Evaluate
\frac{36}{11}\approx 3.272727273
Factor
\frac{2 ^ {2} \cdot 3 ^ {2}}{11} = 3\frac{3}{11} = 3.272727272727273
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\begin{array}{l}\phantom{55)}\phantom{1}\\55\overline{)180}\\\end{array}
Use the 1^{st} digit 1 from dividend 180
\begin{array}{l}\phantom{55)}0\phantom{2}\\55\overline{)180}\\\end{array}
Since 1 is less than 55, use the next digit 8 from dividend 180 and add 0 to the quotient
\begin{array}{l}\phantom{55)}0\phantom{3}\\55\overline{)180}\\\end{array}
Use the 2^{nd} digit 8 from dividend 180
\begin{array}{l}\phantom{55)}00\phantom{4}\\55\overline{)180}\\\end{array}
Since 18 is less than 55, use the next digit 0 from dividend 180 and add 0 to the quotient
\begin{array}{l}\phantom{55)}00\phantom{5}\\55\overline{)180}\\\end{array}
Use the 3^{rd} digit 0 from dividend 180
\begin{array}{l}\phantom{55)}003\phantom{6}\\55\overline{)180}\\\phantom{55)}\underline{\phantom{}165\phantom{}}\\\phantom{55)9}15\\\end{array}
Find closest multiple of 55 to 180. We see that 3 \times 55 = 165 is the nearest. Now subtract 165 from 180 to get reminder 15. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }15
Since 15 is less than 55, stop the division. The reminder is 15. 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}