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\begin{array}{l}\phantom{3000)}\phantom{1}\\3000\overline{)9000}\\\end{array}
Use the 1^{st} digit 9 from dividend 9000
\begin{array}{l}\phantom{3000)}0\phantom{2}\\3000\overline{)9000}\\\end{array}
Since 9 is less than 3000, use the next digit 0 from dividend 9000 and add 0 to the quotient
\begin{array}{l}\phantom{3000)}0\phantom{3}\\3000\overline{)9000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 9000
\begin{array}{l}\phantom{3000)}00\phantom{4}\\3000\overline{)9000}\\\end{array}
Since 90 is less than 3000, use the next digit 0 from dividend 9000 and add 0 to the quotient
\begin{array}{l}\phantom{3000)}00\phantom{5}\\3000\overline{)9000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 9000
\begin{array}{l}\phantom{3000)}000\phantom{6}\\3000\overline{)9000}\\\end{array}
Since 900 is less than 3000, use the next digit 0 from dividend 9000 and add 0 to the quotient
\begin{array}{l}\phantom{3000)}000\phantom{7}\\3000\overline{)9000}\\\end{array}
Use the 4^{th} digit 0 from dividend 9000
\begin{array}{l}\phantom{3000)}0003\phantom{8}\\3000\overline{)9000}\\\phantom{3000)}\underline{\phantom{}9000\phantom{}}\\\phantom{3000)9999}0\\\end{array}
Find closest multiple of 3000 to 9000. We see that 3 \times 3000 = 9000 is the nearest. Now subtract 9000 from 9000 to get reminder 0. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }0
Since 0 is less than 3000, stop the division. The reminder is 0. The topmost line 0003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}