Evaluate
\frac{5}{2}=2.5
Factor
\frac{5}{2} = 2\frac{1}{2} = 2.5
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\begin{array}{l}\phantom{150)}\phantom{1}\\150\overline{)375}\\\end{array}
Use the 1^{st} digit 3 from dividend 375
\begin{array}{l}\phantom{150)}0\phantom{2}\\150\overline{)375}\\\end{array}
Since 3 is less than 150, use the next digit 7 from dividend 375 and add 0 to the quotient
\begin{array}{l}\phantom{150)}0\phantom{3}\\150\overline{)375}\\\end{array}
Use the 2^{nd} digit 7 from dividend 375
\begin{array}{l}\phantom{150)}00\phantom{4}\\150\overline{)375}\\\end{array}
Since 37 is less than 150, use the next digit 5 from dividend 375 and add 0 to the quotient
\begin{array}{l}\phantom{150)}00\phantom{5}\\150\overline{)375}\\\end{array}
Use the 3^{rd} digit 5 from dividend 375
\begin{array}{l}\phantom{150)}002\phantom{6}\\150\overline{)375}\\\phantom{150)}\underline{\phantom{}300\phantom{}}\\\phantom{150)9}75\\\end{array}
Find closest multiple of 150 to 375. We see that 2 \times 150 = 300 is the nearest. Now subtract 300 from 375 to get reminder 75. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }75
Since 75 is less than 150, stop the division. The reminder is 75. 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}