Evaluate
\frac{9}{20}=0.45
Factor
\frac{3 ^ {2}}{2 ^ {2} \cdot 5} = 0.45
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\frac{1\left(\frac{3}{6}-\frac{2}{6}\right)\left(2-\frac{1}{5}\right)}{1-\frac{1}{3}}
Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.
\frac{1\times \frac{3-2}{6}\left(2-\frac{1}{5}\right)}{1-\frac{1}{3}}
Since \frac{3}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.
\frac{1\times \frac{1}{6}\left(2-\frac{1}{5}\right)}{1-\frac{1}{3}}
Subtract 2 from 3 to get 1.
\frac{\frac{1}{6}\left(2-\frac{1}{5}\right)}{1-\frac{1}{3}}
Multiply 1 and \frac{1}{6} to get \frac{1}{6}.
\frac{\frac{1}{6}\left(\frac{10}{5}-\frac{1}{5}\right)}{1-\frac{1}{3}}
Convert 2 to fraction \frac{10}{5}.
\frac{\frac{1}{6}\times \frac{10-1}{5}}{1-\frac{1}{3}}
Since \frac{10}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{1}{6}\times \frac{9}{5}}{1-\frac{1}{3}}
Subtract 1 from 10 to get 9.
\frac{\frac{1\times 9}{6\times 5}}{1-\frac{1}{3}}
Multiply \frac{1}{6} times \frac{9}{5} by multiplying numerator times numerator and denominator times denominator.
\frac{\frac{9}{30}}{1-\frac{1}{3}}
Do the multiplications in the fraction \frac{1\times 9}{6\times 5}.
\frac{\frac{3}{10}}{1-\frac{1}{3}}
Reduce the fraction \frac{9}{30} to lowest terms by extracting and canceling out 3.
\frac{\frac{3}{10}}{\frac{3}{3}-\frac{1}{3}}
Convert 1 to fraction \frac{3}{3}.
\frac{\frac{3}{10}}{\frac{3-1}{3}}
Since \frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{3}{10}}{\frac{2}{3}}
Subtract 1 from 3 to get 2.
\frac{3}{10}\times \frac{3}{2}
Divide \frac{3}{10} by \frac{2}{3} by multiplying \frac{3}{10} by the reciprocal of \frac{2}{3}.
\frac{3\times 3}{10\times 2}
Multiply \frac{3}{10} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{9}{20}
Do the multiplications in the fraction \frac{3\times 3}{10\times 2}.
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}