Evaluate
\frac{25}{2}=12.5
Factor
\frac{5 ^ {2}}{2} = 12\frac{1}{2} = 12.5
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\begin{array}{l}\phantom{800)}\phantom{1}\\800\overline{)10000}\\\end{array}
Use the 1^{st} digit 1 from dividend 10000
\begin{array}{l}\phantom{800)}0\phantom{2}\\800\overline{)10000}\\\end{array}
Since 1 is less than 800, use the next digit 0 from dividend 10000 and add 0 to the quotient
\begin{array}{l}\phantom{800)}0\phantom{3}\\800\overline{)10000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 10000
\begin{array}{l}\phantom{800)}00\phantom{4}\\800\overline{)10000}\\\end{array}
Since 10 is less than 800, use the next digit 0 from dividend 10000 and add 0 to the quotient
\begin{array}{l}\phantom{800)}00\phantom{5}\\800\overline{)10000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 10000
\begin{array}{l}\phantom{800)}000\phantom{6}\\800\overline{)10000}\\\end{array}
Since 100 is less than 800, use the next digit 0 from dividend 10000 and add 0 to the quotient
\begin{array}{l}\phantom{800)}000\phantom{7}\\800\overline{)10000}\\\end{array}
Use the 4^{th} digit 0 from dividend 10000
\begin{array}{l}\phantom{800)}0001\phantom{8}\\800\overline{)10000}\\\phantom{800)}\underline{\phantom{9}800\phantom{9}}\\\phantom{800)9}200\\\end{array}
Find closest multiple of 800 to 1000. We see that 1 \times 800 = 800 is the nearest. Now subtract 800 from 1000 to get reminder 200. Add 1 to quotient.
\begin{array}{l}\phantom{800)}0001\phantom{9}\\800\overline{)10000}\\\phantom{800)}\underline{\phantom{9}800\phantom{9}}\\\phantom{800)9}2000\\\end{array}
Use the 5^{th} digit 0 from dividend 10000
\begin{array}{l}\phantom{800)}00012\phantom{10}\\800\overline{)10000}\\\phantom{800)}\underline{\phantom{9}800\phantom{9}}\\\phantom{800)9}2000\\\phantom{800)}\underline{\phantom{9}1600\phantom{}}\\\phantom{800)99}400\\\end{array}
Find closest multiple of 800 to 2000. We see that 2 \times 800 = 1600 is the nearest. Now subtract 1600 from 2000 to get reminder 400. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }400
Since 400 is less than 800, stop the division. The reminder is 400. The topmost line 00012 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 12.
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}