Evaluate
\frac{5}{2}=2.5
Factor
\frac{5}{2} = 2\frac{1}{2} = 2.5
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\begin{array}{l}\phantom{200)}\phantom{1}\\200\overline{)500}\\\end{array}
Use the 1^{st} digit 5 from dividend 500
\begin{array}{l}\phantom{200)}0\phantom{2}\\200\overline{)500}\\\end{array}
Since 5 is less than 200, use the next digit 0 from dividend 500 and add 0 to the quotient
\begin{array}{l}\phantom{200)}0\phantom{3}\\200\overline{)500}\\\end{array}
Use the 2^{nd} digit 0 from dividend 500
\begin{array}{l}\phantom{200)}00\phantom{4}\\200\overline{)500}\\\end{array}
Since 50 is less than 200, use the next digit 0 from dividend 500 and add 0 to the quotient
\begin{array}{l}\phantom{200)}00\phantom{5}\\200\overline{)500}\\\end{array}
Use the 3^{rd} digit 0 from dividend 500
\begin{array}{l}\phantom{200)}002\phantom{6}\\200\overline{)500}\\\phantom{200)}\underline{\phantom{}400\phantom{}}\\\phantom{200)}100\\\end{array}
Find closest multiple of 200 to 500. We see that 2 \times 200 = 400 is the nearest. Now subtract 400 from 500 to get reminder 100. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }100
Since 100 is less than 200, stop the division. The reminder is 100. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}