Evaluate
\frac{135}{11}\approx 12.272727273
Factor
\frac{3 ^ {3} \cdot 5}{11} = 12\frac{3}{11} = 12.272727272727273
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\begin{array}{l}\phantom{11)}\phantom{1}\\11\overline{)135}\\\end{array}
Use the 1^{st} digit 1 from dividend 135
\begin{array}{l}\phantom{11)}0\phantom{2}\\11\overline{)135}\\\end{array}
Since 1 is less than 11, use the next digit 3 from dividend 135 and add 0 to the quotient
\begin{array}{l}\phantom{11)}0\phantom{3}\\11\overline{)135}\\\end{array}
Use the 2^{nd} digit 3 from dividend 135
\begin{array}{l}\phantom{11)}01\phantom{4}\\11\overline{)135}\\\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{)135}\\\phantom{11)}\underline{\phantom{}11\phantom{9}}\\\phantom{11)9}25\\\end{array}
Use the 3^{rd} digit 5 from dividend 135
\begin{array}{l}\phantom{11)}012\phantom{6}\\11\overline{)135}\\\phantom{11)}\underline{\phantom{}11\phantom{9}}\\\phantom{11)9}25\\\phantom{11)}\underline{\phantom{9}22\phantom{}}\\\phantom{11)99}3\\\end{array}
Find closest multiple of 11 to 25. We see that 2 \times 11 = 22 is the nearest. Now subtract 22 from 25 to get reminder 3. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }3
Since 3 is less than 11, stop the division. The reminder is 3. 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}