Evaluate
2
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2
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\begin{array}{l}\phantom{1256)}\phantom{1}\\1256\overline{)2512}\\\end{array}
Use the 1^{st} digit 2 from dividend 2512
\begin{array}{l}\phantom{1256)}0\phantom{2}\\1256\overline{)2512}\\\end{array}
Since 2 is less than 1256, use the next digit 5 from dividend 2512 and add 0 to the quotient
\begin{array}{l}\phantom{1256)}0\phantom{3}\\1256\overline{)2512}\\\end{array}
Use the 2^{nd} digit 5 from dividend 2512
\begin{array}{l}\phantom{1256)}00\phantom{4}\\1256\overline{)2512}\\\end{array}
Since 25 is less than 1256, use the next digit 1 from dividend 2512 and add 0 to the quotient
\begin{array}{l}\phantom{1256)}00\phantom{5}\\1256\overline{)2512}\\\end{array}
Use the 3^{rd} digit 1 from dividend 2512
\begin{array}{l}\phantom{1256)}000\phantom{6}\\1256\overline{)2512}\\\end{array}
Since 251 is less than 1256, use the next digit 2 from dividend 2512 and add 0 to the quotient
\begin{array}{l}\phantom{1256)}000\phantom{7}\\1256\overline{)2512}\\\end{array}
Use the 4^{th} digit 2 from dividend 2512
\begin{array}{l}\phantom{1256)}0002\phantom{8}\\1256\overline{)2512}\\\phantom{1256)}\underline{\phantom{}2512\phantom{}}\\\phantom{1256)9999}0\\\end{array}
Find closest multiple of 1256 to 2512. We see that 2 \times 1256 = 2512 is the nearest. Now subtract 2512 from 2512 to get reminder 0. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }0
Since 0 is less than 1256, stop the division. The reminder is 0. 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}