Evaluate
\frac{13}{6}\approx 2.166666667
Factor
\frac{13}{2 \cdot 3} = 2\frac{1}{6} = 2.1666666666666665
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\begin{array}{l}\phantom{6000000)}\phantom{1}\\6000000\overline{)13000000}\\\end{array}
Use the 1^{st} digit 1 from dividend 13000000
\begin{array}{l}\phantom{6000000)}0\phantom{2}\\6000000\overline{)13000000}\\\end{array}
Since 1 is less than 6000000, use the next digit 3 from dividend 13000000 and add 0 to the quotient
\begin{array}{l}\phantom{6000000)}0\phantom{3}\\6000000\overline{)13000000}\\\end{array}
Use the 2^{nd} digit 3 from dividend 13000000
\begin{array}{l}\phantom{6000000)}00\phantom{4}\\6000000\overline{)13000000}\\\end{array}
Since 13 is less than 6000000, use the next digit 0 from dividend 13000000 and add 0 to the quotient
\begin{array}{l}\phantom{6000000)}00\phantom{5}\\6000000\overline{)13000000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 13000000
\begin{array}{l}\phantom{6000000)}000\phantom{6}\\6000000\overline{)13000000}\\\end{array}
Since 130 is less than 6000000, use the next digit 0 from dividend 13000000 and add 0 to the quotient
\begin{array}{l}\phantom{6000000)}000\phantom{7}\\6000000\overline{)13000000}\\\end{array}
Use the 4^{th} digit 0 from dividend 13000000
\begin{array}{l}\phantom{6000000)}0000\phantom{8}\\6000000\overline{)13000000}\\\end{array}
Since 1300 is less than 6000000, use the next digit 0 from dividend 13000000 and add 0 to the quotient
\begin{array}{l}\phantom{6000000)}0000\phantom{9}\\6000000\overline{)13000000}\\\end{array}
Use the 5^{th} digit 0 from dividend 13000000
\begin{array}{l}\phantom{6000000)}00000\phantom{10}\\6000000\overline{)13000000}\\\end{array}
Since 13000 is less than 6000000, use the next digit 0 from dividend 13000000 and add 0 to the quotient
\begin{array}{l}\phantom{6000000)}00000\phantom{11}\\6000000\overline{)13000000}\\\end{array}
Use the 6^{th} digit 0 from dividend 13000000
\begin{array}{l}\phantom{6000000)}000000\phantom{12}\\6000000\overline{)13000000}\\\end{array}
Since 130000 is less than 6000000, use the next digit 0 from dividend 13000000 and add 0 to the quotient
\begin{array}{l}\phantom{6000000)}000000\phantom{13}\\6000000\overline{)13000000}\\\end{array}
Use the 7^{th} digit 0 from dividend 13000000
\begin{array}{l}\phantom{6000000)}0000000\phantom{14}\\6000000\overline{)13000000}\\\end{array}
Since 1300000 is less than 6000000, use the next digit 0 from dividend 13000000 and add 0 to the quotient
\begin{array}{l}\phantom{6000000)}0000000\phantom{15}\\6000000\overline{)13000000}\\\end{array}
Use the 8^{th} digit 0 from dividend 13000000
\begin{array}{l}\phantom{6000000)}00000002\phantom{16}\\6000000\overline{)13000000}\\\phantom{6000000)}\underline{\phantom{}12000000\phantom{}}\\\phantom{6000000)9}1000000\\\end{array}
Find closest multiple of 6000000 to 13000000. We see that 2 \times 6000000 = 12000000 is the nearest. Now subtract 12000000 from 13000000 to get reminder 1000000. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }1000000
Since 1000000 is less than 6000000, stop the division. The reminder is 1000000. The topmost line 00000002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}