Evaluate
\frac{141}{11}\approx 12.818181818
Factor
\frac{3 \cdot 47}{11} = 12\frac{9}{11} = 12.818181818181818
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\begin{array}{l}\phantom{11)}\phantom{1}\\11\overline{)141}\\\end{array}
Use the 1^{st} digit 1 from dividend 141
\begin{array}{l}\phantom{11)}0\phantom{2}\\11\overline{)141}\\\end{array}
Since 1 is less than 11, use the next digit 4 from dividend 141 and add 0 to the quotient
\begin{array}{l}\phantom{11)}0\phantom{3}\\11\overline{)141}\\\end{array}
Use the 2^{nd} digit 4 from dividend 141
\begin{array}{l}\phantom{11)}01\phantom{4}\\11\overline{)141}\\\phantom{11)}\underline{\phantom{}11\phantom{9}}\\\phantom{11)9}3\\\end{array}
Find closest multiple of 11 to 14. We see that 1 \times 11 = 11 is the nearest. Now subtract 11 from 14 to get reminder 3. Add 1 to quotient.
\begin{array}{l}\phantom{11)}01\phantom{5}\\11\overline{)141}\\\phantom{11)}\underline{\phantom{}11\phantom{9}}\\\phantom{11)9}31\\\end{array}
Use the 3^{rd} digit 1 from dividend 141
\begin{array}{l}\phantom{11)}012\phantom{6}\\11\overline{)141}\\\phantom{11)}\underline{\phantom{}11\phantom{9}}\\\phantom{11)9}31\\\phantom{11)}\underline{\phantom{9}22\phantom{}}\\\phantom{11)99}9\\\end{array}
Find closest multiple of 11 to 31. We see that 2 \times 11 = 22 is the nearest. Now subtract 22 from 31 to get reminder 9. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }9
Since 9 is less than 11, stop the division. The reminder is 9. 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}