Evaluate
\frac{1212}{1211}\approx 1.000825764
Factor
\frac{2 ^ {2} \cdot 3 \cdot 101}{7 \cdot 173} = 1\frac{1}{1211} = 1.000825763831544
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\begin{array}{l}\phantom{1211)}\phantom{1}\\1211\overline{)1212}\\\end{array}
Use the 1^{st} digit 1 from dividend 1212
\begin{array}{l}\phantom{1211)}0\phantom{2}\\1211\overline{)1212}\\\end{array}
Since 1 is less than 1211, use the next digit 2 from dividend 1212 and add 0 to the quotient
\begin{array}{l}\phantom{1211)}0\phantom{3}\\1211\overline{)1212}\\\end{array}
Use the 2^{nd} digit 2 from dividend 1212
\begin{array}{l}\phantom{1211)}00\phantom{4}\\1211\overline{)1212}\\\end{array}
Since 12 is less than 1211, use the next digit 1 from dividend 1212 and add 0 to the quotient
\begin{array}{l}\phantom{1211)}00\phantom{5}\\1211\overline{)1212}\\\end{array}
Use the 3^{rd} digit 1 from dividend 1212
\begin{array}{l}\phantom{1211)}000\phantom{6}\\1211\overline{)1212}\\\end{array}
Since 121 is less than 1211, use the next digit 2 from dividend 1212 and add 0 to the quotient
\begin{array}{l}\phantom{1211)}000\phantom{7}\\1211\overline{)1212}\\\end{array}
Use the 4^{th} digit 2 from dividend 1212
\begin{array}{l}\phantom{1211)}0001\phantom{8}\\1211\overline{)1212}\\\phantom{1211)}\underline{\phantom{}1211\phantom{}}\\\phantom{1211)999}1\\\end{array}
Find closest multiple of 1211 to 1212. We see that 1 \times 1211 = 1211 is the nearest. Now subtract 1211 from 1212 to get reminder 1. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }1
Since 1 is less than 1211, stop the division. The reminder is 1. The topmost line 0001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}