Evaluate
\frac{123}{11}\approx 11.181818182
Factor
\frac{3 \cdot 41}{11} = 11\frac{2}{11} = 11.181818181818182
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\begin{array}{l}\phantom{33)}\phantom{1}\\33\overline{)369}\\\end{array}
Use the 1^{st} digit 3 from dividend 369
\begin{array}{l}\phantom{33)}0\phantom{2}\\33\overline{)369}\\\end{array}
Since 3 is less than 33, use the next digit 6 from dividend 369 and add 0 to the quotient
\begin{array}{l}\phantom{33)}0\phantom{3}\\33\overline{)369}\\\end{array}
Use the 2^{nd} digit 6 from dividend 369
\begin{array}{l}\phantom{33)}01\phantom{4}\\33\overline{)369}\\\phantom{33)}\underline{\phantom{}33\phantom{9}}\\\phantom{33)9}3\\\end{array}
Find closest multiple of 33 to 36. We see that 1 \times 33 = 33 is the nearest. Now subtract 33 from 36 to get reminder 3. Add 1 to quotient.
\begin{array}{l}\phantom{33)}01\phantom{5}\\33\overline{)369}\\\phantom{33)}\underline{\phantom{}33\phantom{9}}\\\phantom{33)9}39\\\end{array}
Use the 3^{rd} digit 9 from dividend 369
\begin{array}{l}\phantom{33)}011\phantom{6}\\33\overline{)369}\\\phantom{33)}\underline{\phantom{}33\phantom{9}}\\\phantom{33)9}39\\\phantom{33)}\underline{\phantom{9}33\phantom{}}\\\phantom{33)99}6\\\end{array}
Find closest multiple of 33 to 39. We see that 1 \times 33 = 33 is the nearest. Now subtract 33 from 39 to get reminder 6. Add 1 to quotient.
\text{Quotient: }11 \text{Reminder: }6
Since 6 is less than 33, stop the division. The reminder is 6. 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}