Evaluate
\frac{5500}{9}\approx 611.111111111
Factor
\frac{2 ^ {2} \cdot 5 ^ {3} \cdot 11}{3 ^ {2}} = 611\frac{1}{9} = 611.1111111111111
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\begin{array}{l}\phantom{900)}\phantom{1}\\900\overline{)550000}\\\end{array}
Use the 1^{st} digit 5 from dividend 550000
\begin{array}{l}\phantom{900)}0\phantom{2}\\900\overline{)550000}\\\end{array}
Since 5 is less than 900, use the next digit 5 from dividend 550000 and add 0 to the quotient
\begin{array}{l}\phantom{900)}0\phantom{3}\\900\overline{)550000}\\\end{array}
Use the 2^{nd} digit 5 from dividend 550000
\begin{array}{l}\phantom{900)}00\phantom{4}\\900\overline{)550000}\\\end{array}
Since 55 is less than 900, use the next digit 0 from dividend 550000 and add 0 to the quotient
\begin{array}{l}\phantom{900)}00\phantom{5}\\900\overline{)550000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 550000
\begin{array}{l}\phantom{900)}000\phantom{6}\\900\overline{)550000}\\\end{array}
Since 550 is less than 900, use the next digit 0 from dividend 550000 and add 0 to the quotient
\begin{array}{l}\phantom{900)}000\phantom{7}\\900\overline{)550000}\\\end{array}
Use the 4^{th} digit 0 from dividend 550000
\begin{array}{l}\phantom{900)}0006\phantom{8}\\900\overline{)550000}\\\phantom{900)}\underline{\phantom{}5400\phantom{99}}\\\phantom{900)9}100\\\end{array}
Find closest multiple of 900 to 5500. We see that 6 \times 900 = 5400 is the nearest. Now subtract 5400 from 5500 to get reminder 100. Add 6 to quotient.
\begin{array}{l}\phantom{900)}0006\phantom{9}\\900\overline{)550000}\\\phantom{900)}\underline{\phantom{}5400\phantom{99}}\\\phantom{900)9}1000\\\end{array}
Use the 5^{th} digit 0 from dividend 550000
\begin{array}{l}\phantom{900)}00061\phantom{10}\\900\overline{)550000}\\\phantom{900)}\underline{\phantom{}5400\phantom{99}}\\\phantom{900)9}1000\\\phantom{900)}\underline{\phantom{99}900\phantom{9}}\\\phantom{900)99}100\\\end{array}
Find closest multiple of 900 to 1000. We see that 1 \times 900 = 900 is the nearest. Now subtract 900 from 1000 to get reminder 100. Add 1 to quotient.
\begin{array}{l}\phantom{900)}00061\phantom{11}\\900\overline{)550000}\\\phantom{900)}\underline{\phantom{}5400\phantom{99}}\\\phantom{900)9}1000\\\phantom{900)}\underline{\phantom{99}900\phantom{9}}\\\phantom{900)99}1000\\\end{array}
Use the 6^{th} digit 0 from dividend 550000
\begin{array}{l}\phantom{900)}000611\phantom{12}\\900\overline{)550000}\\\phantom{900)}\underline{\phantom{}5400\phantom{99}}\\\phantom{900)9}1000\\\phantom{900)}\underline{\phantom{99}900\phantom{9}}\\\phantom{900)99}1000\\\phantom{900)}\underline{\phantom{999}900\phantom{}}\\\phantom{900)999}100\\\end{array}
Find closest multiple of 900 to 1000. We see that 1 \times 900 = 900 is the nearest. Now subtract 900 from 1000 to get reminder 100. Add 1 to quotient.
\text{Quotient: }611 \text{Reminder: }100
Since 100 is less than 900, stop the division. The reminder is 100. The topmost line 000611 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 611.
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}