- \frac { 5 } { 6 } : ( - 3 + \frac { 7 } { 2 } ) - \frac { 1 } { 2 } \cdot [ - 3 \cdot ( - ( \frac { 1 } { 2 } - \frac { 1 } { 1 } ) + 1 ]
Evaluate
\frac{7}{12}\approx 0.583333333
Factor
\frac{7}{2 ^ {2} \cdot 3} = 0.5833333333333334
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\frac{-\frac{5}{6}}{-3+\frac{7}{2}}-\frac{1}{2}\left(-3\right)\left(-\left(\frac{1}{2}-1\right)+1\right)
Divide 1 by 1 to get 1.
\frac{-\frac{5}{6}}{-\frac{6}{2}+\frac{7}{2}}-\frac{1}{2}\left(-3\right)\left(-\left(\frac{1}{2}-1\right)+1\right)
Convert -3 to fraction -\frac{6}{2}.
\frac{-\frac{5}{6}}{\frac{-6+7}{2}}-\frac{1}{2}\left(-3\right)\left(-\left(\frac{1}{2}-1\right)+1\right)
Since -\frac{6}{2} and \frac{7}{2} have the same denominator, add them by adding their numerators.
\frac{-\frac{5}{6}}{\frac{1}{2}}-\frac{1}{2}\left(-3\right)\left(-\left(\frac{1}{2}-1\right)+1\right)
Add -6 and 7 to get 1.
-\frac{5}{6}\times 2-\frac{1}{2}\left(-3\right)\left(-\left(\frac{1}{2}-1\right)+1\right)
Divide -\frac{5}{6} by \frac{1}{2} by multiplying -\frac{5}{6} by the reciprocal of \frac{1}{2}.
\frac{-5\times 2}{6}-\frac{1}{2}\left(-3\right)\left(-\left(\frac{1}{2}-1\right)+1\right)
Express -\frac{5}{6}\times 2 as a single fraction.
\frac{-10}{6}-\frac{1}{2}\left(-3\right)\left(-\left(\frac{1}{2}-1\right)+1\right)
Multiply -5 and 2 to get -10.
-\frac{5}{3}-\frac{1}{2}\left(-3\right)\left(-\left(\frac{1}{2}-1\right)+1\right)
Reduce the fraction \frac{-10}{6} to lowest terms by extracting and canceling out 2.
-\frac{5}{3}-\frac{-3}{2}\left(-\left(\frac{1}{2}-1\right)+1\right)
Multiply \frac{1}{2} and -3 to get \frac{-3}{2}.
-\frac{5}{3}-\left(-\frac{3}{2}\left(-\left(\frac{1}{2}-1\right)+1\right)\right)
Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.
-\frac{5}{3}-\left(-\frac{3}{2}\left(-\left(\frac{1}{2}-\frac{2}{2}\right)+1\right)\right)
Convert 1 to fraction \frac{2}{2}.
-\frac{5}{3}-\left(-\frac{3}{2}\left(-\frac{1-2}{2}+1\right)\right)
Since \frac{1}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.
-\frac{5}{3}-\left(-\frac{3}{2}\left(-\left(-\frac{1}{2}\right)+1\right)\right)
Subtract 2 from 1 to get -1.
-\frac{5}{3}-\left(-\frac{3}{2}\left(\frac{1}{2}+1\right)\right)
The opposite of -\frac{1}{2} is \frac{1}{2}.
-\frac{5}{3}-\left(-\frac{3}{2}\left(\frac{1}{2}+\frac{2}{2}\right)\right)
Convert 1 to fraction \frac{2}{2}.
-\frac{5}{3}-\left(-\frac{3}{2}\times \frac{1+2}{2}\right)
Since \frac{1}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.
-\frac{5}{3}-\left(-\frac{3}{2}\times \frac{3}{2}\right)
Add 1 and 2 to get 3.
-\frac{5}{3}-\frac{-3\times 3}{2\times 2}
Multiply -\frac{3}{2} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.
-\frac{5}{3}-\frac{-9}{4}
Do the multiplications in the fraction \frac{-3\times 3}{2\times 2}.
-\frac{5}{3}-\left(-\frac{9}{4}\right)
Fraction \frac{-9}{4} can be rewritten as -\frac{9}{4} by extracting the negative sign.
-\frac{5}{3}+\frac{9}{4}
The opposite of -\frac{9}{4} is \frac{9}{4}.
-\frac{20}{12}+\frac{27}{12}
Least common multiple of 3 and 4 is 12. Convert -\frac{5}{3} and \frac{9}{4} to fractions with denominator 12.
\frac{-20+27}{12}
Since -\frac{20}{12} and \frac{27}{12} have the same denominator, add them by adding their numerators.
\frac{7}{12}
Add -20 and 27 to get 7.
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}