Evaluate
\frac{13}{11}\approx 1.181818182
Factor
\frac{13}{11} = 1\frac{2}{11} = 1.1818181818181819
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\begin{array}{l}\phantom{66)}\phantom{1}\\66\overline{)78}\\\end{array}
Use the 1^{st} digit 7 from dividend 78
\begin{array}{l}\phantom{66)}0\phantom{2}\\66\overline{)78}\\\end{array}
Since 7 is less than 66, use the next digit 8 from dividend 78 and add 0 to the quotient
\begin{array}{l}\phantom{66)}0\phantom{3}\\66\overline{)78}\\\end{array}
Use the 2^{nd} digit 8 from dividend 78
\begin{array}{l}\phantom{66)}01\phantom{4}\\66\overline{)78}\\\phantom{66)}\underline{\phantom{}66\phantom{}}\\\phantom{66)}12\\\end{array}
Find closest multiple of 66 to 78. We see that 1 \times 66 = 66 is the nearest. Now subtract 66 from 78 to get reminder 12. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }12
Since 12 is less than 66, stop the division. The reminder is 12. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}