Evaluate
5
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5
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\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)65}\\\end{array}
Use the 1^{st} digit 6 from dividend 65
\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)65}\\\end{array}
Since 6 is less than 13, use the next digit 5 from dividend 65 and add 0 to the quotient
\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)65}\\\end{array}
Use the 2^{nd} digit 5 from dividend 65
\begin{array}{l}\phantom{13)}05\phantom{4}\\13\overline{)65}\\\phantom{13)}\underline{\phantom{}65\phantom{}}\\\phantom{13)99}0\\\end{array}
Find closest multiple of 13 to 65. We see that 5 \times 13 = 65 is the nearest. Now subtract 65 from 65 to get reminder 0. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }0
Since 0 is less than 13, stop the division. The reminder is 0. The topmost line 05 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}