Evaluate
\frac{221}{164}\approx 1.347560976
Factor
\frac{13 \cdot 17}{2 ^ {2} \cdot 41} = 1\frac{57}{164} = 1.3475609756097562
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\begin{array}{l}\phantom{492)}\phantom{1}\\492\overline{)663}\\\end{array}
Use the 1^{st} digit 6 from dividend 663
\begin{array}{l}\phantom{492)}0\phantom{2}\\492\overline{)663}\\\end{array}
Since 6 is less than 492, use the next digit 6 from dividend 663 and add 0 to the quotient
\begin{array}{l}\phantom{492)}0\phantom{3}\\492\overline{)663}\\\end{array}
Use the 2^{nd} digit 6 from dividend 663
\begin{array}{l}\phantom{492)}00\phantom{4}\\492\overline{)663}\\\end{array}
Since 66 is less than 492, use the next digit 3 from dividend 663 and add 0 to the quotient
\begin{array}{l}\phantom{492)}00\phantom{5}\\492\overline{)663}\\\end{array}
Use the 3^{rd} digit 3 from dividend 663
\begin{array}{l}\phantom{492)}001\phantom{6}\\492\overline{)663}\\\phantom{492)}\underline{\phantom{}492\phantom{}}\\\phantom{492)}171\\\end{array}
Find closest multiple of 492 to 663. We see that 1 \times 492 = 492 is the nearest. Now subtract 492 from 663 to get reminder 171. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }171
Since 171 is less than 492, stop the division. The reminder is 171. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}