Evaluate
\frac{855}{218}\approx 3.922018349
Factor
\frac{3 ^ {2} \cdot 5 \cdot 19}{2 \cdot 109} = 3\frac{201}{218} = 3.9220183486238533
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\begin{array}{l}\phantom{218)}\phantom{1}\\218\overline{)855}\\\end{array}
Use the 1^{st} digit 8 from dividend 855
\begin{array}{l}\phantom{218)}0\phantom{2}\\218\overline{)855}\\\end{array}
Since 8 is less than 218, use the next digit 5 from dividend 855 and add 0 to the quotient
\begin{array}{l}\phantom{218)}0\phantom{3}\\218\overline{)855}\\\end{array}
Use the 2^{nd} digit 5 from dividend 855
\begin{array}{l}\phantom{218)}00\phantom{4}\\218\overline{)855}\\\end{array}
Since 85 is less than 218, use the next digit 5 from dividend 855 and add 0 to the quotient
\begin{array}{l}\phantom{218)}00\phantom{5}\\218\overline{)855}\\\end{array}
Use the 3^{rd} digit 5 from dividend 855
\begin{array}{l}\phantom{218)}003\phantom{6}\\218\overline{)855}\\\phantom{218)}\underline{\phantom{}654\phantom{}}\\\phantom{218)}201\\\end{array}
Find closest multiple of 218 to 855. We see that 3 \times 218 = 654 is the nearest. Now subtract 654 from 855 to get reminder 201. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }201
Since 201 is less than 218, stop the division. The reminder is 201. 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}