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\begin{array}{l}\phantom{123)}\phantom{1}\\123\overline{)123}\\\end{array}
Use the 1^{st} digit 1 from dividend 123
\begin{array}{l}\phantom{123)}0\phantom{2}\\123\overline{)123}\\\end{array}
Since 1 is less than 123, use the next digit 2 from dividend 123 and add 0 to the quotient
\begin{array}{l}\phantom{123)}0\phantom{3}\\123\overline{)123}\\\end{array}
Use the 2^{nd} digit 2 from dividend 123
\begin{array}{l}\phantom{123)}00\phantom{4}\\123\overline{)123}\\\end{array}
Since 12 is less than 123, use the next digit 3 from dividend 123 and add 0 to the quotient
\begin{array}{l}\phantom{123)}00\phantom{5}\\123\overline{)123}\\\end{array}
Use the 3^{rd} digit 3 from dividend 123
\begin{array}{l}\phantom{123)}001\phantom{6}\\123\overline{)123}\\\phantom{123)}\underline{\phantom{}123\phantom{}}\\\phantom{123)999}0\\\end{array}
Find closest multiple of 123 to 123. We see that 1 \times 123 = 123 is the nearest. Now subtract 123 from 123 to get reminder 0. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }0
Since 0 is less than 123, stop the division. The reminder is 0. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}