Evaluate
12
Factor
2^{2}\times 3
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\begin{array}{l}\phantom{11)}\phantom{1}\\11\overline{)132}\\\end{array}
Use the 1^{st} digit 1 from dividend 132
\begin{array}{l}\phantom{11)}0\phantom{2}\\11\overline{)132}\\\end{array}
Since 1 is less than 11, use the next digit 3 from dividend 132 and add 0 to the quotient
\begin{array}{l}\phantom{11)}0\phantom{3}\\11\overline{)132}\\\end{array}
Use the 2^{nd} digit 3 from dividend 132
\begin{array}{l}\phantom{11)}01\phantom{4}\\11\overline{)132}\\\phantom{11)}\underline{\phantom{}11\phantom{9}}\\\phantom{11)9}2\\\end{array}
Find closest multiple of 11 to 13. We see that 1 \times 11 = 11 is the nearest. Now subtract 11 from 13 to get reminder 2. Add 1 to quotient.
\begin{array}{l}\phantom{11)}01\phantom{5}\\11\overline{)132}\\\phantom{11)}\underline{\phantom{}11\phantom{9}}\\\phantom{11)9}22\\\end{array}
Use the 3^{rd} digit 2 from dividend 132
\begin{array}{l}\phantom{11)}012\phantom{6}\\11\overline{)132}\\\phantom{11)}\underline{\phantom{}11\phantom{9}}\\\phantom{11)9}22\\\phantom{11)}\underline{\phantom{9}22\phantom{}}\\\phantom{11)999}0\\\end{array}
Find closest multiple of 11 to 22. We see that 2 \times 11 = 22 is the nearest. Now subtract 22 from 22 to get reminder 0. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }0
Since 0 is less than 11, 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}