Evaluate
\frac{13}{8}=1.625
Factor
\frac{13}{2 ^ {3}} = 1\frac{5}{8} = 1.625
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\begin{array}{l}\phantom{40)}\phantom{1}\\40\overline{)65}\\\end{array}
Use the 1^{st} digit 6 from dividend 65
\begin{array}{l}\phantom{40)}0\phantom{2}\\40\overline{)65}\\\end{array}
Since 6 is less than 40, use the next digit 5 from dividend 65 and add 0 to the quotient
\begin{array}{l}\phantom{40)}0\phantom{3}\\40\overline{)65}\\\end{array}
Use the 2^{nd} digit 5 from dividend 65
\begin{array}{l}\phantom{40)}01\phantom{4}\\40\overline{)65}\\\phantom{40)}\underline{\phantom{}40\phantom{}}\\\phantom{40)}25\\\end{array}
Find closest multiple of 40 to 65. We see that 1 \times 40 = 40 is the nearest. Now subtract 40 from 65 to get reminder 25. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }25
Since 25 is less than 40, stop the division. The reminder is 25. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}