Evaluate
\frac{74000}{33333}\approx 2.2200222
Factor
\frac{2 ^ {4} \cdot 5 ^ {3} \cdot 37}{3 \cdot 41 \cdot 271} = 2\frac{7334}{33333} = 2.2200222002220023
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\begin{array}{l}\phantom{99999)}\phantom{1}\\99999\overline{)222000}\\\end{array}
Use the 1^{st} digit 2 from dividend 222000
\begin{array}{l}\phantom{99999)}0\phantom{2}\\99999\overline{)222000}\\\end{array}
Since 2 is less than 99999, use the next digit 2 from dividend 222000 and add 0 to the quotient
\begin{array}{l}\phantom{99999)}0\phantom{3}\\99999\overline{)222000}\\\end{array}
Use the 2^{nd} digit 2 from dividend 222000
\begin{array}{l}\phantom{99999)}00\phantom{4}\\99999\overline{)222000}\\\end{array}
Since 22 is less than 99999, use the next digit 2 from dividend 222000 and add 0 to the quotient
\begin{array}{l}\phantom{99999)}00\phantom{5}\\99999\overline{)222000}\\\end{array}
Use the 3^{rd} digit 2 from dividend 222000
\begin{array}{l}\phantom{99999)}000\phantom{6}\\99999\overline{)222000}\\\end{array}
Since 222 is less than 99999, use the next digit 0 from dividend 222000 and add 0 to the quotient
\begin{array}{l}\phantom{99999)}000\phantom{7}\\99999\overline{)222000}\\\end{array}
Use the 4^{th} digit 0 from dividend 222000
\begin{array}{l}\phantom{99999)}0000\phantom{8}\\99999\overline{)222000}\\\end{array}
Since 2220 is less than 99999, use the next digit 0 from dividend 222000 and add 0 to the quotient
\begin{array}{l}\phantom{99999)}0000\phantom{9}\\99999\overline{)222000}\\\end{array}
Use the 5^{th} digit 0 from dividend 222000
\begin{array}{l}\phantom{99999)}00000\phantom{10}\\99999\overline{)222000}\\\end{array}
Since 22200 is less than 99999, use the next digit 0 from dividend 222000 and add 0 to the quotient
\begin{array}{l}\phantom{99999)}00000\phantom{11}\\99999\overline{)222000}\\\end{array}
Use the 6^{th} digit 0 from dividend 222000
\begin{array}{l}\phantom{99999)}000002\phantom{12}\\99999\overline{)222000}\\\phantom{99999)}\underline{\phantom{}199998\phantom{}}\\\phantom{99999)9}22002\\\end{array}
Find closest multiple of 99999 to 222000. We see that 2 \times 99999 = 199998 is the nearest. Now subtract 199998 from 222000 to get reminder 22002. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }22002
Since 22002 is less than 99999, stop the division. The reminder is 22002. The topmost line 000002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}