Evaluate
\frac{125}{9}\approx 13.888888889
Factor
\frac{5 ^ {3}}{3 ^ {2}} = 13\frac{8}{9} = 13.88888888888889
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\begin{array}{l}\phantom{3600)}\phantom{1}\\3600\overline{)50000}\\\end{array}
Use the 1^{st} digit 5 from dividend 50000
\begin{array}{l}\phantom{3600)}0\phantom{2}\\3600\overline{)50000}\\\end{array}
Since 5 is less than 3600, use the next digit 0 from dividend 50000 and add 0 to the quotient
\begin{array}{l}\phantom{3600)}0\phantom{3}\\3600\overline{)50000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 50000
\begin{array}{l}\phantom{3600)}00\phantom{4}\\3600\overline{)50000}\\\end{array}
Since 50 is less than 3600, use the next digit 0 from dividend 50000 and add 0 to the quotient
\begin{array}{l}\phantom{3600)}00\phantom{5}\\3600\overline{)50000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 50000
\begin{array}{l}\phantom{3600)}000\phantom{6}\\3600\overline{)50000}\\\end{array}
Since 500 is less than 3600, use the next digit 0 from dividend 50000 and add 0 to the quotient
\begin{array}{l}\phantom{3600)}000\phantom{7}\\3600\overline{)50000}\\\end{array}
Use the 4^{th} digit 0 from dividend 50000
\begin{array}{l}\phantom{3600)}0001\phantom{8}\\3600\overline{)50000}\\\phantom{3600)}\underline{\phantom{}3600\phantom{9}}\\\phantom{3600)}1400\\\end{array}
Find closest multiple of 3600 to 5000. We see that 1 \times 3600 = 3600 is the nearest. Now subtract 3600 from 5000 to get reminder 1400. Add 1 to quotient.
\begin{array}{l}\phantom{3600)}0001\phantom{9}\\3600\overline{)50000}\\\phantom{3600)}\underline{\phantom{}3600\phantom{9}}\\\phantom{3600)}14000\\\end{array}
Use the 5^{th} digit 0 from dividend 50000
\begin{array}{l}\phantom{3600)}00013\phantom{10}\\3600\overline{)50000}\\\phantom{3600)}\underline{\phantom{}3600\phantom{9}}\\\phantom{3600)}14000\\\phantom{3600)}\underline{\phantom{}10800\phantom{}}\\\phantom{3600)9}3200\\\end{array}
Find closest multiple of 3600 to 14000. We see that 3 \times 3600 = 10800 is the nearest. Now subtract 10800 from 14000 to get reminder 3200. Add 3 to quotient.
\text{Quotient: }13 \text{Reminder: }3200
Since 3200 is less than 3600, stop the division. The reminder is 3200. The topmost line 00013 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 13.
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}