Evaluate
12
Factor
2^{2}\times 3
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\begin{array}{l}\phantom{55)}\phantom{1}\\55\overline{)660}\\\end{array}
Use the 1^{st} digit 6 from dividend 660
\begin{array}{l}\phantom{55)}0\phantom{2}\\55\overline{)660}\\\end{array}
Since 6 is less than 55, use the next digit 6 from dividend 660 and add 0 to the quotient
\begin{array}{l}\phantom{55)}0\phantom{3}\\55\overline{)660}\\\end{array}
Use the 2^{nd} digit 6 from dividend 660
\begin{array}{l}\phantom{55)}01\phantom{4}\\55\overline{)660}\\\phantom{55)}\underline{\phantom{}55\phantom{9}}\\\phantom{55)}11\\\end{array}
Find closest multiple of 55 to 66. We see that 1 \times 55 = 55 is the nearest. Now subtract 55 from 66 to get reminder 11. Add 1 to quotient.
\begin{array}{l}\phantom{55)}01\phantom{5}\\55\overline{)660}\\\phantom{55)}\underline{\phantom{}55\phantom{9}}\\\phantom{55)}110\\\end{array}
Use the 3^{rd} digit 0 from dividend 660
\begin{array}{l}\phantom{55)}012\phantom{6}\\55\overline{)660}\\\phantom{55)}\underline{\phantom{}55\phantom{9}}\\\phantom{55)}110\\\phantom{55)}\underline{\phantom{}110\phantom{}}\\\phantom{55)999}0\\\end{array}
Find closest multiple of 55 to 110. We see that 2 \times 55 = 110 is the nearest. Now subtract 110 from 110 to get reminder 0. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }0
Since 0 is less than 55, stop the division. The reminder is 0. The topmost line 012 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 12.
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}