Evaluate
\frac{57}{11}\approx 5.181818182
Factor
\frac{3 \cdot 19}{11} = 5\frac{2}{11} = 5.181818181818182
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\begin{array}{l}\phantom{11)}\phantom{1}\\11\overline{)57}\\\end{array}
Use the 1^{st} digit 5 from dividend 57
\begin{array}{l}\phantom{11)}0\phantom{2}\\11\overline{)57}\\\end{array}
Since 5 is less than 11, use the next digit 7 from dividend 57 and add 0 to the quotient
\begin{array}{l}\phantom{11)}0\phantom{3}\\11\overline{)57}\\\end{array}
Use the 2^{nd} digit 7 from dividend 57
\begin{array}{l}\phantom{11)}05\phantom{4}\\11\overline{)57}\\\phantom{11)}\underline{\phantom{}55\phantom{}}\\\phantom{11)9}2\\\end{array}
Find closest multiple of 11 to 57. We see that 5 \times 11 = 55 is the nearest. Now subtract 55 from 57 to get reminder 2. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }2
Since 2 is less than 11, stop the division. The reminder is 2. The topmost line 05 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}