Evaluate
\frac{290}{61}\approx 4.754098361
Factor
\frac{2 \cdot 5 \cdot 29}{61} = 4\frac{46}{61} = 4.754098360655738
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\begin{array}{l}\phantom{61)}\phantom{1}\\61\overline{)290}\\\end{array}
Use the 1^{st} digit 2 from dividend 290
\begin{array}{l}\phantom{61)}0\phantom{2}\\61\overline{)290}\\\end{array}
Since 2 is less than 61, use the next digit 9 from dividend 290 and add 0 to the quotient
\begin{array}{l}\phantom{61)}0\phantom{3}\\61\overline{)290}\\\end{array}
Use the 2^{nd} digit 9 from dividend 290
\begin{array}{l}\phantom{61)}00\phantom{4}\\61\overline{)290}\\\end{array}
Since 29 is less than 61, use the next digit 0 from dividend 290 and add 0 to the quotient
\begin{array}{l}\phantom{61)}00\phantom{5}\\61\overline{)290}\\\end{array}
Use the 3^{rd} digit 0 from dividend 290
\begin{array}{l}\phantom{61)}004\phantom{6}\\61\overline{)290}\\\phantom{61)}\underline{\phantom{}244\phantom{}}\\\phantom{61)9}46\\\end{array}
Find closest multiple of 61 to 290. We see that 4 \times 61 = 244 is the nearest. Now subtract 244 from 290 to get reminder 46. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }46
Since 46 is less than 61, stop the division. The reminder is 46. The topmost line 004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}