Evaluate
\frac{362}{55}\approx 6.581818182
Factor
\frac{2 \cdot 181}{5 \cdot 11} = 6\frac{32}{55} = 6.581818181818182
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\begin{array}{l}\phantom{55)}\phantom{1}\\55\overline{)362}\\\end{array}
Use the 1^{st} digit 3 from dividend 362
\begin{array}{l}\phantom{55)}0\phantom{2}\\55\overline{)362}\\\end{array}
Since 3 is less than 55, use the next digit 6 from dividend 362 and add 0 to the quotient
\begin{array}{l}\phantom{55)}0\phantom{3}\\55\overline{)362}\\\end{array}
Use the 2^{nd} digit 6 from dividend 362
\begin{array}{l}\phantom{55)}00\phantom{4}\\55\overline{)362}\\\end{array}
Since 36 is less than 55, use the next digit 2 from dividend 362 and add 0 to the quotient
\begin{array}{l}\phantom{55)}00\phantom{5}\\55\overline{)362}\\\end{array}
Use the 3^{rd} digit 2 from dividend 362
\begin{array}{l}\phantom{55)}006\phantom{6}\\55\overline{)362}\\\phantom{55)}\underline{\phantom{}330\phantom{}}\\\phantom{55)9}32\\\end{array}
Find closest multiple of 55 to 362. We see that 6 \times 55 = 330 is the nearest. Now subtract 330 from 362 to get reminder 32. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }32
Since 32 is less than 55, stop the division. The reminder is 32. 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}