Evaluate
\frac{200}{9}\approx 22.222222222
Factor
\frac{2 ^ {3} \cdot 5 ^ {2}}{3 ^ {2}} = 22\frac{2}{9} = 22.22222222222222
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\begin{array}{l}\phantom{18)}\phantom{1}\\18\overline{)400}\\\end{array}
Use the 1^{st} digit 4 from dividend 400
\begin{array}{l}\phantom{18)}0\phantom{2}\\18\overline{)400}\\\end{array}
Since 4 is less than 18, use the next digit 0 from dividend 400 and add 0 to the quotient
\begin{array}{l}\phantom{18)}0\phantom{3}\\18\overline{)400}\\\end{array}
Use the 2^{nd} digit 0 from dividend 400
\begin{array}{l}\phantom{18)}02\phantom{4}\\18\overline{)400}\\\phantom{18)}\underline{\phantom{}36\phantom{9}}\\\phantom{18)9}4\\\end{array}
Find closest multiple of 18 to 40. We see that 2 \times 18 = 36 is the nearest. Now subtract 36 from 40 to get reminder 4. Add 2 to quotient.
\begin{array}{l}\phantom{18)}02\phantom{5}\\18\overline{)400}\\\phantom{18)}\underline{\phantom{}36\phantom{9}}\\\phantom{18)9}40\\\end{array}
Use the 3^{rd} digit 0 from dividend 400
\begin{array}{l}\phantom{18)}022\phantom{6}\\18\overline{)400}\\\phantom{18)}\underline{\phantom{}36\phantom{9}}\\\phantom{18)9}40\\\phantom{18)}\underline{\phantom{9}36\phantom{}}\\\phantom{18)99}4\\\end{array}
Find closest multiple of 18 to 40. We see that 2 \times 18 = 36 is the nearest. Now subtract 36 from 40 to get reminder 4. Add 2 to quotient.
\text{Quotient: }22 \text{Reminder: }4
Since 4 is less than 18, stop the division. The reminder is 4. The topmost line 022 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 22.
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}