Evaluate
\frac{50000}{469}\approx 106.609808102
Factor
\frac{2 ^ {4} \cdot 5 ^ {5}}{7 \cdot 67} = 106\frac{286}{469} = 106.60980810234541
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\begin{array}{l}\phantom{469)}\phantom{1}\\469\overline{)50000}\\\end{array}
Use the 1^{st} digit 5 from dividend 50000
\begin{array}{l}\phantom{469)}0\phantom{2}\\469\overline{)50000}\\\end{array}
Since 5 is less than 469, use the next digit 0 from dividend 50000 and add 0 to the quotient
\begin{array}{l}\phantom{469)}0\phantom{3}\\469\overline{)50000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 50000
\begin{array}{l}\phantom{469)}00\phantom{4}\\469\overline{)50000}\\\end{array}
Since 50 is less than 469, use the next digit 0 from dividend 50000 and add 0 to the quotient
\begin{array}{l}\phantom{469)}00\phantom{5}\\469\overline{)50000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 50000
\begin{array}{l}\phantom{469)}001\phantom{6}\\469\overline{)50000}\\\phantom{469)}\underline{\phantom{}469\phantom{99}}\\\phantom{469)9}31\\\end{array}
Find closest multiple of 469 to 500. We see that 1 \times 469 = 469 is the nearest. Now subtract 469 from 500 to get reminder 31. Add 1 to quotient.
\begin{array}{l}\phantom{469)}001\phantom{7}\\469\overline{)50000}\\\phantom{469)}\underline{\phantom{}469\phantom{99}}\\\phantom{469)9}310\\\end{array}
Use the 4^{th} digit 0 from dividend 50000
\begin{array}{l}\phantom{469)}0010\phantom{8}\\469\overline{)50000}\\\phantom{469)}\underline{\phantom{}469\phantom{99}}\\\phantom{469)9}310\\\end{array}
Since 310 is less than 469, use the next digit 0 from dividend 50000 and add 0 to the quotient
\begin{array}{l}\phantom{469)}0010\phantom{9}\\469\overline{)50000}\\\phantom{469)}\underline{\phantom{}469\phantom{99}}\\\phantom{469)9}3100\\\end{array}
Use the 5^{th} digit 0 from dividend 50000
\begin{array}{l}\phantom{469)}00106\phantom{10}\\469\overline{)50000}\\\phantom{469)}\underline{\phantom{}469\phantom{99}}\\\phantom{469)9}3100\\\phantom{469)}\underline{\phantom{9}2814\phantom{}}\\\phantom{469)99}286\\\end{array}
Find closest multiple of 469 to 3100. We see that 6 \times 469 = 2814 is the nearest. Now subtract 2814 from 3100 to get reminder 286. Add 6 to quotient.
\text{Quotient: }106 \text{Reminder: }286
Since 286 is less than 469, stop the division. The reminder is 286. The topmost line 00106 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 106.
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}