Evaluate
\frac{219}{10}=21.9
Factor
\frac{3 \cdot 73}{2 \cdot 5} = 21\frac{9}{10} = 21.9
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\begin{array}{l}\phantom{3120)}\phantom{1}\\3120\overline{)68328}\\\end{array}
Use the 1^{st} digit 6 from dividend 68328
\begin{array}{l}\phantom{3120)}0\phantom{2}\\3120\overline{)68328}\\\end{array}
Since 6 is less than 3120, use the next digit 8 from dividend 68328 and add 0 to the quotient
\begin{array}{l}\phantom{3120)}0\phantom{3}\\3120\overline{)68328}\\\end{array}
Use the 2^{nd} digit 8 from dividend 68328
\begin{array}{l}\phantom{3120)}00\phantom{4}\\3120\overline{)68328}\\\end{array}
Since 68 is less than 3120, use the next digit 3 from dividend 68328 and add 0 to the quotient
\begin{array}{l}\phantom{3120)}00\phantom{5}\\3120\overline{)68328}\\\end{array}
Use the 3^{rd} digit 3 from dividend 68328
\begin{array}{l}\phantom{3120)}000\phantom{6}\\3120\overline{)68328}\\\end{array}
Since 683 is less than 3120, use the next digit 2 from dividend 68328 and add 0 to the quotient
\begin{array}{l}\phantom{3120)}000\phantom{7}\\3120\overline{)68328}\\\end{array}
Use the 4^{th} digit 2 from dividend 68328
\begin{array}{l}\phantom{3120)}0002\phantom{8}\\3120\overline{)68328}\\\phantom{3120)}\underline{\phantom{}6240\phantom{9}}\\\phantom{3120)9}592\\\end{array}
Find closest multiple of 3120 to 6832. We see that 2 \times 3120 = 6240 is the nearest. Now subtract 6240 from 6832 to get reminder 592. Add 2 to quotient.
\begin{array}{l}\phantom{3120)}0002\phantom{9}\\3120\overline{)68328}\\\phantom{3120)}\underline{\phantom{}6240\phantom{9}}\\\phantom{3120)9}5928\\\end{array}
Use the 5^{th} digit 8 from dividend 68328
\begin{array}{l}\phantom{3120)}00021\phantom{10}\\3120\overline{)68328}\\\phantom{3120)}\underline{\phantom{}6240\phantom{9}}\\\phantom{3120)9}5928\\\phantom{3120)}\underline{\phantom{9}3120\phantom{}}\\\phantom{3120)9}2808\\\end{array}
Find closest multiple of 3120 to 5928. We see that 1 \times 3120 = 3120 is the nearest. Now subtract 3120 from 5928 to get reminder 2808. Add 1 to quotient.
\text{Quotient: }21 \text{Reminder: }2808
Since 2808 is less than 3120, stop the division. The reminder is 2808. The topmost line 00021 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 21.
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}