Evaluate
\frac{391}{91}\approx 4.296703297
Factor
\frac{17 \cdot 23}{7 \cdot 13} = 4\frac{27}{91} = 4.2967032967032965
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\begin{array}{l}\phantom{91)}\phantom{1}\\91\overline{)391}\\\end{array}
Use the 1^{st} digit 3 from dividend 391
\begin{array}{l}\phantom{91)}0\phantom{2}\\91\overline{)391}\\\end{array}
Since 3 is less than 91, use the next digit 9 from dividend 391 and add 0 to the quotient
\begin{array}{l}\phantom{91)}0\phantom{3}\\91\overline{)391}\\\end{array}
Use the 2^{nd} digit 9 from dividend 391
\begin{array}{l}\phantom{91)}00\phantom{4}\\91\overline{)391}\\\end{array}
Since 39 is less than 91, use the next digit 1 from dividend 391 and add 0 to the quotient
\begin{array}{l}\phantom{91)}00\phantom{5}\\91\overline{)391}\\\end{array}
Use the 3^{rd} digit 1 from dividend 391
\begin{array}{l}\phantom{91)}004\phantom{6}\\91\overline{)391}\\\phantom{91)}\underline{\phantom{}364\phantom{}}\\\phantom{91)9}27\\\end{array}
Find closest multiple of 91 to 391. We see that 4 \times 91 = 364 is the nearest. Now subtract 364 from 391 to get reminder 27. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }27
Since 27 is less than 91, stop the division. The reminder is 27. The topmost line 004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}