Evaluate
\frac{68}{29}\approx 2.344827586
Factor
\frac{2 ^ {2} \cdot 17}{29} = 2\frac{10}{29} = 2.3448275862068964
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\begin{array}{l}\phantom{261)}\phantom{1}\\261\overline{)612}\\\end{array}
Use the 1^{st} digit 6 from dividend 612
\begin{array}{l}\phantom{261)}0\phantom{2}\\261\overline{)612}\\\end{array}
Since 6 is less than 261, use the next digit 1 from dividend 612 and add 0 to the quotient
\begin{array}{l}\phantom{261)}0\phantom{3}\\261\overline{)612}\\\end{array}
Use the 2^{nd} digit 1 from dividend 612
\begin{array}{l}\phantom{261)}00\phantom{4}\\261\overline{)612}\\\end{array}
Since 61 is less than 261, use the next digit 2 from dividend 612 and add 0 to the quotient
\begin{array}{l}\phantom{261)}00\phantom{5}\\261\overline{)612}\\\end{array}
Use the 3^{rd} digit 2 from dividend 612
\begin{array}{l}\phantom{261)}002\phantom{6}\\261\overline{)612}\\\phantom{261)}\underline{\phantom{}522\phantom{}}\\\phantom{261)9}90\\\end{array}
Find closest multiple of 261 to 612. We see that 2 \times 261 = 522 is the nearest. Now subtract 522 from 612 to get reminder 90. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }90
Since 90 is less than 261, stop the division. The reminder is 90. 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}