Evaluate
\frac{50}{33}\approx 1.515151515
Factor
\frac{2 \cdot 5 ^ {2}}{3 \cdot 11} = 1\frac{17}{33} = 1.5151515151515151
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\begin{array}{l}\phantom{330000000)}\phantom{1}\\330000000\overline{)500000000}\\\end{array}
Use the 1^{st} digit 5 from dividend 500000000
\begin{array}{l}\phantom{330000000)}0\phantom{2}\\330000000\overline{)500000000}\\\end{array}
Since 5 is less than 330000000, use the next digit 0 from dividend 500000000 and add 0 to the quotient
\begin{array}{l}\phantom{330000000)}0\phantom{3}\\330000000\overline{)500000000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 500000000
\begin{array}{l}\phantom{330000000)}00\phantom{4}\\330000000\overline{)500000000}\\\end{array}
Since 50 is less than 330000000, use the next digit 0 from dividend 500000000 and add 0 to the quotient
\begin{array}{l}\phantom{330000000)}00\phantom{5}\\330000000\overline{)500000000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 500000000
\begin{array}{l}\phantom{330000000)}000\phantom{6}\\330000000\overline{)500000000}\\\end{array}
Since 500 is less than 330000000, use the next digit 0 from dividend 500000000 and add 0 to the quotient
\begin{array}{l}\phantom{330000000)}000\phantom{7}\\330000000\overline{)500000000}\\\end{array}
Use the 4^{th} digit 0 from dividend 500000000
\begin{array}{l}\phantom{330000000)}0000\phantom{8}\\330000000\overline{)500000000}\\\end{array}
Since 5000 is less than 330000000, use the next digit 0 from dividend 500000000 and add 0 to the quotient
\begin{array}{l}\phantom{330000000)}0000\phantom{9}\\330000000\overline{)500000000}\\\end{array}
Use the 5^{th} digit 0 from dividend 500000000
\begin{array}{l}\phantom{330000000)}00000\phantom{10}\\330000000\overline{)500000000}\\\end{array}
Since 50000 is less than 330000000, use the next digit 0 from dividend 500000000 and add 0 to the quotient
\begin{array}{l}\phantom{330000000)}00000\phantom{11}\\330000000\overline{)500000000}\\\end{array}
Use the 6^{th} digit 0 from dividend 500000000
\begin{array}{l}\phantom{330000000)}000000\phantom{12}\\330000000\overline{)500000000}\\\end{array}
Since 500000 is less than 330000000, use the next digit 0 from dividend 500000000 and add 0 to the quotient
\begin{array}{l}\phantom{330000000)}000000\phantom{13}\\330000000\overline{)500000000}\\\end{array}
Use the 7^{th} digit 0 from dividend 500000000
\begin{array}{l}\phantom{330000000)}0000000\phantom{14}\\330000000\overline{)500000000}\\\end{array}
Since 5000000 is less than 330000000, use the next digit 0 from dividend 500000000 and add 0 to the quotient
\begin{array}{l}\phantom{330000000)}0000000\phantom{15}\\330000000\overline{)500000000}\\\end{array}
Use the 8^{th} digit 0 from dividend 500000000
\begin{array}{l}\phantom{330000000)}00000000\phantom{16}\\330000000\overline{)500000000}\\\end{array}
Since 50000000 is less than 330000000, use the next digit 0 from dividend 500000000 and add 0 to the quotient
\begin{array}{l}\phantom{330000000)}00000000\phantom{17}\\330000000\overline{)500000000}\\\end{array}
Use the 9^{th} digit 0 from dividend 500000000
\begin{array}{l}\phantom{330000000)}000000001\phantom{18}\\330000000\overline{)500000000}\\\phantom{330000000)}\underline{\phantom{}330000000\phantom{}}\\\phantom{330000000)}170000000\\\end{array}
Find closest multiple of 330000000 to 500000000. We see that 1 \times 330000000 = 330000000 is the nearest. Now subtract 330000000 from 500000000 to get reminder 170000000. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }170000000
Since 170000000 is less than 330000000, stop the division. The reminder is 170000000. The topmost line 000000001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}