Evaluate
\frac{31}{30}\approx 1.033333333
Factor
\frac{31}{2 \cdot 3 \cdot 5} = 1\frac{1}{30} = 1.0333333333333334
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\frac{1}{2}+\left(\frac{9}{12}-\frac{1}{12}\right)\times \frac{4}{5}
Least common multiple of 4 and 12 is 12. Convert \frac{3}{4} and \frac{1}{12} to fractions with denominator 12.
\frac{1}{2}+\frac{9-1}{12}\times \frac{4}{5}
Since \frac{9}{12} and \frac{1}{12} have the same denominator, subtract them by subtracting their numerators.
\frac{1}{2}+\frac{8}{12}\times \frac{4}{5}
Subtract 1 from 9 to get 8.
\frac{1}{2}+\frac{2}{3}\times \frac{4}{5}
Reduce the fraction \frac{8}{12} to lowest terms by extracting and canceling out 4.
\frac{1}{2}+\frac{2\times 4}{3\times 5}
Multiply \frac{2}{3} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.
\frac{1}{2}+\frac{8}{15}
Do the multiplications in the fraction \frac{2\times 4}{3\times 5}.
\frac{15}{30}+\frac{16}{30}
Least common multiple of 2 and 15 is 30. Convert \frac{1}{2} and \frac{8}{15} to fractions with denominator 30.
\frac{15+16}{30}
Since \frac{15}{30} and \frac{16}{30} have the same denominator, add them by adding their numerators.
\frac{31}{30}
Add 15 and 16 to get 31.
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}