Evaluate
\frac{55}{6}\approx 9.166666667
Factor
\frac{5 \cdot 11}{2 \cdot 3} = 9\frac{1}{6} = 9.166666666666666
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\begin{array}{l}\phantom{12)}\phantom{1}\\12\overline{)110}\\\end{array}
Use the 1^{st} digit 1 from dividend 110
\begin{array}{l}\phantom{12)}0\phantom{2}\\12\overline{)110}\\\end{array}
Since 1 is less than 12, use the next digit 1 from dividend 110 and add 0 to the quotient
\begin{array}{l}\phantom{12)}0\phantom{3}\\12\overline{)110}\\\end{array}
Use the 2^{nd} digit 1 from dividend 110
\begin{array}{l}\phantom{12)}00\phantom{4}\\12\overline{)110}\\\end{array}
Since 11 is less than 12, use the next digit 0 from dividend 110 and add 0 to the quotient
\begin{array}{l}\phantom{12)}00\phantom{5}\\12\overline{)110}\\\end{array}
Use the 3^{rd} digit 0 from dividend 110
\begin{array}{l}\phantom{12)}009\phantom{6}\\12\overline{)110}\\\phantom{12)}\underline{\phantom{}108\phantom{}}\\\phantom{12)99}2\\\end{array}
Find closest multiple of 12 to 110. We see that 9 \times 12 = 108 is the nearest. Now subtract 108 from 110 to get reminder 2. Add 9 to quotient.
\text{Quotient: }9 \text{Reminder: }2
Since 2 is less than 12, stop the division. The reminder is 2. The topmost line 009 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 9.
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}