Evaluate
\frac{271}{111}\approx 2.441441441
Factor
\frac{271}{3 \cdot 37} = 2\frac{49}{111} = 2.4414414414414414
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\begin{array}{l}\phantom{999)}\phantom{1}\\999\overline{)2439}\\\end{array}
Use the 1^{st} digit 2 from dividend 2439
\begin{array}{l}\phantom{999)}0\phantom{2}\\999\overline{)2439}\\\end{array}
Since 2 is less than 999, use the next digit 4 from dividend 2439 and add 0 to the quotient
\begin{array}{l}\phantom{999)}0\phantom{3}\\999\overline{)2439}\\\end{array}
Use the 2^{nd} digit 4 from dividend 2439
\begin{array}{l}\phantom{999)}00\phantom{4}\\999\overline{)2439}\\\end{array}
Since 24 is less than 999, use the next digit 3 from dividend 2439 and add 0 to the quotient
\begin{array}{l}\phantom{999)}00\phantom{5}\\999\overline{)2439}\\\end{array}
Use the 3^{rd} digit 3 from dividend 2439
\begin{array}{l}\phantom{999)}000\phantom{6}\\999\overline{)2439}\\\end{array}
Since 243 is less than 999, use the next digit 9 from dividend 2439 and add 0 to the quotient
\begin{array}{l}\phantom{999)}000\phantom{7}\\999\overline{)2439}\\\end{array}
Use the 4^{th} digit 9 from dividend 2439
\begin{array}{l}\phantom{999)}0002\phantom{8}\\999\overline{)2439}\\\phantom{999)}\underline{\phantom{}1998\phantom{}}\\\phantom{999)9}441\\\end{array}
Find closest multiple of 999 to 2439. We see that 2 \times 999 = 1998 is the nearest. Now subtract 1998 from 2439 to get reminder 441. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }441
Since 441 is less than 999, stop the division. The reminder is 441. The topmost line 0002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}