Evaluate
\frac{63}{22}\approx 2.863636364
Factor
\frac{3 ^ {2} \cdot 7}{2 \cdot 11} = 2\frac{19}{22} = 2.8636363636363638
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\begin{array}{l}\phantom{22)}\phantom{1}\\22\overline{)63}\\\end{array}
Use the 1^{st} digit 6 from dividend 63
\begin{array}{l}\phantom{22)}0\phantom{2}\\22\overline{)63}\\\end{array}
Since 6 is less than 22, use the next digit 3 from dividend 63 and add 0 to the quotient
\begin{array}{l}\phantom{22)}0\phantom{3}\\22\overline{)63}\\\end{array}
Use the 2^{nd} digit 3 from dividend 63
\begin{array}{l}\phantom{22)}02\phantom{4}\\22\overline{)63}\\\phantom{22)}\underline{\phantom{}44\phantom{}}\\\phantom{22)}19\\\end{array}
Find closest multiple of 22 to 63. We see that 2 \times 22 = 44 is the nearest. Now subtract 44 from 63 to get reminder 19. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }19
Since 19 is less than 22, stop the division. The reminder is 19. 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}