Evaluate
9
Factor
3^{2}
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\begin{array}{l}\phantom{27)}\phantom{1}\\27\overline{)243}\\\end{array}
Use the 1^{st} digit 2 from dividend 243
\begin{array}{l}\phantom{27)}0\phantom{2}\\27\overline{)243}\\\end{array}
Since 2 is less than 27, use the next digit 4 from dividend 243 and add 0 to the quotient
\begin{array}{l}\phantom{27)}0\phantom{3}\\27\overline{)243}\\\end{array}
Use the 2^{nd} digit 4 from dividend 243
\begin{array}{l}\phantom{27)}00\phantom{4}\\27\overline{)243}\\\end{array}
Since 24 is less than 27, use the next digit 3 from dividend 243 and add 0 to the quotient
\begin{array}{l}\phantom{27)}00\phantom{5}\\27\overline{)243}\\\end{array}
Use the 3^{rd} digit 3 from dividend 243
\begin{array}{l}\phantom{27)}009\phantom{6}\\27\overline{)243}\\\phantom{27)}\underline{\phantom{}243\phantom{}}\\\phantom{27)999}0\\\end{array}
Find closest multiple of 27 to 243. We see that 9 \times 27 = 243 is the nearest. Now subtract 243 from 243 to get reminder 0. Add 9 to quotient.
\text{Quotient: }9 \text{Reminder: }0
Since 0 is less than 27, stop the division. The reminder is 0. The topmost line 009 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 9.
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}