Evaluate
55
Factor
5\times 11
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\begin{array}{l}\phantom{12)}\phantom{1}\\12\overline{)660}\\\end{array}
Use the 1^{st} digit 6 from dividend 660
\begin{array}{l}\phantom{12)}0\phantom{2}\\12\overline{)660}\\\end{array}
Since 6 is less than 12, use the next digit 6 from dividend 660 and add 0 to the quotient
\begin{array}{l}\phantom{12)}0\phantom{3}\\12\overline{)660}\\\end{array}
Use the 2^{nd} digit 6 from dividend 660
\begin{array}{l}\phantom{12)}05\phantom{4}\\12\overline{)660}\\\phantom{12)}\underline{\phantom{}60\phantom{9}}\\\phantom{12)9}6\\\end{array}
Find closest multiple of 12 to 66. We see that 5 \times 12 = 60 is the nearest. Now subtract 60 from 66 to get reminder 6. Add 5 to quotient.
\begin{array}{l}\phantom{12)}05\phantom{5}\\12\overline{)660}\\\phantom{12)}\underline{\phantom{}60\phantom{9}}\\\phantom{12)9}60\\\end{array}
Use the 3^{rd} digit 0 from dividend 660
\begin{array}{l}\phantom{12)}055\phantom{6}\\12\overline{)660}\\\phantom{12)}\underline{\phantom{}60\phantom{9}}\\\phantom{12)9}60\\\phantom{12)}\underline{\phantom{9}60\phantom{}}\\\phantom{12)999}0\\\end{array}
Find closest multiple of 12 to 60. We see that 5 \times 12 = 60 is the nearest. Now subtract 60 from 60 to get reminder 0. Add 5 to quotient.
\text{Quotient: }55 \text{Reminder: }0
Since 0 is less than 12, stop the division. The reminder is 0. The topmost line 055 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 55.
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}