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{363)}\phantom{1}\\363\overline{)429}\\\end{array}
Use the 1^{st} digit 4 from dividend 429
\begin{array}{l}\phantom{363)}0\phantom{2}\\363\overline{)429}\\\end{array}
Since 4 is less than 363, use the next digit 2 from dividend 429 and add 0 to the quotient
\begin{array}{l}\phantom{363)}0\phantom{3}\\363\overline{)429}\\\end{array}
Use the 2^{nd} digit 2 from dividend 429
\begin{array}{l}\phantom{363)}00\phantom{4}\\363\overline{)429}\\\end{array}
Since 42 is less than 363, use the next digit 9 from dividend 429 and add 0 to the quotient
\begin{array}{l}\phantom{363)}00\phantom{5}\\363\overline{)429}\\\end{array}
Use the 3^{rd} digit 9 from dividend 429
\begin{array}{l}\phantom{363)}001\phantom{6}\\363\overline{)429}\\\phantom{363)}\underline{\phantom{}363\phantom{}}\\\phantom{363)9}66\\\end{array}
Find closest multiple of 363 to 429. We see that 1 \times 363 = 363 is the nearest. Now subtract 363 from 429 to get reminder 66. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }66
Since 66 is less than 363, stop the division. The reminder is 66. The topmost line 001 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}