Evaluate
5
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5
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\begin{array}{l}\phantom{54)}\phantom{1}\\54\overline{)270}\\\end{array}
Use the 1^{st} digit 2 from dividend 270
\begin{array}{l}\phantom{54)}0\phantom{2}\\54\overline{)270}\\\end{array}
Since 2 is less than 54, use the next digit 7 from dividend 270 and add 0 to the quotient
\begin{array}{l}\phantom{54)}0\phantom{3}\\54\overline{)270}\\\end{array}
Use the 2^{nd} digit 7 from dividend 270
\begin{array}{l}\phantom{54)}00\phantom{4}\\54\overline{)270}\\\end{array}
Since 27 is less than 54, use the next digit 0 from dividend 270 and add 0 to the quotient
\begin{array}{l}\phantom{54)}00\phantom{5}\\54\overline{)270}\\\end{array}
Use the 3^{rd} digit 0 from dividend 270
\begin{array}{l}\phantom{54)}005\phantom{6}\\54\overline{)270}\\\phantom{54)}\underline{\phantom{}270\phantom{}}\\\phantom{54)999}0\\\end{array}
Find closest multiple of 54 to 270. We see that 5 \times 54 = 270 is the nearest. Now subtract 270 from 270 to get reminder 0. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }0
Since 0 is less than 54, stop the division. The reminder is 0. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}