Evaluate
\frac{152}{33}\approx 4.606060606
Factor
\frac{2 ^ {3} \cdot 19}{3 \cdot 11} = 4\frac{20}{33} = 4.606060606060606
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\begin{array}{l}\phantom{66)}\phantom{1}\\66\overline{)304}\\\end{array}
Use the 1^{st} digit 3 from dividend 304
\begin{array}{l}\phantom{66)}0\phantom{2}\\66\overline{)304}\\\end{array}
Since 3 is less than 66, use the next digit 0 from dividend 304 and add 0 to the quotient
\begin{array}{l}\phantom{66)}0\phantom{3}\\66\overline{)304}\\\end{array}
Use the 2^{nd} digit 0 from dividend 304
\begin{array}{l}\phantom{66)}00\phantom{4}\\66\overline{)304}\\\end{array}
Since 30 is less than 66, use the next digit 4 from dividend 304 and add 0 to the quotient
\begin{array}{l}\phantom{66)}00\phantom{5}\\66\overline{)304}\\\end{array}
Use the 3^{rd} digit 4 from dividend 304
\begin{array}{l}\phantom{66)}004\phantom{6}\\66\overline{)304}\\\phantom{66)}\underline{\phantom{}264\phantom{}}\\\phantom{66)9}40\\\end{array}
Find closest multiple of 66 to 304. We see that 4 \times 66 = 264 is the nearest. Now subtract 264 from 304 to get reminder 40. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }40
Since 40 is less than 66, stop the division. The reminder is 40. The topmost line 004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}