Evaluate
\frac{130}{9}\approx 14.444444444
Factor
\frac{2 \cdot 5 \cdot 13}{3 ^ {2}} = 14\frac{4}{9} = 14.444444444444445
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\begin{array}{l}\phantom{4500)}\phantom{1}\\4500\overline{)65000}\\\end{array}
Use the 1^{st} digit 6 from dividend 65000
\begin{array}{l}\phantom{4500)}0\phantom{2}\\4500\overline{)65000}\\\end{array}
Since 6 is less than 4500, use the next digit 5 from dividend 65000 and add 0 to the quotient
\begin{array}{l}\phantom{4500)}0\phantom{3}\\4500\overline{)65000}\\\end{array}
Use the 2^{nd} digit 5 from dividend 65000
\begin{array}{l}\phantom{4500)}00\phantom{4}\\4500\overline{)65000}\\\end{array}
Since 65 is less than 4500, use the next digit 0 from dividend 65000 and add 0 to the quotient
\begin{array}{l}\phantom{4500)}00\phantom{5}\\4500\overline{)65000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 65000
\begin{array}{l}\phantom{4500)}000\phantom{6}\\4500\overline{)65000}\\\end{array}
Since 650 is less than 4500, use the next digit 0 from dividend 65000 and add 0 to the quotient
\begin{array}{l}\phantom{4500)}000\phantom{7}\\4500\overline{)65000}\\\end{array}
Use the 4^{th} digit 0 from dividend 65000
\begin{array}{l}\phantom{4500)}0001\phantom{8}\\4500\overline{)65000}\\\phantom{4500)}\underline{\phantom{}4500\phantom{9}}\\\phantom{4500)}2000\\\end{array}
Find closest multiple of 4500 to 6500. We see that 1 \times 4500 = 4500 is the nearest. Now subtract 4500 from 6500 to get reminder 2000. Add 1 to quotient.
\begin{array}{l}\phantom{4500)}0001\phantom{9}\\4500\overline{)65000}\\\phantom{4500)}\underline{\phantom{}4500\phantom{9}}\\\phantom{4500)}20000\\\end{array}
Use the 5^{th} digit 0 from dividend 65000
\begin{array}{l}\phantom{4500)}00014\phantom{10}\\4500\overline{)65000}\\\phantom{4500)}\underline{\phantom{}4500\phantom{9}}\\\phantom{4500)}20000\\\phantom{4500)}\underline{\phantom{}18000\phantom{}}\\\phantom{4500)9}2000\\\end{array}
Find closest multiple of 4500 to 20000. We see that 4 \times 4500 = 18000 is the nearest. Now subtract 18000 from 20000 to get reminder 2000. Add 4 to quotient.
\text{Quotient: }14 \text{Reminder: }2000
Since 2000 is less than 4500, stop the division. The reminder is 2000. The topmost line 00014 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 14.
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}