Evaluate
\frac{18827}{46}\approx 409.282608696
Factor
\frac{67 \cdot 281}{2 \cdot 23} = 409\frac{13}{46} = 409.2826086956522
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\begin{array}{l}\phantom{92)}\phantom{1}\\92\overline{)37654}\\\end{array}
Use the 1^{st} digit 3 from dividend 37654
\begin{array}{l}\phantom{92)}0\phantom{2}\\92\overline{)37654}\\\end{array}
Since 3 is less than 92, use the next digit 7 from dividend 37654 and add 0 to the quotient
\begin{array}{l}\phantom{92)}0\phantom{3}\\92\overline{)37654}\\\end{array}
Use the 2^{nd} digit 7 from dividend 37654
\begin{array}{l}\phantom{92)}00\phantom{4}\\92\overline{)37654}\\\end{array}
Since 37 is less than 92, use the next digit 6 from dividend 37654 and add 0 to the quotient
\begin{array}{l}\phantom{92)}00\phantom{5}\\92\overline{)37654}\\\end{array}
Use the 3^{rd} digit 6 from dividend 37654
\begin{array}{l}\phantom{92)}004\phantom{6}\\92\overline{)37654}\\\phantom{92)}\underline{\phantom{}368\phantom{99}}\\\phantom{92)99}8\\\end{array}
Find closest multiple of 92 to 376. We see that 4 \times 92 = 368 is the nearest. Now subtract 368 from 376 to get reminder 8. Add 4 to quotient.
\begin{array}{l}\phantom{92)}004\phantom{7}\\92\overline{)37654}\\\phantom{92)}\underline{\phantom{}368\phantom{99}}\\\phantom{92)99}85\\\end{array}
Use the 4^{th} digit 5 from dividend 37654
\begin{array}{l}\phantom{92)}0040\phantom{8}\\92\overline{)37654}\\\phantom{92)}\underline{\phantom{}368\phantom{99}}\\\phantom{92)99}85\\\end{array}
Since 85 is less than 92, use the next digit 4 from dividend 37654 and add 0 to the quotient
\begin{array}{l}\phantom{92)}0040\phantom{9}\\92\overline{)37654}\\\phantom{92)}\underline{\phantom{}368\phantom{99}}\\\phantom{92)99}854\\\end{array}
Use the 5^{th} digit 4 from dividend 37654
\begin{array}{l}\phantom{92)}00409\phantom{10}\\92\overline{)37654}\\\phantom{92)}\underline{\phantom{}368\phantom{99}}\\\phantom{92)99}854\\\phantom{92)}\underline{\phantom{99}828\phantom{}}\\\phantom{92)999}26\\\end{array}
Find closest multiple of 92 to 854. We see that 9 \times 92 = 828 is the nearest. Now subtract 828 from 854 to get reminder 26. Add 9 to quotient.
\text{Quotient: }409 \text{Reminder: }26
Since 26 is less than 92, stop the division. The reminder is 26. The topmost line 00409 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 409.
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}