Evaluate
12
Factor
2^{2}\times 3
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\begin{array}{l}\phantom{36)}\phantom{1}\\36\overline{)432}\\\end{array}
Use the 1^{st} digit 4 from dividend 432
\begin{array}{l}\phantom{36)}0\phantom{2}\\36\overline{)432}\\\end{array}
Since 4 is less than 36, use the next digit 3 from dividend 432 and add 0 to the quotient
\begin{array}{l}\phantom{36)}0\phantom{3}\\36\overline{)432}\\\end{array}
Use the 2^{nd} digit 3 from dividend 432
\begin{array}{l}\phantom{36)}01\phantom{4}\\36\overline{)432}\\\phantom{36)}\underline{\phantom{}36\phantom{9}}\\\phantom{36)9}7\\\end{array}
Find closest multiple of 36 to 43. We see that 1 \times 36 = 36 is the nearest. Now subtract 36 from 43 to get reminder 7. Add 1 to quotient.
\begin{array}{l}\phantom{36)}01\phantom{5}\\36\overline{)432}\\\phantom{36)}\underline{\phantom{}36\phantom{9}}\\\phantom{36)9}72\\\end{array}
Use the 3^{rd} digit 2 from dividend 432
\begin{array}{l}\phantom{36)}012\phantom{6}\\36\overline{)432}\\\phantom{36)}\underline{\phantom{}36\phantom{9}}\\\phantom{36)9}72\\\phantom{36)}\underline{\phantom{9}72\phantom{}}\\\phantom{36)999}0\\\end{array}
Find closest multiple of 36 to 72. We see that 2 \times 36 = 72 is the nearest. Now subtract 72 from 72 to get reminder 0. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }0
Since 0 is less than 36, stop the division. The reminder is 0. The topmost line 012 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 12.
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}