Evaluate
\frac{90}{41}\approx 2.195121951
Factor
\frac{2 \cdot 3 ^ {2} \cdot 5}{41} = 2\frac{8}{41} = 2.1951219512195124
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\begin{array}{l}\phantom{82)}\phantom{1}\\82\overline{)180}\\\end{array}
Use the 1^{st} digit 1 from dividend 180
\begin{array}{l}\phantom{82)}0\phantom{2}\\82\overline{)180}\\\end{array}
Since 1 is less than 82, use the next digit 8 from dividend 180 and add 0 to the quotient
\begin{array}{l}\phantom{82)}0\phantom{3}\\82\overline{)180}\\\end{array}
Use the 2^{nd} digit 8 from dividend 180
\begin{array}{l}\phantom{82)}00\phantom{4}\\82\overline{)180}\\\end{array}
Since 18 is less than 82, use the next digit 0 from dividend 180 and add 0 to the quotient
\begin{array}{l}\phantom{82)}00\phantom{5}\\82\overline{)180}\\\end{array}
Use the 3^{rd} digit 0 from dividend 180
\begin{array}{l}\phantom{82)}002\phantom{6}\\82\overline{)180}\\\phantom{82)}\underline{\phantom{}164\phantom{}}\\\phantom{82)9}16\\\end{array}
Find closest multiple of 82 to 180. We see that 2 \times 82 = 164 is the nearest. Now subtract 164 from 180 to get reminder 16. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }16
Since 16 is less than 82, stop the division. The reminder is 16. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 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}