Evaluate
\frac{200}{9}\approx 22.222222222
Factor
\frac{2 ^ {3} \cdot 5 ^ {2}}{3 ^ {2}} = 22\frac{2}{9} = 22.22222222222222
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\begin{array}{l}\phantom{180000)}\phantom{1}\\180000\overline{)4000000}\\\end{array}
Use the 1^{st} digit 4 from dividend 4000000
\begin{array}{l}\phantom{180000)}0\phantom{2}\\180000\overline{)4000000}\\\end{array}
Since 4 is less than 180000, use the next digit 0 from dividend 4000000 and add 0 to the quotient
\begin{array}{l}\phantom{180000)}0\phantom{3}\\180000\overline{)4000000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 4000000
\begin{array}{l}\phantom{180000)}00\phantom{4}\\180000\overline{)4000000}\\\end{array}
Since 40 is less than 180000, use the next digit 0 from dividend 4000000 and add 0 to the quotient
\begin{array}{l}\phantom{180000)}00\phantom{5}\\180000\overline{)4000000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 4000000
\begin{array}{l}\phantom{180000)}000\phantom{6}\\180000\overline{)4000000}\\\end{array}
Since 400 is less than 180000, use the next digit 0 from dividend 4000000 and add 0 to the quotient
\begin{array}{l}\phantom{180000)}000\phantom{7}\\180000\overline{)4000000}\\\end{array}
Use the 4^{th} digit 0 from dividend 4000000
\begin{array}{l}\phantom{180000)}0000\phantom{8}\\180000\overline{)4000000}\\\end{array}
Since 4000 is less than 180000, use the next digit 0 from dividend 4000000 and add 0 to the quotient
\begin{array}{l}\phantom{180000)}0000\phantom{9}\\180000\overline{)4000000}\\\end{array}
Use the 5^{th} digit 0 from dividend 4000000
\begin{array}{l}\phantom{180000)}00000\phantom{10}\\180000\overline{)4000000}\\\end{array}
Since 40000 is less than 180000, use the next digit 0 from dividend 4000000 and add 0 to the quotient
\begin{array}{l}\phantom{180000)}00000\phantom{11}\\180000\overline{)4000000}\\\end{array}
Use the 6^{th} digit 0 from dividend 4000000
\begin{array}{l}\phantom{180000)}000002\phantom{12}\\180000\overline{)4000000}\\\phantom{180000)}\underline{\phantom{}360000\phantom{9}}\\\phantom{180000)9}40000\\\end{array}
Find closest multiple of 180000 to 400000. We see that 2 \times 180000 = 360000 is the nearest. Now subtract 360000 from 400000 to get reminder 40000. Add 2 to quotient.
\begin{array}{l}\phantom{180000)}000002\phantom{13}\\180000\overline{)4000000}\\\phantom{180000)}\underline{\phantom{}360000\phantom{9}}\\\phantom{180000)9}400000\\\end{array}
Use the 7^{th} digit 0 from dividend 4000000
\begin{array}{l}\phantom{180000)}0000022\phantom{14}\\180000\overline{)4000000}\\\phantom{180000)}\underline{\phantom{}360000\phantom{9}}\\\phantom{180000)9}400000\\\phantom{180000)}\underline{\phantom{9}360000\phantom{}}\\\phantom{180000)99}40000\\\end{array}
Find closest multiple of 180000 to 400000. We see that 2 \times 180000 = 360000 is the nearest. Now subtract 360000 from 400000 to get reminder 40000. Add 2 to quotient.
\text{Quotient: }22 \text{Reminder: }40000
Since 40000 is less than 180000, stop the division. The reminder is 40000. The topmost line 0000022 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 22.
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}