Evaluate
\frac{41}{9}\approx 4.555555556
Factor
\frac{41}{3 ^ {2}} = 4\frac{5}{9} = 4.555555555555555
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\begin{array}{l}\phantom{18)}\phantom{1}\\18\overline{)82}\\\end{array}
Use the 1^{st} digit 8 from dividend 82
\begin{array}{l}\phantom{18)}0\phantom{2}\\18\overline{)82}\\\end{array}
Since 8 is less than 18, use the next digit 2 from dividend 82 and add 0 to the quotient
\begin{array}{l}\phantom{18)}0\phantom{3}\\18\overline{)82}\\\end{array}
Use the 2^{nd} digit 2 from dividend 82
\begin{array}{l}\phantom{18)}04\phantom{4}\\18\overline{)82}\\\phantom{18)}\underline{\phantom{}72\phantom{}}\\\phantom{18)}10\\\end{array}
Find closest multiple of 18 to 82. We see that 4 \times 18 = 72 is the nearest. Now subtract 72 from 82 to get reminder 10. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }10
Since 10 is less than 18, stop the division. The reminder is 10. The topmost line 04 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}