Evaluate
27
Factor
3^{3}
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\begin{array}{l}\phantom{18)}\phantom{1}\\18\overline{)486}\\\end{array}
Use the 1^{st} digit 4 from dividend 486
\begin{array}{l}\phantom{18)}0\phantom{2}\\18\overline{)486}\\\end{array}
Since 4 is less than 18, use the next digit 8 from dividend 486 and add 0 to the quotient
\begin{array}{l}\phantom{18)}0\phantom{3}\\18\overline{)486}\\\end{array}
Use the 2^{nd} digit 8 from dividend 486
\begin{array}{l}\phantom{18)}02\phantom{4}\\18\overline{)486}\\\phantom{18)}\underline{\phantom{}36\phantom{9}}\\\phantom{18)}12\\\end{array}
Find closest multiple of 18 to 48. We see that 2 \times 18 = 36 is the nearest. Now subtract 36 from 48 to get reminder 12. Add 2 to quotient.
\begin{array}{l}\phantom{18)}02\phantom{5}\\18\overline{)486}\\\phantom{18)}\underline{\phantom{}36\phantom{9}}\\\phantom{18)}126\\\end{array}
Use the 3^{rd} digit 6 from dividend 486
\begin{array}{l}\phantom{18)}027\phantom{6}\\18\overline{)486}\\\phantom{18)}\underline{\phantom{}36\phantom{9}}\\\phantom{18)}126\\\phantom{18)}\underline{\phantom{}126\phantom{}}\\\phantom{18)999}0\\\end{array}
Find closest multiple of 18 to 126. We see that 7 \times 18 = 126 is the nearest. Now subtract 126 from 126 to get reminder 0. Add 7 to quotient.
\text{Quotient: }27 \text{Reminder: }0
Since 0 is less than 18, stop the division. The reminder is 0. The topmost line 027 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 27.
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}