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\begin{array}{l}\phantom{41)}\phantom{1}\\41\overline{)82}\\\end{array}
Use the 1^{st} digit 8 from dividend 82
\begin{array}{l}\phantom{41)}0\phantom{2}\\41\overline{)82}\\\end{array}
Since 8 is less than 41, use the next digit 2 from dividend 82 and add 0 to the quotient
\begin{array}{l}\phantom{41)}0\phantom{3}\\41\overline{)82}\\\end{array}
Use the 2^{nd} digit 2 from dividend 82
\begin{array}{l}\phantom{41)}02\phantom{4}\\41\overline{)82}\\\phantom{41)}\underline{\phantom{}82\phantom{}}\\\phantom{41)99}0\\\end{array}
Find closest multiple of 41 to 82. We see that 2 \times 41 = 82 is the nearest. Now subtract 82 from 82 to get reminder 0. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }0
Since 0 is less than 41, stop the division. The reminder is 0. The topmost line 02 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}