Evaluate
\frac{611}{90}\approx 6.788888889
Factor
\frac{13 \cdot 47}{2 \cdot 3 ^ {2} \cdot 5} = 6\frac{71}{90} = 6.788888888888889
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\begin{array}{l}\phantom{90)}\phantom{1}\\90\overline{)611}\\\end{array}
Use the 1^{st} digit 6 from dividend 611
\begin{array}{l}\phantom{90)}0\phantom{2}\\90\overline{)611}\\\end{array}
Since 6 is less than 90, use the next digit 1 from dividend 611 and add 0 to the quotient
\begin{array}{l}\phantom{90)}0\phantom{3}\\90\overline{)611}\\\end{array}
Use the 2^{nd} digit 1 from dividend 611
\begin{array}{l}\phantom{90)}00\phantom{4}\\90\overline{)611}\\\end{array}
Since 61 is less than 90, use the next digit 1 from dividend 611 and add 0 to the quotient
\begin{array}{l}\phantom{90)}00\phantom{5}\\90\overline{)611}\\\end{array}
Use the 3^{rd} digit 1 from dividend 611
\begin{array}{l}\phantom{90)}006\phantom{6}\\90\overline{)611}\\\phantom{90)}\underline{\phantom{}540\phantom{}}\\\phantom{90)9}71\\\end{array}
Find closest multiple of 90 to 611. We see that 6 \times 90 = 540 is the nearest. Now subtract 540 from 611 to get reminder 71. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }71
Since 71 is less than 90, stop the division. The reminder is 71. 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}