
Multiply 62 and 365 to get 22630.
\frac{365+22630}{63}
Since \frac{365}{63} and \frac{22630}{63} have the same denominator, add them by adding their numerators.
\frac{22995}{63}
Add 365 and 22630 to get 22995.
365
Divide 22995 by 63 to get 365.
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}