Evaluate
\frac{93}{4}=23.25
Factor
\frac{3 \cdot 31}{2 ^ {2}} = 23\frac{1}{4} = 23.25
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\begin{array}{l}\phantom{20000)}\phantom{1}\\20000\overline{)465000}\\\end{array}
Use the 1^{st} digit 4 from dividend 465000
\begin{array}{l}\phantom{20000)}0\phantom{2}\\20000\overline{)465000}\\\end{array}
Since 4 is less than 20000, use the next digit 6 from dividend 465000 and add 0 to the quotient
\begin{array}{l}\phantom{20000)}0\phantom{3}\\20000\overline{)465000}\\\end{array}
Use the 2^{nd} digit 6 from dividend 465000
\begin{array}{l}\phantom{20000)}00\phantom{4}\\20000\overline{)465000}\\\end{array}
Since 46 is less than 20000, use the next digit 5 from dividend 465000 and add 0 to the quotient
\begin{array}{l}\phantom{20000)}00\phantom{5}\\20000\overline{)465000}\\\end{array}
Use the 3^{rd} digit 5 from dividend 465000
\begin{array}{l}\phantom{20000)}000\phantom{6}\\20000\overline{)465000}\\\end{array}
Since 465 is less than 20000, use the next digit 0 from dividend 465000 and add 0 to the quotient
\begin{array}{l}\phantom{20000)}000\phantom{7}\\20000\overline{)465000}\\\end{array}
Use the 4^{th} digit 0 from dividend 465000
\begin{array}{l}\phantom{20000)}0000\phantom{8}\\20000\overline{)465000}\\\end{array}
Since 4650 is less than 20000, use the next digit 0 from dividend 465000 and add 0 to the quotient
\begin{array}{l}\phantom{20000)}0000\phantom{9}\\20000\overline{)465000}\\\end{array}
Use the 5^{th} digit 0 from dividend 465000
\begin{array}{l}\phantom{20000)}00002\phantom{10}\\20000\overline{)465000}\\\phantom{20000)}\underline{\phantom{}40000\phantom{9}}\\\phantom{20000)9}6500\\\end{array}
Find closest multiple of 20000 to 46500. We see that 2 \times 20000 = 40000 is the nearest. Now subtract 40000 from 46500 to get reminder 6500. Add 2 to quotient.
\begin{array}{l}\phantom{20000)}00002\phantom{11}\\20000\overline{)465000}\\\phantom{20000)}\underline{\phantom{}40000\phantom{9}}\\\phantom{20000)9}65000\\\end{array}
Use the 6^{th} digit 0 from dividend 465000
\begin{array}{l}\phantom{20000)}000023\phantom{12}\\20000\overline{)465000}\\\phantom{20000)}\underline{\phantom{}40000\phantom{9}}\\\phantom{20000)9}65000\\\phantom{20000)}\underline{\phantom{9}60000\phantom{}}\\\phantom{20000)99}5000\\\end{array}
Find closest multiple of 20000 to 65000. We see that 3 \times 20000 = 60000 is the nearest. Now subtract 60000 from 65000 to get reminder 5000. Add 3 to quotient.
\text{Quotient: }23 \text{Reminder: }5000
Since 5000 is less than 20000, stop the division. The reminder is 5000. The topmost line 000023 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 23.
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}