Evaluate
\frac{100}{9}\approx 11.111111111
Factor
\frac{2 ^ {2} \cdot 5 ^ {2}}{3 ^ {2}} = 11\frac{1}{9} = 11.11111111111111
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\begin{array}{l}\phantom{4500)}\phantom{1}\\4500\overline{)50000}\\\end{array}
Use the 1^{st} digit 5 from dividend 50000
\begin{array}{l}\phantom{4500)}0\phantom{2}\\4500\overline{)50000}\\\end{array}
Since 5 is less than 4500, use the next digit 0 from dividend 50000 and add 0 to the quotient
\begin{array}{l}\phantom{4500)}0\phantom{3}\\4500\overline{)50000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 50000
\begin{array}{l}\phantom{4500)}00\phantom{4}\\4500\overline{)50000}\\\end{array}
Since 50 is less than 4500, use the next digit 0 from dividend 50000 and add 0 to the quotient
\begin{array}{l}\phantom{4500)}00\phantom{5}\\4500\overline{)50000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 50000
\begin{array}{l}\phantom{4500)}000\phantom{6}\\4500\overline{)50000}\\\end{array}
Since 500 is less than 4500, use the next digit 0 from dividend 50000 and add 0 to the quotient
\begin{array}{l}\phantom{4500)}000\phantom{7}\\4500\overline{)50000}\\\end{array}
Use the 4^{th} digit 0 from dividend 50000
\begin{array}{l}\phantom{4500)}0001\phantom{8}\\4500\overline{)50000}\\\phantom{4500)}\underline{\phantom{}4500\phantom{9}}\\\phantom{4500)9}500\\\end{array}
Find closest multiple of 4500 to 5000. We see that 1 \times 4500 = 4500 is the nearest. Now subtract 4500 from 5000 to get reminder 500. Add 1 to quotient.
\begin{array}{l}\phantom{4500)}0001\phantom{9}\\4500\overline{)50000}\\\phantom{4500)}\underline{\phantom{}4500\phantom{9}}\\\phantom{4500)9}5000\\\end{array}
Use the 5^{th} digit 0 from dividend 50000
\begin{array}{l}\phantom{4500)}00011\phantom{10}\\4500\overline{)50000}\\\phantom{4500)}\underline{\phantom{}4500\phantom{9}}\\\phantom{4500)9}5000\\\phantom{4500)}\underline{\phantom{9}4500\phantom{}}\\\phantom{4500)99}500\\\end{array}
Find closest multiple of 4500 to 5000. We see that 1 \times 4500 = 4500 is the nearest. Now subtract 4500 from 5000 to get reminder 500. Add 1 to quotient.
\text{Quotient: }11 \text{Reminder: }500
Since 500 is less than 4500, stop the division. The reminder is 500. The topmost line 00011 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 11.
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}