Evaluate
\frac{2000}{9}\approx 222.222222222
Factor
\frac{2 ^ {4} \cdot 5 ^ {3}}{3 ^ {2}} = 222\frac{2}{9} = 222.22222222222223
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\begin{array}{l}\phantom{180)}\phantom{1}\\180\overline{)40000}\\\end{array}
Use the 1^{st} digit 4 from dividend 40000
\begin{array}{l}\phantom{180)}0\phantom{2}\\180\overline{)40000}\\\end{array}
Since 4 is less than 180, use the next digit 0 from dividend 40000 and add 0 to the quotient
\begin{array}{l}\phantom{180)}0\phantom{3}\\180\overline{)40000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 40000
\begin{array}{l}\phantom{180)}00\phantom{4}\\180\overline{)40000}\\\end{array}
Since 40 is less than 180, use the next digit 0 from dividend 40000 and add 0 to the quotient
\begin{array}{l}\phantom{180)}00\phantom{5}\\180\overline{)40000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 40000
\begin{array}{l}\phantom{180)}002\phantom{6}\\180\overline{)40000}\\\phantom{180)}\underline{\phantom{}360\phantom{99}}\\\phantom{180)9}40\\\end{array}
Find closest multiple of 180 to 400. We see that 2 \times 180 = 360 is the nearest. Now subtract 360 from 400 to get reminder 40. Add 2 to quotient.
\begin{array}{l}\phantom{180)}002\phantom{7}\\180\overline{)40000}\\\phantom{180)}\underline{\phantom{}360\phantom{99}}\\\phantom{180)9}400\\\end{array}
Use the 4^{th} digit 0 from dividend 40000
\begin{array}{l}\phantom{180)}0022\phantom{8}\\180\overline{)40000}\\\phantom{180)}\underline{\phantom{}360\phantom{99}}\\\phantom{180)9}400\\\phantom{180)}\underline{\phantom{9}360\phantom{9}}\\\phantom{180)99}40\\\end{array}
Find closest multiple of 180 to 400. We see that 2 \times 180 = 360 is the nearest. Now subtract 360 from 400 to get reminder 40. Add 2 to quotient.
\begin{array}{l}\phantom{180)}0022\phantom{9}\\180\overline{)40000}\\\phantom{180)}\underline{\phantom{}360\phantom{99}}\\\phantom{180)9}400\\\phantom{180)}\underline{\phantom{9}360\phantom{9}}\\\phantom{180)99}400\\\end{array}
Use the 5^{th} digit 0 from dividend 40000
\begin{array}{l}\phantom{180)}00222\phantom{10}\\180\overline{)40000}\\\phantom{180)}\underline{\phantom{}360\phantom{99}}\\\phantom{180)9}400\\\phantom{180)}\underline{\phantom{9}360\phantom{9}}\\\phantom{180)99}400\\\phantom{180)}\underline{\phantom{99}360\phantom{}}\\\phantom{180)999}40\\\end{array}
Find closest multiple of 180 to 400. We see that 2 \times 180 = 360 is the nearest. Now subtract 360 from 400 to get reminder 40. Add 2 to quotient.
\text{Quotient: }222 \text{Reminder: }40
Since 40 is less than 180, stop the division. The reminder is 40. The topmost line 00222 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 222.
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}