Evaluate
84
Factor
2^{2}\times 3\times 7
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\begin{array}{l}\phantom{12)}\phantom{1}\\12\overline{)1008}\\\end{array}
Use the 1^{st} digit 1 from dividend 1008
\begin{array}{l}\phantom{12)}0\phantom{2}\\12\overline{)1008}\\\end{array}
Since 1 is less than 12, use the next digit 0 from dividend 1008 and add 0 to the quotient
\begin{array}{l}\phantom{12)}0\phantom{3}\\12\overline{)1008}\\\end{array}
Use the 2^{nd} digit 0 from dividend 1008
\begin{array}{l}\phantom{12)}00\phantom{4}\\12\overline{)1008}\\\end{array}
Since 10 is less than 12, use the next digit 0 from dividend 1008 and add 0 to the quotient
\begin{array}{l}\phantom{12)}00\phantom{5}\\12\overline{)1008}\\\end{array}
Use the 3^{rd} digit 0 from dividend 1008
\begin{array}{l}\phantom{12)}008\phantom{6}\\12\overline{)1008}\\\phantom{12)}\underline{\phantom{9}96\phantom{9}}\\\phantom{12)99}4\\\end{array}
Find closest multiple of 12 to 100. We see that 8 \times 12 = 96 is the nearest. Now subtract 96 from 100 to get reminder 4. Add 8 to quotient.
\begin{array}{l}\phantom{12)}008\phantom{7}\\12\overline{)1008}\\\phantom{12)}\underline{\phantom{9}96\phantom{9}}\\\phantom{12)99}48\\\end{array}
Use the 4^{th} digit 8 from dividend 1008
\begin{array}{l}\phantom{12)}0084\phantom{8}\\12\overline{)1008}\\\phantom{12)}\underline{\phantom{9}96\phantom{9}}\\\phantom{12)99}48\\\phantom{12)}\underline{\phantom{99}48\phantom{}}\\\phantom{12)9999}0\\\end{array}
Find closest multiple of 12 to 48. We see that 4 \times 12 = 48 is the nearest. Now subtract 48 from 48 to get reminder 0. Add 4 to quotient.
\text{Quotient: }84 \text{Reminder: }0
Since 0 is less than 12, stop the division. The reminder is 0. The topmost line 0084 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 84.
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}