Evaluate
\frac{3189}{808}\approx 3.946782178
Factor
\frac{3 \cdot 1063}{2 ^ {3} \cdot 101} = 3\frac{765}{808} = 3.9467821782178216
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\begin{array}{l}\phantom{808)}\phantom{1}\\808\overline{)3189}\\\end{array}
Use the 1^{st} digit 3 from dividend 3189
\begin{array}{l}\phantom{808)}0\phantom{2}\\808\overline{)3189}\\\end{array}
Since 3 is less than 808, use the next digit 1 from dividend 3189 and add 0 to the quotient
\begin{array}{l}\phantom{808)}0\phantom{3}\\808\overline{)3189}\\\end{array}
Use the 2^{nd} digit 1 from dividend 3189
\begin{array}{l}\phantom{808)}00\phantom{4}\\808\overline{)3189}\\\end{array}
Since 31 is less than 808, use the next digit 8 from dividend 3189 and add 0 to the quotient
\begin{array}{l}\phantom{808)}00\phantom{5}\\808\overline{)3189}\\\end{array}
Use the 3^{rd} digit 8 from dividend 3189
\begin{array}{l}\phantom{808)}000\phantom{6}\\808\overline{)3189}\\\end{array}
Since 318 is less than 808, use the next digit 9 from dividend 3189 and add 0 to the quotient
\begin{array}{l}\phantom{808)}000\phantom{7}\\808\overline{)3189}\\\end{array}
Use the 4^{th} digit 9 from dividend 3189
\begin{array}{l}\phantom{808)}0003\phantom{8}\\808\overline{)3189}\\\phantom{808)}\underline{\phantom{}2424\phantom{}}\\\phantom{808)9}765\\\end{array}
Find closest multiple of 808 to 3189. We see that 3 \times 808 = 2424 is the nearest. Now subtract 2424 from 3189 to get reminder 765. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }765
Since 765 is less than 808, stop the division. The reminder is 765. The topmost line 0003 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}