Evaluate
\frac{18}{5}=3.6
Factor
\frac{2 \cdot 3 ^ {2}}{5} = 3\frac{3}{5} = 3.6
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\begin{array}{l}\phantom{75)}\phantom{1}\\75\overline{)270}\\\end{array}
Use the 1^{st} digit 2 from dividend 270
\begin{array}{l}\phantom{75)}0\phantom{2}\\75\overline{)270}\\\end{array}
Since 2 is less than 75, use the next digit 7 from dividend 270 and add 0 to the quotient
\begin{array}{l}\phantom{75)}0\phantom{3}\\75\overline{)270}\\\end{array}
Use the 2^{nd} digit 7 from dividend 270
\begin{array}{l}\phantom{75)}00\phantom{4}\\75\overline{)270}\\\end{array}
Since 27 is less than 75, use the next digit 0 from dividend 270 and add 0 to the quotient
\begin{array}{l}\phantom{75)}00\phantom{5}\\75\overline{)270}\\\end{array}
Use the 3^{rd} digit 0 from dividend 270
\begin{array}{l}\phantom{75)}003\phantom{6}\\75\overline{)270}\\\phantom{75)}\underline{\phantom{}225\phantom{}}\\\phantom{75)9}45\\\end{array}
Find closest multiple of 75 to 270. We see that 3 \times 75 = 225 is the nearest. Now subtract 225 from 270 to get reminder 45. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }45
Since 45 is less than 75, stop the division. The reminder is 45. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}