Evaluate
33
Factor
3\times 11
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\begin{array}{l}\phantom{11)}\phantom{1}\\11\overline{)363}\\\end{array}
Use the 1^{st} digit 3 from dividend 363
\begin{array}{l}\phantom{11)}0\phantom{2}\\11\overline{)363}\\\end{array}
Since 3 is less than 11, use the next digit 6 from dividend 363 and add 0 to the quotient
\begin{array}{l}\phantom{11)}0\phantom{3}\\11\overline{)363}\\\end{array}
Use the 2^{nd} digit 6 from dividend 363
\begin{array}{l}\phantom{11)}03\phantom{4}\\11\overline{)363}\\\phantom{11)}\underline{\phantom{}33\phantom{9}}\\\phantom{11)9}3\\\end{array}
Find closest multiple of 11 to 36. We see that 3 \times 11 = 33 is the nearest. Now subtract 33 from 36 to get reminder 3. Add 3 to quotient.
\begin{array}{l}\phantom{11)}03\phantom{5}\\11\overline{)363}\\\phantom{11)}\underline{\phantom{}33\phantom{9}}\\\phantom{11)9}33\\\end{array}
Use the 3^{rd} digit 3 from dividend 363
\begin{array}{l}\phantom{11)}033\phantom{6}\\11\overline{)363}\\\phantom{11)}\underline{\phantom{}33\phantom{9}}\\\phantom{11)9}33\\\phantom{11)}\underline{\phantom{9}33\phantom{}}\\\phantom{11)999}0\\\end{array}
Find closest multiple of 11 to 33. We see that 3 \times 11 = 33 is the nearest. Now subtract 33 from 33 to get reminder 0. Add 3 to quotient.
\text{Quotient: }33 \text{Reminder: }0
Since 0 is less than 11, stop the division. The reminder is 0. The topmost line 033 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 33.
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}