Evaluate
\frac{85}{66}\approx 1.287878788
Factor
\frac{5 \cdot 17}{2 \cdot 3 \cdot 11} = 1\frac{19}{66} = 1.2878787878787878
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\begin{array}{l}\phantom{66)}\phantom{1}\\66\overline{)85}\\\end{array}
Use the 1^{st} digit 8 from dividend 85
\begin{array}{l}\phantom{66)}0\phantom{2}\\66\overline{)85}\\\end{array}
Since 8 is less than 66, use the next digit 5 from dividend 85 and add 0 to the quotient
\begin{array}{l}\phantom{66)}0\phantom{3}\\66\overline{)85}\\\end{array}
Use the 2^{nd} digit 5 from dividend 85
\begin{array}{l}\phantom{66)}01\phantom{4}\\66\overline{)85}\\\phantom{66)}\underline{\phantom{}66\phantom{}}\\\phantom{66)}19\\\end{array}
Find closest multiple of 66 to 85. We see that 1 \times 66 = 66 is the nearest. Now subtract 66 from 85 to get reminder 19. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }19
Since 19 is less than 66, stop the division. The reminder is 19. 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}