Evaluate
\frac{19}{2}=9.5
Factor
\frac{19}{2} = 9\frac{1}{2} = 9.5
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\begin{array}{l}\phantom{66)}\phantom{1}\\66\overline{)627}\\\end{array}
Use the 1^{st} digit 6 from dividend 627
\begin{array}{l}\phantom{66)}0\phantom{2}\\66\overline{)627}\\\end{array}
Since 6 is less than 66, use the next digit 2 from dividend 627 and add 0 to the quotient
\begin{array}{l}\phantom{66)}0\phantom{3}\\66\overline{)627}\\\end{array}
Use the 2^{nd} digit 2 from dividend 627
\begin{array}{l}\phantom{66)}00\phantom{4}\\66\overline{)627}\\\end{array}
Since 62 is less than 66, use the next digit 7 from dividend 627 and add 0 to the quotient
\begin{array}{l}\phantom{66)}00\phantom{5}\\66\overline{)627}\\\end{array}
Use the 3^{rd} digit 7 from dividend 627
\begin{array}{l}\phantom{66)}009\phantom{6}\\66\overline{)627}\\\phantom{66)}\underline{\phantom{}594\phantom{}}\\\phantom{66)9}33\\\end{array}
Find closest multiple of 66 to 627. We see that 9 \times 66 = 594 is the nearest. Now subtract 594 from 627 to get reminder 33. Add 9 to quotient.
\text{Quotient: }9 \text{Reminder: }33
Since 33 is less than 66, stop the division. The reminder is 33. The topmost line 009 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 9.
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}