Evaluate
\frac{32}{5}=6.4
Factor
\frac{2 ^ {5}}{5} = 6\frac{2}{5} = 6.4
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\begin{array}{l}\phantom{100)}\phantom{1}\\100\overline{)640}\\\end{array}
Use the 1^{st} digit 6 from dividend 640
\begin{array}{l}\phantom{100)}0\phantom{2}\\100\overline{)640}\\\end{array}
Since 6 is less than 100, use the next digit 4 from dividend 640 and add 0 to the quotient
\begin{array}{l}\phantom{100)}0\phantom{3}\\100\overline{)640}\\\end{array}
Use the 2^{nd} digit 4 from dividend 640
\begin{array}{l}\phantom{100)}00\phantom{4}\\100\overline{)640}\\\end{array}
Since 64 is less than 100, use the next digit 0 from dividend 640 and add 0 to the quotient
\begin{array}{l}\phantom{100)}00\phantom{5}\\100\overline{)640}\\\end{array}
Use the 3^{rd} digit 0 from dividend 640
\begin{array}{l}\phantom{100)}006\phantom{6}\\100\overline{)640}\\\phantom{100)}\underline{\phantom{}600\phantom{}}\\\phantom{100)9}40\\\end{array}
Find closest multiple of 100 to 640. We see that 6 \times 100 = 600 is the nearest. Now subtract 600 from 640 to get reminder 40. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }40
Since 40 is less than 100, stop the division. The reminder is 40. The topmost line 006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}