Evaluate
\frac{23}{2}=11.5
Factor
\frac{23}{2} = 11\frac{1}{2} = 11.5
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\begin{array}{l}\phantom{20)}\phantom{1}\\20\overline{)230}\\\end{array}
Use the 1^{st} digit 2 from dividend 230
\begin{array}{l}\phantom{20)}0\phantom{2}\\20\overline{)230}\\\end{array}
Since 2 is less than 20, use the next digit 3 from dividend 230 and add 0 to the quotient
\begin{array}{l}\phantom{20)}0\phantom{3}\\20\overline{)230}\\\end{array}
Use the 2^{nd} digit 3 from dividend 230
\begin{array}{l}\phantom{20)}01\phantom{4}\\20\overline{)230}\\\phantom{20)}\underline{\phantom{}20\phantom{9}}\\\phantom{20)9}3\\\end{array}
Find closest multiple of 20 to 23. We see that 1 \times 20 = 20 is the nearest. Now subtract 20 from 23 to get reminder 3. Add 1 to quotient.
\begin{array}{l}\phantom{20)}01\phantom{5}\\20\overline{)230}\\\phantom{20)}\underline{\phantom{}20\phantom{9}}\\\phantom{20)9}30\\\end{array}
Use the 3^{rd} digit 0 from dividend 230
\begin{array}{l}\phantom{20)}011\phantom{6}\\20\overline{)230}\\\phantom{20)}\underline{\phantom{}20\phantom{9}}\\\phantom{20)9}30\\\phantom{20)}\underline{\phantom{9}20\phantom{}}\\\phantom{20)9}10\\\end{array}
Find closest multiple of 20 to 30. We see that 1 \times 20 = 20 is the nearest. Now subtract 20 from 30 to get reminder 10. Add 1 to quotient.
\text{Quotient: }11 \text{Reminder: }10
Since 10 is less than 20, stop the division. The reminder is 10. The topmost line 011 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 11.
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}