Evaluate
\frac{530}{163}\approx 3.251533742
Factor
\frac{2 \cdot 5 \cdot 53}{163} = 3\frac{41}{163} = 3.2515337423312882
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\begin{array}{l}\phantom{163)}\phantom{1}\\163\overline{)530}\\\end{array}
Use the 1^{st} digit 5 from dividend 530
\begin{array}{l}\phantom{163)}0\phantom{2}\\163\overline{)530}\\\end{array}
Since 5 is less than 163, use the next digit 3 from dividend 530 and add 0 to the quotient
\begin{array}{l}\phantom{163)}0\phantom{3}\\163\overline{)530}\\\end{array}
Use the 2^{nd} digit 3 from dividend 530
\begin{array}{l}\phantom{163)}00\phantom{4}\\163\overline{)530}\\\end{array}
Since 53 is less than 163, use the next digit 0 from dividend 530 and add 0 to the quotient
\begin{array}{l}\phantom{163)}00\phantom{5}\\163\overline{)530}\\\end{array}
Use the 3^{rd} digit 0 from dividend 530
\begin{array}{l}\phantom{163)}003\phantom{6}\\163\overline{)530}\\\phantom{163)}\underline{\phantom{}489\phantom{}}\\\phantom{163)9}41\\\end{array}
Find closest multiple of 163 to 530. We see that 3 \times 163 = 489 is the nearest. Now subtract 489 from 530 to get reminder 41. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }41
Since 41 is less than 163, stop the division. The reminder is 41. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}