Evaluate
\frac{63}{20}=3.15
Factor
\frac{3 ^ {2} \cdot 7}{2 ^ {2} \cdot 5} = 3\frac{3}{20} = 3.15
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\begin{array}{l}\phantom{20)}\phantom{1}\\20\overline{)63}\\\end{array}
Use the 1^{st} digit 6 from dividend 63
\begin{array}{l}\phantom{20)}0\phantom{2}\\20\overline{)63}\\\end{array}
Since 6 is less than 20, use the next digit 3 from dividend 63 and add 0 to the quotient
\begin{array}{l}\phantom{20)}0\phantom{3}\\20\overline{)63}\\\end{array}
Use the 2^{nd} digit 3 from dividend 63
\begin{array}{l}\phantom{20)}03\phantom{4}\\20\overline{)63}\\\phantom{20)}\underline{\phantom{}60\phantom{}}\\\phantom{20)9}3\\\end{array}
Find closest multiple of 20 to 63. We see that 3 \times 20 = 60 is the nearest. Now subtract 60 from 63 to get reminder 3. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }3
Since 3 is less than 20, stop the division. The reminder is 3. The topmost line 03 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}