Evaluate
\frac{53}{11}\approx 4.818181818
Factor
\frac{53}{11} = 4\frac{9}{11} = 4.818181818181818
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\begin{array}{l}\phantom{22)}\phantom{1}\\22\overline{)106}\\\end{array}
Use the 1^{st} digit 1 from dividend 106
\begin{array}{l}\phantom{22)}0\phantom{2}\\22\overline{)106}\\\end{array}
Since 1 is less than 22, use the next digit 0 from dividend 106 and add 0 to the quotient
\begin{array}{l}\phantom{22)}0\phantom{3}\\22\overline{)106}\\\end{array}
Use the 2^{nd} digit 0 from dividend 106
\begin{array}{l}\phantom{22)}00\phantom{4}\\22\overline{)106}\\\end{array}
Since 10 is less than 22, use the next digit 6 from dividend 106 and add 0 to the quotient
\begin{array}{l}\phantom{22)}00\phantom{5}\\22\overline{)106}\\\end{array}
Use the 3^{rd} digit 6 from dividend 106
\begin{array}{l}\phantom{22)}004\phantom{6}\\22\overline{)106}\\\phantom{22)}\underline{\phantom{9}88\phantom{}}\\\phantom{22)9}18\\\end{array}
Find closest multiple of 22 to 106. We see that 4 \times 22 = 88 is the nearest. Now subtract 88 from 106 to get reminder 18. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }18
Since 18 is less than 22, stop the division. The reminder is 18. 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}