Evaluate
\frac{20150}{241}\approx 83.609958506
Factor
\frac{2 \cdot 5 ^ {2} \cdot 13 \cdot 31}{241} = 83\frac{147}{241} = 83.60995850622406
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\begin{array}{l}\phantom{120500)}\phantom{1}\\120500\overline{)10075000}\\\end{array}
Use the 1^{st} digit 1 from dividend 10075000
\begin{array}{l}\phantom{120500)}0\phantom{2}\\120500\overline{)10075000}\\\end{array}
Since 1 is less than 120500, use the next digit 0 from dividend 10075000 and add 0 to the quotient
\begin{array}{l}\phantom{120500)}0\phantom{3}\\120500\overline{)10075000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 10075000
\begin{array}{l}\phantom{120500)}00\phantom{4}\\120500\overline{)10075000}\\\end{array}
Since 10 is less than 120500, use the next digit 0 from dividend 10075000 and add 0 to the quotient
\begin{array}{l}\phantom{120500)}00\phantom{5}\\120500\overline{)10075000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 10075000
\begin{array}{l}\phantom{120500)}000\phantom{6}\\120500\overline{)10075000}\\\end{array}
Since 100 is less than 120500, use the next digit 7 from dividend 10075000 and add 0 to the quotient
\begin{array}{l}\phantom{120500)}000\phantom{7}\\120500\overline{)10075000}\\\end{array}
Use the 4^{th} digit 7 from dividend 10075000
\begin{array}{l}\phantom{120500)}0000\phantom{8}\\120500\overline{)10075000}\\\end{array}
Since 1007 is less than 120500, use the next digit 5 from dividend 10075000 and add 0 to the quotient
\begin{array}{l}\phantom{120500)}0000\phantom{9}\\120500\overline{)10075000}\\\end{array}
Use the 5^{th} digit 5 from dividend 10075000
\begin{array}{l}\phantom{120500)}00000\phantom{10}\\120500\overline{)10075000}\\\end{array}
Since 10075 is less than 120500, use the next digit 0 from dividend 10075000 and add 0 to the quotient
\begin{array}{l}\phantom{120500)}00000\phantom{11}\\120500\overline{)10075000}\\\end{array}
Use the 6^{th} digit 0 from dividend 10075000
\begin{array}{l}\phantom{120500)}000000\phantom{12}\\120500\overline{)10075000}\\\end{array}
Since 100750 is less than 120500, use the next digit 0 from dividend 10075000 and add 0 to the quotient
\begin{array}{l}\phantom{120500)}000000\phantom{13}\\120500\overline{)10075000}\\\end{array}
Use the 7^{th} digit 0 from dividend 10075000
\begin{array}{l}\phantom{120500)}0000008\phantom{14}\\120500\overline{)10075000}\\\phantom{120500)}\underline{\phantom{9}964000\phantom{9}}\\\phantom{120500)99}43500\\\end{array}
Find closest multiple of 120500 to 1007500. We see that 8 \times 120500 = 964000 is the nearest. Now subtract 964000 from 1007500 to get reminder 43500. Add 8 to quotient.
\begin{array}{l}\phantom{120500)}0000008\phantom{15}\\120500\overline{)10075000}\\\phantom{120500)}\underline{\phantom{9}964000\phantom{9}}\\\phantom{120500)99}435000\\\end{array}
Use the 8^{th} digit 0 from dividend 10075000
\begin{array}{l}\phantom{120500)}00000083\phantom{16}\\120500\overline{)10075000}\\\phantom{120500)}\underline{\phantom{9}964000\phantom{9}}\\\phantom{120500)99}435000\\\phantom{120500)}\underline{\phantom{99}361500\phantom{}}\\\phantom{120500)999}73500\\\end{array}
Find closest multiple of 120500 to 435000. We see that 3 \times 120500 = 361500 is the nearest. Now subtract 361500 from 435000 to get reminder 73500. Add 3 to quotient.
\text{Quotient: }83 \text{Reminder: }73500
Since 73500 is less than 120500, stop the division. The reminder is 73500. The topmost line 00000083 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 83.
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}