Evaluate
\frac{205}{33}\approx 6.212121212
Factor
\frac{5 \cdot 41}{3 \cdot 11} = 6\frac{7}{33} = 6.212121212121212
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\begin{array}{l}\phantom{330)}\phantom{1}\\330\overline{)2050}\\\end{array}
Use the 1^{st} digit 2 from dividend 2050
\begin{array}{l}\phantom{330)}0\phantom{2}\\330\overline{)2050}\\\end{array}
Since 2 is less than 330, use the next digit 0 from dividend 2050 and add 0 to the quotient
\begin{array}{l}\phantom{330)}0\phantom{3}\\330\overline{)2050}\\\end{array}
Use the 2^{nd} digit 0 from dividend 2050
\begin{array}{l}\phantom{330)}00\phantom{4}\\330\overline{)2050}\\\end{array}
Since 20 is less than 330, use the next digit 5 from dividend 2050 and add 0 to the quotient
\begin{array}{l}\phantom{330)}00\phantom{5}\\330\overline{)2050}\\\end{array}
Use the 3^{rd} digit 5 from dividend 2050
\begin{array}{l}\phantom{330)}000\phantom{6}\\330\overline{)2050}\\\end{array}
Since 205 is less than 330, use the next digit 0 from dividend 2050 and add 0 to the quotient
\begin{array}{l}\phantom{330)}000\phantom{7}\\330\overline{)2050}\\\end{array}
Use the 4^{th} digit 0 from dividend 2050
\begin{array}{l}\phantom{330)}0006\phantom{8}\\330\overline{)2050}\\\phantom{330)}\underline{\phantom{}1980\phantom{}}\\\phantom{330)99}70\\\end{array}
Find closest multiple of 330 to 2050. We see that 6 \times 330 = 1980 is the nearest. Now subtract 1980 from 2050 to get reminder 70. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }70
Since 70 is less than 330, stop the division. The reminder is 70. The topmost line 0006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}