Evaluate
\frac{530}{17}\approx 31.176470588
Factor
\frac{2 \cdot 5 \cdot 53}{17} = 31\frac{3}{17} = 31.176470588235293
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\begin{array}{l}\phantom{17)}\phantom{1}\\17\overline{)530}\\\end{array}
Use the 1^{st} digit 5 from dividend 530
\begin{array}{l}\phantom{17)}0\phantom{2}\\17\overline{)530}\\\end{array}
Since 5 is less than 17, use the next digit 3 from dividend 530 and add 0 to the quotient
\begin{array}{l}\phantom{17)}0\phantom{3}\\17\overline{)530}\\\end{array}
Use the 2^{nd} digit 3 from dividend 530
\begin{array}{l}\phantom{17)}03\phantom{4}\\17\overline{)530}\\\phantom{17)}\underline{\phantom{}51\phantom{9}}\\\phantom{17)9}2\\\end{array}
Find closest multiple of 17 to 53. We see that 3 \times 17 = 51 is the nearest. Now subtract 51 from 53 to get reminder 2. Add 3 to quotient.
\begin{array}{l}\phantom{17)}03\phantom{5}\\17\overline{)530}\\\phantom{17)}\underline{\phantom{}51\phantom{9}}\\\phantom{17)9}20\\\end{array}
Use the 3^{rd} digit 0 from dividend 530
\begin{array}{l}\phantom{17)}031\phantom{6}\\17\overline{)530}\\\phantom{17)}\underline{\phantom{}51\phantom{9}}\\\phantom{17)9}20\\\phantom{17)}\underline{\phantom{9}17\phantom{}}\\\phantom{17)99}3\\\end{array}
Find closest multiple of 17 to 20. We see that 1 \times 17 = 17 is the nearest. Now subtract 17 from 20 to get reminder 3. Add 1 to quotient.
\text{Quotient: }31 \text{Reminder: }3
Since 3 is less than 17, stop the division. The reminder is 3. The topmost line 031 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 31.
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}