Evaluate
\frac{36}{13}\approx 2.769230769
Factor
\frac{2 ^ {2} \cdot 3 ^ {2}}{13} = 2\frac{10}{13} = 2.769230769230769
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\begin{array}{l}\phantom{65)}\phantom{1}\\65\overline{)180}\\\end{array}
Use the 1^{st} digit 1 from dividend 180
\begin{array}{l}\phantom{65)}0\phantom{2}\\65\overline{)180}\\\end{array}
Since 1 is less than 65, use the next digit 8 from dividend 180 and add 0 to the quotient
\begin{array}{l}\phantom{65)}0\phantom{3}\\65\overline{)180}\\\end{array}
Use the 2^{nd} digit 8 from dividend 180
\begin{array}{l}\phantom{65)}00\phantom{4}\\65\overline{)180}\\\end{array}
Since 18 is less than 65, use the next digit 0 from dividend 180 and add 0 to the quotient
\begin{array}{l}\phantom{65)}00\phantom{5}\\65\overline{)180}\\\end{array}
Use the 3^{rd} digit 0 from dividend 180
\begin{array}{l}\phantom{65)}002\phantom{6}\\65\overline{)180}\\\phantom{65)}\underline{\phantom{}130\phantom{}}\\\phantom{65)9}50\\\end{array}
Find closest multiple of 65 to 180. We see that 2 \times 65 = 130 is the nearest. Now subtract 130 from 180 to get reminder 50. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }50
Since 50 is less than 65, stop the division. The reminder is 50. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}