Evaluate
\frac{65}{18}\approx 3.611111111
Factor
\frac{5 \cdot 13}{2 \cdot 3 ^ {2}} = 3\frac{11}{18} = 3.611111111111111
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\begin{array}{l}\phantom{36)}\phantom{1}\\36\overline{)130}\\\end{array}
Use the 1^{st} digit 1 from dividend 130
\begin{array}{l}\phantom{36)}0\phantom{2}\\36\overline{)130}\\\end{array}
Since 1 is less than 36, use the next digit 3 from dividend 130 and add 0 to the quotient
\begin{array}{l}\phantom{36)}0\phantom{3}\\36\overline{)130}\\\end{array}
Use the 2^{nd} digit 3 from dividend 130
\begin{array}{l}\phantom{36)}00\phantom{4}\\36\overline{)130}\\\end{array}
Since 13 is less than 36, use the next digit 0 from dividend 130 and add 0 to the quotient
\begin{array}{l}\phantom{36)}00\phantom{5}\\36\overline{)130}\\\end{array}
Use the 3^{rd} digit 0 from dividend 130
\begin{array}{l}\phantom{36)}003\phantom{6}\\36\overline{)130}\\\phantom{36)}\underline{\phantom{}108\phantom{}}\\\phantom{36)9}22\\\end{array}
Find closest multiple of 36 to 130. We see that 3 \times 36 = 108 is the nearest. Now subtract 108 from 130 to get reminder 22. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }22
Since 22 is less than 36, stop the division. The reminder is 22. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}