Evaluate
\frac{6836}{999}\approx 6.842842843
Factor
\frac{2 ^ {2} \cdot 1709}{3 ^ {3} \cdot 37} = 6\frac{842}{999} = 6.842842842842843
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\begin{array}{l}\phantom{999)}\phantom{1}\\999\overline{)6836}\\\end{array}
Use the 1^{st} digit 6 from dividend 6836
\begin{array}{l}\phantom{999)}0\phantom{2}\\999\overline{)6836}\\\end{array}
Since 6 is less than 999, use the next digit 8 from dividend 6836 and add 0 to the quotient
\begin{array}{l}\phantom{999)}0\phantom{3}\\999\overline{)6836}\\\end{array}
Use the 2^{nd} digit 8 from dividend 6836
\begin{array}{l}\phantom{999)}00\phantom{4}\\999\overline{)6836}\\\end{array}
Since 68 is less than 999, use the next digit 3 from dividend 6836 and add 0 to the quotient
\begin{array}{l}\phantom{999)}00\phantom{5}\\999\overline{)6836}\\\end{array}
Use the 3^{rd} digit 3 from dividend 6836
\begin{array}{l}\phantom{999)}000\phantom{6}\\999\overline{)6836}\\\end{array}
Since 683 is less than 999, use the next digit 6 from dividend 6836 and add 0 to the quotient
\begin{array}{l}\phantom{999)}000\phantom{7}\\999\overline{)6836}\\\end{array}
Use the 4^{th} digit 6 from dividend 6836
\begin{array}{l}\phantom{999)}0006\phantom{8}\\999\overline{)6836}\\\phantom{999)}\underline{\phantom{}5994\phantom{}}\\\phantom{999)9}842\\\end{array}
Find closest multiple of 999 to 6836. We see that 6 \times 999 = 5994 is the nearest. Now subtract 5994 from 6836 to get reminder 842. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }842
Since 842 is less than 999, stop the division. The reminder is 842. The topmost line 0006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}