Evaluate
18
Factor
2\times 3^{2}
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\begin{array}{l}\phantom{27)}\phantom{1}\\27\overline{)486}\\\end{array}
Use the 1^{st} digit 4 from dividend 486
\begin{array}{l}\phantom{27)}0\phantom{2}\\27\overline{)486}\\\end{array}
Since 4 is less than 27, use the next digit 8 from dividend 486 and add 0 to the quotient
\begin{array}{l}\phantom{27)}0\phantom{3}\\27\overline{)486}\\\end{array}
Use the 2^{nd} digit 8 from dividend 486
\begin{array}{l}\phantom{27)}01\phantom{4}\\27\overline{)486}\\\phantom{27)}\underline{\phantom{}27\phantom{9}}\\\phantom{27)}21\\\end{array}
Find closest multiple of 27 to 48. We see that 1 \times 27 = 27 is the nearest. Now subtract 27 from 48 to get reminder 21. Add 1 to quotient.
\begin{array}{l}\phantom{27)}01\phantom{5}\\27\overline{)486}\\\phantom{27)}\underline{\phantom{}27\phantom{9}}\\\phantom{27)}216\\\end{array}
Use the 3^{rd} digit 6 from dividend 486
\begin{array}{l}\phantom{27)}018\phantom{6}\\27\overline{)486}\\\phantom{27)}\underline{\phantom{}27\phantom{9}}\\\phantom{27)}216\\\phantom{27)}\underline{\phantom{}216\phantom{}}\\\phantom{27)999}0\\\end{array}
Find closest multiple of 27 to 216. We see that 8 \times 27 = 216 is the nearest. Now subtract 216 from 216 to get reminder 0. Add 8 to quotient.
\text{Quotient: }18 \text{Reminder: }0
Since 0 is less than 27, stop the division. The reminder is 0. The topmost line 018 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 18.
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}