Evaluate
\frac{63}{13}\approx 4.846153846
Factor
\frac{3 ^ {2} \cdot 7}{13} = 4\frac{11}{13} = 4.846153846153846
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\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)63}\\\end{array}
Use the 1^{st} digit 6 from dividend 63
\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)63}\\\end{array}
Since 6 is less than 13, use the next digit 3 from dividend 63 and add 0 to the quotient
\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)63}\\\end{array}
Use the 2^{nd} digit 3 from dividend 63
\begin{array}{l}\phantom{13)}04\phantom{4}\\13\overline{)63}\\\phantom{13)}\underline{\phantom{}52\phantom{}}\\\phantom{13)}11\\\end{array}
Find closest multiple of 13 to 63. We see that 4 \times 13 = 52 is the nearest. Now subtract 52 from 63 to get reminder 11. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }11
Since 11 is less than 13, stop the division. The reminder is 11. The topmost line 04 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}