Evaluate
\frac{934}{109}\approx 8.568807339
Factor
\frac{2 \cdot 467}{109} = 8\frac{62}{109} = 8.568807339449542
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\begin{array}{l}\phantom{1853)}\phantom{1}\\1853\overline{)15878}\\\end{array}
Use the 1^{st} digit 1 from dividend 15878
\begin{array}{l}\phantom{1853)}0\phantom{2}\\1853\overline{)15878}\\\end{array}
Since 1 is less than 1853, use the next digit 5 from dividend 15878 and add 0 to the quotient
\begin{array}{l}\phantom{1853)}0\phantom{3}\\1853\overline{)15878}\\\end{array}
Use the 2^{nd} digit 5 from dividend 15878
\begin{array}{l}\phantom{1853)}00\phantom{4}\\1853\overline{)15878}\\\end{array}
Since 15 is less than 1853, use the next digit 8 from dividend 15878 and add 0 to the quotient
\begin{array}{l}\phantom{1853)}00\phantom{5}\\1853\overline{)15878}\\\end{array}
Use the 3^{rd} digit 8 from dividend 15878
\begin{array}{l}\phantom{1853)}000\phantom{6}\\1853\overline{)15878}\\\end{array}
Since 158 is less than 1853, use the next digit 7 from dividend 15878 and add 0 to the quotient
\begin{array}{l}\phantom{1853)}000\phantom{7}\\1853\overline{)15878}\\\end{array}
Use the 4^{th} digit 7 from dividend 15878
\begin{array}{l}\phantom{1853)}0000\phantom{8}\\1853\overline{)15878}\\\end{array}
Since 1587 is less than 1853, use the next digit 8 from dividend 15878 and add 0 to the quotient
\begin{array}{l}\phantom{1853)}0000\phantom{9}\\1853\overline{)15878}\\\end{array}
Use the 5^{th} digit 8 from dividend 15878
\begin{array}{l}\phantom{1853)}00008\phantom{10}\\1853\overline{)15878}\\\phantom{1853)}\underline{\phantom{}14824\phantom{}}\\\phantom{1853)9}1054\\\end{array}
Find closest multiple of 1853 to 15878. We see that 8 \times 1853 = 14824 is the nearest. Now subtract 14824 from 15878 to get reminder 1054. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }1054
Since 1054 is less than 1853, stop the division. The reminder is 1054. The topmost line 00008 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8.
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}