Evaluate
\frac{400}{41}\approx 9.756097561
Factor
\frac{2 ^ {4} \cdot 5 ^ {2}}{41} = 9\frac{31}{41} = 9.75609756097561
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\begin{array}{l}\phantom{41)}\phantom{1}\\41\overline{)400}\\\end{array}
Use the 1^{st} digit 4 from dividend 400
\begin{array}{l}\phantom{41)}0\phantom{2}\\41\overline{)400}\\\end{array}
Since 4 is less than 41, use the next digit 0 from dividend 400 and add 0 to the quotient
\begin{array}{l}\phantom{41)}0\phantom{3}\\41\overline{)400}\\\end{array}
Use the 2^{nd} digit 0 from dividend 400
\begin{array}{l}\phantom{41)}00\phantom{4}\\41\overline{)400}\\\end{array}
Since 40 is less than 41, use the next digit 0 from dividend 400 and add 0 to the quotient
\begin{array}{l}\phantom{41)}00\phantom{5}\\41\overline{)400}\\\end{array}
Use the 3^{rd} digit 0 from dividend 400
\begin{array}{l}\phantom{41)}009\phantom{6}\\41\overline{)400}\\\phantom{41)}\underline{\phantom{}369\phantom{}}\\\phantom{41)9}31\\\end{array}
Find closest multiple of 41 to 400. We see that 9 \times 41 = 369 is the nearest. Now subtract 369 from 400 to get reminder 31. Add 9 to quotient.
\text{Quotient: }9 \text{Reminder: }31
Since 31 is less than 41, stop the division. The reminder is 31. The topmost line 009 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 9.
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}