Evaluate
\frac{76}{33}\approx 2.303030303
Factor
\frac{2 ^ {2} \cdot 19}{3 \cdot 11} = 2\frac{10}{33} = 2.303030303030303
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\begin{array}{l}\phantom{33)}\phantom{1}\\33\overline{)76}\\\end{array}
Use the 1^{st} digit 7 from dividend 76
\begin{array}{l}\phantom{33)}0\phantom{2}\\33\overline{)76}\\\end{array}
Since 7 is less than 33, use the next digit 6 from dividend 76 and add 0 to the quotient
\begin{array}{l}\phantom{33)}0\phantom{3}\\33\overline{)76}\\\end{array}
Use the 2^{nd} digit 6 from dividend 76
\begin{array}{l}\phantom{33)}02\phantom{4}\\33\overline{)76}\\\phantom{33)}\underline{\phantom{}66\phantom{}}\\\phantom{33)}10\\\end{array}
Find closest multiple of 33 to 76. We see that 2 \times 33 = 66 is the nearest. Now subtract 66 from 76 to get reminder 10. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }10
Since 10 is less than 33, stop the division. The reminder is 10. 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}