Evaluate
\frac{91}{23}\approx 3.956521739
Factor
\frac{7 \cdot 13}{23} = 3\frac{22}{23} = 3.9565217391304346
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\begin{array}{l}\phantom{23)}\phantom{1}\\23\overline{)91}\\\end{array}
Use the 1^{st} digit 9 from dividend 91
\begin{array}{l}\phantom{23)}0\phantom{2}\\23\overline{)91}\\\end{array}
Since 9 is less than 23, use the next digit 1 from dividend 91 and add 0 to the quotient
\begin{array}{l}\phantom{23)}0\phantom{3}\\23\overline{)91}\\\end{array}
Use the 2^{nd} digit 1 from dividend 91
\begin{array}{l}\phantom{23)}03\phantom{4}\\23\overline{)91}\\\phantom{23)}\underline{\phantom{}69\phantom{}}\\\phantom{23)}22\\\end{array}
Find closest multiple of 23 to 91. We see that 3 \times 23 = 69 is the nearest. Now subtract 69 from 91 to get reminder 22. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }22
Since 22 is less than 23, stop the division. The reminder is 22. The topmost line 03 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}