Evaluate
\frac{5}{2}=2.5
Factor
\frac{5}{2} = 2\frac{1}{2} = 2.5
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\begin{array}{l}\phantom{50)}\phantom{1}\\50\overline{)125}\\\end{array}
Use the 1^{st} digit 1 from dividend 125
\begin{array}{l}\phantom{50)}0\phantom{2}\\50\overline{)125}\\\end{array}
Since 1 is less than 50, use the next digit 2 from dividend 125 and add 0 to the quotient
\begin{array}{l}\phantom{50)}0\phantom{3}\\50\overline{)125}\\\end{array}
Use the 2^{nd} digit 2 from dividend 125
\begin{array}{l}\phantom{50)}00\phantom{4}\\50\overline{)125}\\\end{array}
Since 12 is less than 50, use the next digit 5 from dividend 125 and add 0 to the quotient
\begin{array}{l}\phantom{50)}00\phantom{5}\\50\overline{)125}\\\end{array}
Use the 3^{rd} digit 5 from dividend 125
\begin{array}{l}\phantom{50)}002\phantom{6}\\50\overline{)125}\\\phantom{50)}\underline{\phantom{}100\phantom{}}\\\phantom{50)9}25\\\end{array}
Find closest multiple of 50 to 125. We see that 2 \times 50 = 100 is the nearest. Now subtract 100 from 125 to get reminder 25. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }25
Since 25 is less than 50, stop the division. The reminder is 25. 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}