Evaluate
\frac{66}{23}\approx 2.869565217
Factor
\frac{2 \cdot 3 \cdot 11}{23} = 2\frac{20}{23} = 2.869565217391304
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\begin{array}{l}\phantom{23)}\phantom{1}\\23\overline{)66}\\\end{array}
Use the 1^{st} digit 6 from dividend 66
\begin{array}{l}\phantom{23)}0\phantom{2}\\23\overline{)66}\\\end{array}
Since 6 is less than 23, use the next digit 6 from dividend 66 and add 0 to the quotient
\begin{array}{l}\phantom{23)}0\phantom{3}\\23\overline{)66}\\\end{array}
Use the 2^{nd} digit 6 from dividend 66
\begin{array}{l}\phantom{23)}02\phantom{4}\\23\overline{)66}\\\phantom{23)}\underline{\phantom{}46\phantom{}}\\\phantom{23)}20\\\end{array}
Find closest multiple of 23 to 66. We see that 2 \times 23 = 46 is the nearest. Now subtract 46 from 66 to get reminder 20. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }20
Since 20 is less than 23, stop the division. The reminder is 20. The topmost line 02 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}