Evaluate
\frac{25299}{6440}\approx 3.928416149
Factor
\frac{3 ^ {3} \cdot 937}{2 ^ {3} \cdot 5 \cdot 7 \cdot 23} = 3\frac{5979}{6440} = 3.928416149068323
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\frac{\frac{-7\left(-45\right)}{18}+\frac{1}{6}\left(-1\right)^{2000}}{\left(-\frac{13\times 3+1}{3}\right)\left(-1\right)^{1009}-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}
Express -\frac{7}{18}\left(-45\right) as a single fraction.
\frac{\frac{315}{18}+\frac{1}{6}\left(-1\right)^{2000}}{\left(-\frac{13\times 3+1}{3}\right)\left(-1\right)^{1009}-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}
Multiply -7 and -45 to get 315.
\frac{\frac{35}{2}+\frac{1}{6}\left(-1\right)^{2000}}{\left(-\frac{13\times 3+1}{3}\right)\left(-1\right)^{1009}-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}
Reduce the fraction \frac{315}{18} to lowest terms by extracting and canceling out 9.
\frac{\frac{35}{2}+\frac{1}{6}\times 1}{\left(-\frac{13\times 3+1}{3}\right)\left(-1\right)^{1009}-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}
Calculate -1 to the power of 2000 and get 1.
\frac{\frac{35}{2}+\frac{1}{6}}{\left(-\frac{13\times 3+1}{3}\right)\left(-1\right)^{1009}-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}
Multiply \frac{1}{6} and 1 to get \frac{1}{6}.
\frac{\frac{105}{6}+\frac{1}{6}}{\left(-\frac{13\times 3+1}{3}\right)\left(-1\right)^{1009}-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}
Least common multiple of 2 and 6 is 6. Convert \frac{35}{2} and \frac{1}{6} to fractions with denominator 6.
\frac{\frac{105+1}{6}}{\left(-\frac{13\times 3+1}{3}\right)\left(-1\right)^{1009}-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}
Since \frac{105}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.
\frac{\frac{106}{6}}{\left(-\frac{13\times 3+1}{3}\right)\left(-1\right)^{1009}-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}
Add 105 and 1 to get 106.
\frac{\frac{53}{3}}{\left(-\frac{13\times 3+1}{3}\right)\left(-1\right)^{1009}-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}
Reduce the fraction \frac{106}{6} to lowest terms by extracting and canceling out 2.
\frac{\frac{53}{3}}{\left(-\frac{39+1}{3}\right)\left(-1\right)^{1009}-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}
Multiply 13 and 3 to get 39.
\frac{\frac{53}{3}}{-\frac{40}{3}\left(-1\right)^{1009}-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}
Add 39 and 1 to get 40.
\frac{\frac{53}{3}}{-\frac{40}{3}\left(-1\right)-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}
Calculate -1 to the power of 1009 and get -1.
\frac{\frac{53}{3}}{\frac{40}{3}-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}
Multiply -\frac{40}{3} and -1 to get \frac{40}{3}.
\frac{\frac{53}{3}}{\frac{40}{3}-\left(-\frac{12+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}
Multiply 3 and 4 to get 12.
\frac{\frac{53}{3}}{\frac{40}{3}-\left(-\frac{15}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}
Add 12 and 3 to get 15.
\frac{\frac{53}{3}}{\frac{40}{3}+\frac{15}{4}-\frac{5}{16}}+\frac{2\times 8+7}{8}
The opposite of -\frac{15}{4} is \frac{15}{4}.
\frac{\frac{53}{3}}{\frac{160}{12}+\frac{45}{12}-\frac{5}{16}}+\frac{2\times 8+7}{8}
Least common multiple of 3 and 4 is 12. Convert \frac{40}{3} and \frac{15}{4} to fractions with denominator 12.
\frac{\frac{53}{3}}{\frac{160+45}{12}-\frac{5}{16}}+\frac{2\times 8+7}{8}
Since \frac{160}{12} and \frac{45}{12} have the same denominator, add them by adding their numerators.
\frac{\frac{53}{3}}{\frac{205}{12}-\frac{5}{16}}+\frac{2\times 8+7}{8}
Add 160 and 45 to get 205.
\frac{\frac{53}{3}}{\frac{820}{48}-\frac{15}{48}}+\frac{2\times 8+7}{8}
Least common multiple of 12 and 16 is 48. Convert \frac{205}{12} and \frac{5}{16} to fractions with denominator 48.
\frac{\frac{53}{3}}{\frac{820-15}{48}}+\frac{2\times 8+7}{8}
Since \frac{820}{48} and \frac{15}{48} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{53}{3}}{\frac{805}{48}}+\frac{2\times 8+7}{8}
Subtract 15 from 820 to get 805.
\frac{53}{3}\times \frac{48}{805}+\frac{2\times 8+7}{8}
Divide \frac{53}{3} by \frac{805}{48} by multiplying \frac{53}{3} by the reciprocal of \frac{805}{48}.
\frac{53\times 48}{3\times 805}+\frac{2\times 8+7}{8}
Multiply \frac{53}{3} times \frac{48}{805} by multiplying numerator times numerator and denominator times denominator.
\frac{2544}{2415}+\frac{2\times 8+7}{8}
Do the multiplications in the fraction \frac{53\times 48}{3\times 805}.
\frac{848}{805}+\frac{2\times 8+7}{8}
Reduce the fraction \frac{2544}{2415} to lowest terms by extracting and canceling out 3.
\frac{848}{805}+\frac{16+7}{8}
Multiply 2 and 8 to get 16.
\frac{848}{805}+\frac{23}{8}
Add 16 and 7 to get 23.
\frac{6784}{6440}+\frac{18515}{6440}
Least common multiple of 805 and 8 is 6440. Convert \frac{848}{805} and \frac{23}{8} to fractions with denominator 6440.
\frac{6784+18515}{6440}
Since \frac{6784}{6440} and \frac{18515}{6440} have the same denominator, add them by adding their numerators.
\frac{25299}{6440}
Add 6784 and 18515 to get 25299.
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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}