Evaluate
\frac{243}{82}\approx 2.963414634
Factor
\frac{3 ^ {5}}{2 \cdot 41} = 2\frac{79}{82} = 2.9634146341463414
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\begin{array}{l}\phantom{164)}\phantom{1}\\164\overline{)486}\\\end{array}
Use the 1^{st} digit 4 from dividend 486
\begin{array}{l}\phantom{164)}0\phantom{2}\\164\overline{)486}\\\end{array}
Since 4 is less than 164, use the next digit 8 from dividend 486 and add 0 to the quotient
\begin{array}{l}\phantom{164)}0\phantom{3}\\164\overline{)486}\\\end{array}
Use the 2^{nd} digit 8 from dividend 486
\begin{array}{l}\phantom{164)}00\phantom{4}\\164\overline{)486}\\\end{array}
Since 48 is less than 164, use the next digit 6 from dividend 486 and add 0 to the quotient
\begin{array}{l}\phantom{164)}00\phantom{5}\\164\overline{)486}\\\end{array}
Use the 3^{rd} digit 6 from dividend 486
\begin{array}{l}\phantom{164)}002\phantom{6}\\164\overline{)486}\\\phantom{164)}\underline{\phantom{}328\phantom{}}\\\phantom{164)}158\\\end{array}
Find closest multiple of 164 to 486. We see that 2 \times 164 = 328 is the nearest. Now subtract 328 from 486 to get reminder 158. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }158
Since 158 is less than 164, stop the division. The reminder is 158. 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}