Evaluate
\frac{80}{33}\approx 2.424242424
Factor
\frac{2 ^ {4} \cdot 5}{3 \cdot 11} = 2\frac{14}{33} = 2.4242424242424243
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\begin{array}{l}\phantom{33)}\phantom{1}\\33\overline{)80}\\\end{array}
Use the 1^{st} digit 8 from dividend 80
\begin{array}{l}\phantom{33)}0\phantom{2}\\33\overline{)80}\\\end{array}
Since 8 is less than 33, use the next digit 0 from dividend 80 and add 0 to the quotient
\begin{array}{l}\phantom{33)}0\phantom{3}\\33\overline{)80}\\\end{array}
Use the 2^{nd} digit 0 from dividend 80
\begin{array}{l}\phantom{33)}02\phantom{4}\\33\overline{)80}\\\phantom{33)}\underline{\phantom{}66\phantom{}}\\\phantom{33)}14\\\end{array}
Find closest multiple of 33 to 80. We see that 2 \times 33 = 66 is the nearest. Now subtract 66 from 80 to get reminder 14. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }14
Since 14 is less than 33, stop the division. The reminder is 14. 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}