Evaluate
\frac{91}{20}=4.55
Factor
\frac{7 \cdot 13}{2 ^ {2} \cdot 5} = 4\frac{11}{20} = 4.55
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\begin{array}{l}\phantom{20)}\phantom{1}\\20\overline{)91}\\\end{array}
Use the 1^{st} digit 9 from dividend 91
\begin{array}{l}\phantom{20)}0\phantom{2}\\20\overline{)91}\\\end{array}
Since 9 is less than 20, use the next digit 1 from dividend 91 and add 0 to the quotient
\begin{array}{l}\phantom{20)}0\phantom{3}\\20\overline{)91}\\\end{array}
Use the 2^{nd} digit 1 from dividend 91
\begin{array}{l}\phantom{20)}04\phantom{4}\\20\overline{)91}\\\phantom{20)}\underline{\phantom{}80\phantom{}}\\\phantom{20)}11\\\end{array}
Find closest multiple of 20 to 91. We see that 4 \times 20 = 80 is the nearest. Now subtract 80 from 91 to get reminder 11. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }11
Since 11 is less than 20, stop the division. The reminder is 11. The topmost line 04 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}