Evaluate
\frac{684}{275}\approx 2.487272727
Factor
\frac{2 ^ {2} \cdot 3 ^ {2} \cdot 19}{5 ^ {2} \cdot 11} = 2\frac{134}{275} = 2.4872727272727273
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\begin{array}{l}\phantom{275)}\phantom{1}\\275\overline{)684}\\\end{array}
Use the 1^{st} digit 6 from dividend 684
\begin{array}{l}\phantom{275)}0\phantom{2}\\275\overline{)684}\\\end{array}
Since 6 is less than 275, use the next digit 8 from dividend 684 and add 0 to the quotient
\begin{array}{l}\phantom{275)}0\phantom{3}\\275\overline{)684}\\\end{array}
Use the 2^{nd} digit 8 from dividend 684
\begin{array}{l}\phantom{275)}00\phantom{4}\\275\overline{)684}\\\end{array}
Since 68 is less than 275, use the next digit 4 from dividend 684 and add 0 to the quotient
\begin{array}{l}\phantom{275)}00\phantom{5}\\275\overline{)684}\\\end{array}
Use the 3^{rd} digit 4 from dividend 684
\begin{array}{l}\phantom{275)}002\phantom{6}\\275\overline{)684}\\\phantom{275)}\underline{\phantom{}550\phantom{}}\\\phantom{275)}134\\\end{array}
Find closest multiple of 275 to 684. We see that 2 \times 275 = 550 is the nearest. Now subtract 550 from 684 to get reminder 134. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }134
Since 134 is less than 275, stop the division. The reminder is 134. The topmost line 002 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}