Evaluate
\frac{19}{11}\approx 1.727272727
Factor
\frac{19}{11} = 1\frac{8}{11} = 1.7272727272727273
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\begin{array}{l}\phantom{55)}\phantom{1}\\55\overline{)95}\\\end{array}
Use the 1^{st} digit 9 from dividend 95
\begin{array}{l}\phantom{55)}0\phantom{2}\\55\overline{)95}\\\end{array}
Since 9 is less than 55, use the next digit 5 from dividend 95 and add 0 to the quotient
\begin{array}{l}\phantom{55)}0\phantom{3}\\55\overline{)95}\\\end{array}
Use the 2^{nd} digit 5 from dividend 95
\begin{array}{l}\phantom{55)}01\phantom{4}\\55\overline{)95}\\\phantom{55)}\underline{\phantom{}55\phantom{}}\\\phantom{55)}40\\\end{array}
Find closest multiple of 55 to 95. We see that 1 \times 55 = 55 is the nearest. Now subtract 55 from 95 to get reminder 40. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }40
Since 40 is less than 55, stop the division. The reminder is 40. 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}