Evaluate
27
Factor
3^{3}
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\begin{array}{l}\phantom{300)}\phantom{1}\\300\overline{)8100}\\\end{array}
Use the 1^{st} digit 8 from dividend 8100
\begin{array}{l}\phantom{300)}0\phantom{2}\\300\overline{)8100}\\\end{array}
Since 8 is less than 300, use the next digit 1 from dividend 8100 and add 0 to the quotient
\begin{array}{l}\phantom{300)}0\phantom{3}\\300\overline{)8100}\\\end{array}
Use the 2^{nd} digit 1 from dividend 8100
\begin{array}{l}\phantom{300)}00\phantom{4}\\300\overline{)8100}\\\end{array}
Since 81 is less than 300, use the next digit 0 from dividend 8100 and add 0 to the quotient
\begin{array}{l}\phantom{300)}00\phantom{5}\\300\overline{)8100}\\\end{array}
Use the 3^{rd} digit 0 from dividend 8100
\begin{array}{l}\phantom{300)}002\phantom{6}\\300\overline{)8100}\\\phantom{300)}\underline{\phantom{}600\phantom{9}}\\\phantom{300)}210\\\end{array}
Find closest multiple of 300 to 810. We see that 2 \times 300 = 600 is the nearest. Now subtract 600 from 810 to get reminder 210. Add 2 to quotient.
\begin{array}{l}\phantom{300)}002\phantom{7}\\300\overline{)8100}\\\phantom{300)}\underline{\phantom{}600\phantom{9}}\\\phantom{300)}2100\\\end{array}
Use the 4^{th} digit 0 from dividend 8100
\begin{array}{l}\phantom{300)}0027\phantom{8}\\300\overline{)8100}\\\phantom{300)}\underline{\phantom{}600\phantom{9}}\\\phantom{300)}2100\\\phantom{300)}\underline{\phantom{}2100\phantom{}}\\\phantom{300)9999}0\\\end{array}
Find closest multiple of 300 to 2100. We see that 7 \times 300 = 2100 is the nearest. Now subtract 2100 from 2100 to get reminder 0. Add 7 to quotient.
\text{Quotient: }27 \text{Reminder: }0
Since 0 is less than 300, stop the division. The reminder is 0. The topmost line 0027 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}