Evaluate
\frac{62}{13}\approx 4.769230769
Factor
\frac{2 \cdot 31}{13} = 4\frac{10}{13} = 4.769230769230769
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\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)62}\\\end{array}
Use the 1^{st} digit 6 from dividend 62
\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)62}\\\end{array}
Since 6 is less than 13, use the next digit 2 from dividend 62 and add 0 to the quotient
\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)62}\\\end{array}
Use the 2^{nd} digit 2 from dividend 62
\begin{array}{l}\phantom{13)}04\phantom{4}\\13\overline{)62}\\\phantom{13)}\underline{\phantom{}52\phantom{}}\\\phantom{13)}10\\\end{array}
Find closest multiple of 13 to 62. We see that 4 \times 13 = 52 is the nearest. Now subtract 52 from 62 to get reminder 10. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }10
Since 10 is less than 13, stop the division. The reminder is 10. 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}