Evaluate
\frac{65}{17}\approx 3.823529412
Factor
\frac{5 \cdot 13}{17} = 3\frac{14}{17} = 3.823529411764706
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\begin{array}{l}\phantom{17)}\phantom{1}\\17\overline{)65}\\\end{array}
Use the 1^{st} digit 6 from dividend 65
\begin{array}{l}\phantom{17)}0\phantom{2}\\17\overline{)65}\\\end{array}
Since 6 is less than 17, use the next digit 5 from dividend 65 and add 0 to the quotient
\begin{array}{l}\phantom{17)}0\phantom{3}\\17\overline{)65}\\\end{array}
Use the 2^{nd} digit 5 from dividend 65
\begin{array}{l}\phantom{17)}03\phantom{4}\\17\overline{)65}\\\phantom{17)}\underline{\phantom{}51\phantom{}}\\\phantom{17)}14\\\end{array}
Find closest multiple of 17 to 65. We see that 3 \times 17 = 51 is the nearest. Now subtract 51 from 65 to get reminder 14. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }14
Since 14 is less than 17, stop the division. The reminder is 14. The topmost line 03 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}