Evaluate
\frac{27}{10}=2.7
Factor
\frac{3 ^ {3}}{2 \cdot 5} = 2\frac{7}{10} = 2.7
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\begin{array}{l}\phantom{60)}\phantom{1}\\60\overline{)162}\\\end{array}
Use the 1^{st} digit 1 from dividend 162
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)162}\\\end{array}
Since 1 is less than 60, use the next digit 6 from dividend 162 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)162}\\\end{array}
Use the 2^{nd} digit 6 from dividend 162
\begin{array}{l}\phantom{60)}00\phantom{4}\\60\overline{)162}\\\end{array}
Since 16 is less than 60, use the next digit 2 from dividend 162 and add 0 to the quotient
\begin{array}{l}\phantom{60)}00\phantom{5}\\60\overline{)162}\\\end{array}
Use the 3^{rd} digit 2 from dividend 162
\begin{array}{l}\phantom{60)}002\phantom{6}\\60\overline{)162}\\\phantom{60)}\underline{\phantom{}120\phantom{}}\\\phantom{60)9}42\\\end{array}
Find closest multiple of 60 to 162. We see that 2 \times 60 = 120 is the nearest. Now subtract 120 from 162 to get reminder 42. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }42
Since 42 is less than 60, stop the division. The reminder is 42. 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}