Evaluate
\frac{99}{52}\approx 1.903846154
Factor
\frac{3 ^ {2} \cdot 11}{2 ^ {2} \cdot 13} = 1\frac{47}{52} = 1.9038461538461537
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\begin{array}{l}\phantom{52)}\phantom{1}\\52\overline{)99}\\\end{array}
Use the 1^{st} digit 9 from dividend 99
\begin{array}{l}\phantom{52)}0\phantom{2}\\52\overline{)99}\\\end{array}
Since 9 is less than 52, use the next digit 9 from dividend 99 and add 0 to the quotient
\begin{array}{l}\phantom{52)}0\phantom{3}\\52\overline{)99}\\\end{array}
Use the 2^{nd} digit 9 from dividend 99
\begin{array}{l}\phantom{52)}01\phantom{4}\\52\overline{)99}\\\phantom{52)}\underline{\phantom{}52\phantom{}}\\\phantom{52)}47\\\end{array}
Find closest multiple of 52 to 99. We see that 1 \times 52 = 52 is the nearest. Now subtract 52 from 99 to get reminder 47. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }47
Since 47 is less than 52, stop the division. The reminder is 47. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}