Evaluate
\frac{53}{6}\approx 8.833333333
Factor
\frac{53}{2 \cdot 3} = 8\frac{5}{6} = 8.833333333333334
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\begin{array}{l}\phantom{12)}\phantom{1}\\12\overline{)106}\\\end{array}
Use the 1^{st} digit 1 from dividend 106
\begin{array}{l}\phantom{12)}0\phantom{2}\\12\overline{)106}\\\end{array}
Since 1 is less than 12, use the next digit 0 from dividend 106 and add 0 to the quotient
\begin{array}{l}\phantom{12)}0\phantom{3}\\12\overline{)106}\\\end{array}
Use the 2^{nd} digit 0 from dividend 106
\begin{array}{l}\phantom{12)}00\phantom{4}\\12\overline{)106}\\\end{array}
Since 10 is less than 12, use the next digit 6 from dividend 106 and add 0 to the quotient
\begin{array}{l}\phantom{12)}00\phantom{5}\\12\overline{)106}\\\end{array}
Use the 3^{rd} digit 6 from dividend 106
\begin{array}{l}\phantom{12)}008\phantom{6}\\12\overline{)106}\\\phantom{12)}\underline{\phantom{9}96\phantom{}}\\\phantom{12)9}10\\\end{array}
Find closest multiple of 12 to 106. We see that 8 \times 12 = 96 is the nearest. Now subtract 96 from 106 to get reminder 10. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }10
Since 10 is less than 12, stop the division. The reminder is 10. The topmost line 008 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8.
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}