Evaluate
\frac{29}{6}\approx 4.833333333
Factor
\frac{29}{2 \cdot 3} = 4\frac{5}{6} = 4.833333333333333
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|\frac{9+1}{3}-\frac{4\times 3+2}{3}|-\left(-\frac{2\times 6+5}{6}-\left(-1.5\right)-|-\frac{2\times 6+1}{6}|\right)
Multiply 3 and 3 to get 9.
|\frac{10}{3}-\frac{4\times 3+2}{3}|-\left(-\frac{2\times 6+5}{6}-\left(-1.5\right)-|-\frac{2\times 6+1}{6}|\right)
Add 9 and 1 to get 10.
|\frac{10}{3}-\frac{12+2}{3}|-\left(-\frac{2\times 6+5}{6}-\left(-1.5\right)-|-\frac{2\times 6+1}{6}|\right)
Multiply 4 and 3 to get 12.
|\frac{10}{3}-\frac{14}{3}|-\left(-\frac{2\times 6+5}{6}-\left(-1.5\right)-|-\frac{2\times 6+1}{6}|\right)
Add 12 and 2 to get 14.
|\frac{10-14}{3}|-\left(-\frac{2\times 6+5}{6}-\left(-1.5\right)-|-\frac{2\times 6+1}{6}|\right)
Since \frac{10}{3} and \frac{14}{3} have the same denominator, subtract them by subtracting their numerators.
|-\frac{4}{3}|-\left(-\frac{2\times 6+5}{6}-\left(-1.5\right)-|-\frac{2\times 6+1}{6}|\right)
Subtract 14 from 10 to get -4.
\frac{4}{3}-\left(-\frac{2\times 6+5}{6}-\left(-1.5\right)-|-\frac{2\times 6+1}{6}|\right)
The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{4}{3} is \frac{4}{3}.
\frac{4}{3}-\left(-\frac{12+5}{6}-\left(-1.5\right)-|-\frac{2\times 6+1}{6}|\right)
Multiply 2 and 6 to get 12.
\frac{4}{3}-\left(-\frac{17}{6}-\left(-1.5\right)-|-\frac{2\times 6+1}{6}|\right)
Add 12 and 5 to get 17.
\frac{4}{3}-\left(-\frac{17}{6}+1.5-|-\frac{2\times 6+1}{6}|\right)
The opposite of -1.5 is 1.5.
\frac{4}{3}-\left(-\frac{17}{6}+\frac{3}{2}-|-\frac{2\times 6+1}{6}|\right)
Convert decimal number 1.5 to fraction \frac{15}{10}. Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.
\frac{4}{3}-\left(-\frac{17}{6}+\frac{9}{6}-|-\frac{2\times 6+1}{6}|\right)
Least common multiple of 6 and 2 is 6. Convert -\frac{17}{6} and \frac{3}{2} to fractions with denominator 6.
\frac{4}{3}-\left(\frac{-17+9}{6}-|-\frac{2\times 6+1}{6}|\right)
Since -\frac{17}{6} and \frac{9}{6} have the same denominator, add them by adding their numerators.
\frac{4}{3}-\left(\frac{-8}{6}-|-\frac{2\times 6+1}{6}|\right)
Add -17 and 9 to get -8.
\frac{4}{3}-\left(-\frac{4}{3}-|-\frac{2\times 6+1}{6}|\right)
Reduce the fraction \frac{-8}{6} to lowest terms by extracting and canceling out 2.
\frac{4}{3}-\left(-\frac{4}{3}-|-\frac{12+1}{6}|\right)
Multiply 2 and 6 to get 12.
\frac{4}{3}-\left(-\frac{4}{3}-|-\frac{13}{6}|\right)
Add 12 and 1 to get 13.
\frac{4}{3}-\left(-\frac{4}{3}-\frac{13}{6}\right)
The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{13}{6} is \frac{13}{6}.
\frac{4}{3}-\left(-\frac{8}{6}-\frac{13}{6}\right)
Least common multiple of 3 and 6 is 6. Convert -\frac{4}{3} and \frac{13}{6} to fractions with denominator 6.
\frac{4}{3}-\frac{-8-13}{6}
Since -\frac{8}{6} and \frac{13}{6} have the same denominator, subtract them by subtracting their numerators.
\frac{4}{3}-\frac{-21}{6}
Subtract 13 from -8 to get -21.
\frac{4}{3}-\left(-\frac{7}{2}\right)
Reduce the fraction \frac{-21}{6} to lowest terms by extracting and canceling out 3.
\frac{4}{3}+\frac{7}{2}
The opposite of -\frac{7}{2} is \frac{7}{2}.
\frac{8}{6}+\frac{21}{6}
Least common multiple of 3 and 2 is 6. Convert \frac{4}{3} and \frac{7}{2} to fractions with denominator 6.
\frac{8+21}{6}
Since \frac{8}{6} and \frac{21}{6} have the same denominator, add them by adding their numerators.
\frac{29}{6}
Add 8 and 21 to get 29.
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}