Evaluate
\frac{19990}{2111}\approx 9.46944576
Factor
\frac{2 \cdot 5 \cdot 1999}{2111} = 9\frac{991}{2111} = 9.469445760303174
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\begin{array}{l}\phantom{2111)}\phantom{1}\\2111\overline{)19990}\\\end{array}
Use the 1^{st} digit 1 from dividend 19990
\begin{array}{l}\phantom{2111)}0\phantom{2}\\2111\overline{)19990}\\\end{array}
Since 1 is less than 2111, use the next digit 9 from dividend 19990 and add 0 to the quotient
\begin{array}{l}\phantom{2111)}0\phantom{3}\\2111\overline{)19990}\\\end{array}
Use the 2^{nd} digit 9 from dividend 19990
\begin{array}{l}\phantom{2111)}00\phantom{4}\\2111\overline{)19990}\\\end{array}
Since 19 is less than 2111, use the next digit 9 from dividend 19990 and add 0 to the quotient
\begin{array}{l}\phantom{2111)}00\phantom{5}\\2111\overline{)19990}\\\end{array}
Use the 3^{rd} digit 9 from dividend 19990
\begin{array}{l}\phantom{2111)}000\phantom{6}\\2111\overline{)19990}\\\end{array}
Since 199 is less than 2111, use the next digit 9 from dividend 19990 and add 0 to the quotient
\begin{array}{l}\phantom{2111)}000\phantom{7}\\2111\overline{)19990}\\\end{array}
Use the 4^{th} digit 9 from dividend 19990
\begin{array}{l}\phantom{2111)}0000\phantom{8}\\2111\overline{)19990}\\\end{array}
Since 1999 is less than 2111, use the next digit 0 from dividend 19990 and add 0 to the quotient
\begin{array}{l}\phantom{2111)}0000\phantom{9}\\2111\overline{)19990}\\\end{array}
Use the 5^{th} digit 0 from dividend 19990
\begin{array}{l}\phantom{2111)}00009\phantom{10}\\2111\overline{)19990}\\\phantom{2111)}\underline{\phantom{}18999\phantom{}}\\\phantom{2111)99}991\\\end{array}
Find closest multiple of 2111 to 19990. We see that 9 \times 2111 = 18999 is the nearest. Now subtract 18999 from 19990 to get reminder 991. Add 9 to quotient.
\text{Quotient: }9 \text{Reminder: }991
Since 991 is less than 2111, stop the division. The reminder is 991. The topmost line 00009 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 9.
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}