Evaluate
84
Factor
2^{2}\times 3\times 7
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\begin{array}{l}\phantom{20)}\phantom{1}\\20\overline{)1680}\\\end{array}
Use the 1^{st} digit 1 from dividend 1680
\begin{array}{l}\phantom{20)}0\phantom{2}\\20\overline{)1680}\\\end{array}
Since 1 is less than 20, use the next digit 6 from dividend 1680 and add 0 to the quotient
\begin{array}{l}\phantom{20)}0\phantom{3}\\20\overline{)1680}\\\end{array}
Use the 2^{nd} digit 6 from dividend 1680
\begin{array}{l}\phantom{20)}00\phantom{4}\\20\overline{)1680}\\\end{array}
Since 16 is less than 20, use the next digit 8 from dividend 1680 and add 0 to the quotient
\begin{array}{l}\phantom{20)}00\phantom{5}\\20\overline{)1680}\\\end{array}
Use the 3^{rd} digit 8 from dividend 1680
\begin{array}{l}\phantom{20)}008\phantom{6}\\20\overline{)1680}\\\phantom{20)}\underline{\phantom{}160\phantom{9}}\\\phantom{20)99}8\\\end{array}
Find closest multiple of 20 to 168. We see that 8 \times 20 = 160 is the nearest. Now subtract 160 from 168 to get reminder 8. Add 8 to quotient.
\begin{array}{l}\phantom{20)}008\phantom{7}\\20\overline{)1680}\\\phantom{20)}\underline{\phantom{}160\phantom{9}}\\\phantom{20)99}80\\\end{array}
Use the 4^{th} digit 0 from dividend 1680
\begin{array}{l}\phantom{20)}0084\phantom{8}\\20\overline{)1680}\\\phantom{20)}\underline{\phantom{}160\phantom{9}}\\\phantom{20)99}80\\\phantom{20)}\underline{\phantom{99}80\phantom{}}\\\phantom{20)9999}0\\\end{array}
Find closest multiple of 20 to 80. We see that 4 \times 20 = 80 is the nearest. Now subtract 80 from 80 to get reminder 0. Add 4 to quotient.
\text{Quotient: }84 \text{Reminder: }0
Since 0 is less than 20, 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}