Evaluate
\frac{485}{333}\approx 1.456456456
Factor
\frac{5 \cdot 97}{3 ^ {2} \cdot 37} = 1\frac{152}{333} = 1.4564564564564564
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\begin{array}{l}\phantom{333)}\phantom{1}\\333\overline{)485}\\\end{array}
Use the 1^{st} digit 4 from dividend 485
\begin{array}{l}\phantom{333)}0\phantom{2}\\333\overline{)485}\\\end{array}
Since 4 is less than 333, use the next digit 8 from dividend 485 and add 0 to the quotient
\begin{array}{l}\phantom{333)}0\phantom{3}\\333\overline{)485}\\\end{array}
Use the 2^{nd} digit 8 from dividend 485
\begin{array}{l}\phantom{333)}00\phantom{4}\\333\overline{)485}\\\end{array}
Since 48 is less than 333, use the next digit 5 from dividend 485 and add 0 to the quotient
\begin{array}{l}\phantom{333)}00\phantom{5}\\333\overline{)485}\\\end{array}
Use the 3^{rd} digit 5 from dividend 485
\begin{array}{l}\phantom{333)}001\phantom{6}\\333\overline{)485}\\\phantom{333)}\underline{\phantom{}333\phantom{}}\\\phantom{333)}152\\\end{array}
Find closest multiple of 333 to 485. We see that 1 \times 333 = 333 is the nearest. Now subtract 333 from 485 to get reminder 152. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }152
Since 152 is less than 333, stop the division. The reminder is 152. 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}