Evaluate
\frac{473}{405}\approx 1.167901235
Factor
\frac{11 \cdot 43}{3 ^ {4} \cdot 5} = 1\frac{68}{405} = 1.1679012345679012
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\begin{array}{l}\phantom{405)}\phantom{1}\\405\overline{)473}\\\end{array}
Use the 1^{st} digit 4 from dividend 473
\begin{array}{l}\phantom{405)}0\phantom{2}\\405\overline{)473}\\\end{array}
Since 4 is less than 405, use the next digit 7 from dividend 473 and add 0 to the quotient
\begin{array}{l}\phantom{405)}0\phantom{3}\\405\overline{)473}\\\end{array}
Use the 2^{nd} digit 7 from dividend 473
\begin{array}{l}\phantom{405)}00\phantom{4}\\405\overline{)473}\\\end{array}
Since 47 is less than 405, use the next digit 3 from dividend 473 and add 0 to the quotient
\begin{array}{l}\phantom{405)}00\phantom{5}\\405\overline{)473}\\\end{array}
Use the 3^{rd} digit 3 from dividend 473
\begin{array}{l}\phantom{405)}001\phantom{6}\\405\overline{)473}\\\phantom{405)}\underline{\phantom{}405\phantom{}}\\\phantom{405)9}68\\\end{array}
Find closest multiple of 405 to 473. We see that 1 \times 405 = 405 is the nearest. Now subtract 405 from 473 to get reminder 68. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }68
Since 68 is less than 405, stop the division. The reminder is 68. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}