Evaluate
\frac{405}{11}\approx 36.818181818
Factor
\frac{3 ^ {4} \cdot 5}{11} = 36\frac{9}{11} = 36.81818181818182
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\begin{array}{l}\phantom{66)}\phantom{1}\\66\overline{)2430}\\\end{array}
Use the 1^{st} digit 2 from dividend 2430
\begin{array}{l}\phantom{66)}0\phantom{2}\\66\overline{)2430}\\\end{array}
Since 2 is less than 66, use the next digit 4 from dividend 2430 and add 0 to the quotient
\begin{array}{l}\phantom{66)}0\phantom{3}\\66\overline{)2430}\\\end{array}
Use the 2^{nd} digit 4 from dividend 2430
\begin{array}{l}\phantom{66)}00\phantom{4}\\66\overline{)2430}\\\end{array}
Since 24 is less than 66, use the next digit 3 from dividend 2430 and add 0 to the quotient
\begin{array}{l}\phantom{66)}00\phantom{5}\\66\overline{)2430}\\\end{array}
Use the 3^{rd} digit 3 from dividend 2430
\begin{array}{l}\phantom{66)}003\phantom{6}\\66\overline{)2430}\\\phantom{66)}\underline{\phantom{}198\phantom{9}}\\\phantom{66)9}45\\\end{array}
Find closest multiple of 66 to 243. We see that 3 \times 66 = 198 is the nearest. Now subtract 198 from 243 to get reminder 45. Add 3 to quotient.
\begin{array}{l}\phantom{66)}003\phantom{7}\\66\overline{)2430}\\\phantom{66)}\underline{\phantom{}198\phantom{9}}\\\phantom{66)9}450\\\end{array}
Use the 4^{th} digit 0 from dividend 2430
\begin{array}{l}\phantom{66)}0036\phantom{8}\\66\overline{)2430}\\\phantom{66)}\underline{\phantom{}198\phantom{9}}\\\phantom{66)9}450\\\phantom{66)}\underline{\phantom{9}396\phantom{}}\\\phantom{66)99}54\\\end{array}
Find closest multiple of 66 to 450. We see that 6 \times 66 = 396 is the nearest. Now subtract 396 from 450 to get reminder 54. Add 6 to quotient.
\text{Quotient: }36 \text{Reminder: }54
Since 54 is less than 66, stop the division. The reminder is 54. The topmost line 0036 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 36.
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}