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{5500)}\phantom{1}\\5500\overline{)9500}\\\end{array}
Use the 1^{st} digit 9 from dividend 9500
\begin{array}{l}\phantom{5500)}0\phantom{2}\\5500\overline{)9500}\\\end{array}
Since 9 is less than 5500, use the next digit 5 from dividend 9500 and add 0 to the quotient
\begin{array}{l}\phantom{5500)}0\phantom{3}\\5500\overline{)9500}\\\end{array}
Use the 2^{nd} digit 5 from dividend 9500
\begin{array}{l}\phantom{5500)}00\phantom{4}\\5500\overline{)9500}\\\end{array}
Since 95 is less than 5500, use the next digit 0 from dividend 9500 and add 0 to the quotient
\begin{array}{l}\phantom{5500)}00\phantom{5}\\5500\overline{)9500}\\\end{array}
Use the 3^{rd} digit 0 from dividend 9500
\begin{array}{l}\phantom{5500)}000\phantom{6}\\5500\overline{)9500}\\\end{array}
Since 950 is less than 5500, use the next digit 0 from dividend 9500 and add 0 to the quotient
\begin{array}{l}\phantom{5500)}000\phantom{7}\\5500\overline{)9500}\\\end{array}
Use the 4^{th} digit 0 from dividend 9500
\begin{array}{l}\phantom{5500)}0001\phantom{8}\\5500\overline{)9500}\\\phantom{5500)}\underline{\phantom{}5500\phantom{}}\\\phantom{5500)}4000\\\end{array}
Find closest multiple of 5500 to 9500. We see that 1 \times 5500 = 5500 is the nearest. Now subtract 5500 from 9500 to get reminder 4000. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }4000
Since 4000 is less than 5500, stop the division. The reminder is 4000. The topmost line 0001 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}