Evaluate
\frac{19}{13}\approx 1.461538462
Factor
\frac{19}{13} = 1\frac{6}{13} = 1.4615384615384615
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\begin{array}{l}\phantom{65)}\phantom{1}\\65\overline{)95}\\\end{array}
Use the 1^{st} digit 9 from dividend 95
\begin{array}{l}\phantom{65)}0\phantom{2}\\65\overline{)95}\\\end{array}
Since 9 is less than 65, use the next digit 5 from dividend 95 and add 0 to the quotient
\begin{array}{l}\phantom{65)}0\phantom{3}\\65\overline{)95}\\\end{array}
Use the 2^{nd} digit 5 from dividend 95
\begin{array}{l}\phantom{65)}01\phantom{4}\\65\overline{)95}\\\phantom{65)}\underline{\phantom{}65\phantom{}}\\\phantom{65)}30\\\end{array}
Find closest multiple of 65 to 95. We see that 1 \times 65 = 65 is the nearest. Now subtract 65 from 95 to get reminder 30. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }30
Since 30 is less than 65, stop the division. The reminder is 30. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}