Evaluate
\frac{5}{2}=2.5
Factor
\frac{5}{2} = 2\frac{1}{2} = 2.5
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\begin{array}{l}\phantom{40)}\phantom{1}\\40\overline{)100}\\\end{array}
Use the 1^{st} digit 1 from dividend 100
\begin{array}{l}\phantom{40)}0\phantom{2}\\40\overline{)100}\\\end{array}
Since 1 is less than 40, use the next digit 0 from dividend 100 and add 0 to the quotient
\begin{array}{l}\phantom{40)}0\phantom{3}\\40\overline{)100}\\\end{array}
Use the 2^{nd} digit 0 from dividend 100
\begin{array}{l}\phantom{40)}00\phantom{4}\\40\overline{)100}\\\end{array}
Since 10 is less than 40, use the next digit 0 from dividend 100 and add 0 to the quotient
\begin{array}{l}\phantom{40)}00\phantom{5}\\40\overline{)100}\\\end{array}
Use the 3^{rd} digit 0 from dividend 100
\begin{array}{l}\phantom{40)}002\phantom{6}\\40\overline{)100}\\\phantom{40)}\underline{\phantom{9}80\phantom{}}\\\phantom{40)9}20\\\end{array}
Find closest multiple of 40 to 100. We see that 2 \times 40 = 80 is the nearest. Now subtract 80 from 100 to get reminder 20. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }20
Since 20 is less than 40, stop the division. The reminder is 20. 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}