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{18)}\phantom{1}\\18\overline{)39}\\\end{array}
Use the 1^{st} digit 3 from dividend 39
\begin{array}{l}\phantom{18)}0\phantom{2}\\18\overline{)39}\\\end{array}
Since 3 is less than 18, use the next digit 9 from dividend 39 and add 0 to the quotient
\begin{array}{l}\phantom{18)}0\phantom{3}\\18\overline{)39}\\\end{array}
Use the 2^{nd} digit 9 from dividend 39
\begin{array}{l}\phantom{18)}02\phantom{4}\\18\overline{)39}\\\phantom{18)}\underline{\phantom{}36\phantom{}}\\\phantom{18)9}3\\\end{array}
Find closest multiple of 18 to 39. We see that 2 \times 18 = 36 is the nearest. Now subtract 36 from 39 to get reminder 3. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }3
Since 3 is less than 18, stop the division. The reminder is 3. The topmost line 02 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}