Evaluate
27
Factor
3^{3}
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\begin{array}{l}\phantom{12)}\phantom{1}\\12\overline{)324}\\\end{array}
Use the 1^{st} digit 3 from dividend 324
\begin{array}{l}\phantom{12)}0\phantom{2}\\12\overline{)324}\\\end{array}
Since 3 is less than 12, use the next digit 2 from dividend 324 and add 0 to the quotient
\begin{array}{l}\phantom{12)}0\phantom{3}\\12\overline{)324}\\\end{array}
Use the 2^{nd} digit 2 from dividend 324
\begin{array}{l}\phantom{12)}02\phantom{4}\\12\overline{)324}\\\phantom{12)}\underline{\phantom{}24\phantom{9}}\\\phantom{12)9}8\\\end{array}
Find closest multiple of 12 to 32. We see that 2 \times 12 = 24 is the nearest. Now subtract 24 from 32 to get reminder 8. Add 2 to quotient.
\begin{array}{l}\phantom{12)}02\phantom{5}\\12\overline{)324}\\\phantom{12)}\underline{\phantom{}24\phantom{9}}\\\phantom{12)9}84\\\end{array}
Use the 3^{rd} digit 4 from dividend 324
\begin{array}{l}\phantom{12)}027\phantom{6}\\12\overline{)324}\\\phantom{12)}\underline{\phantom{}24\phantom{9}}\\\phantom{12)9}84\\\phantom{12)}\underline{\phantom{9}84\phantom{}}\\\phantom{12)999}0\\\end{array}
Find closest multiple of 12 to 84. We see that 7 \times 12 = 84 is the nearest. Now subtract 84 from 84 to get reminder 0. Add 7 to quotient.
\text{Quotient: }27 \text{Reminder: }0
Since 0 is less than 12, 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}