Evaluate
\frac{24}{11}\approx 2.181818182
Factor
\frac{2 ^ {3} \cdot 3}{11} = 2\frac{2}{11} = 2.1818181818181817
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\begin{array}{l}\phantom{33)}\phantom{1}\\33\overline{)72}\\\end{array}
Use the 1^{st} digit 7 from dividend 72
\begin{array}{l}\phantom{33)}0\phantom{2}\\33\overline{)72}\\\end{array}
Since 7 is less than 33, use the next digit 2 from dividend 72 and add 0 to the quotient
\begin{array}{l}\phantom{33)}0\phantom{3}\\33\overline{)72}\\\end{array}
Use the 2^{nd} digit 2 from dividend 72
\begin{array}{l}\phantom{33)}02\phantom{4}\\33\overline{)72}\\\phantom{33)}\underline{\phantom{}66\phantom{}}\\\phantom{33)9}6\\\end{array}
Find closest multiple of 33 to 72. We see that 2 \times 33 = 66 is the nearest. Now subtract 66 from 72 to get reminder 6. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }6
Since 6 is less than 33, stop the division. The reminder is 6. 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}