Evaluate
\frac{30}{17}\approx 1.764705882
Factor
\frac{2 \cdot 3 \cdot 5}{17} = 1\frac{13}{17} = 1.7647058823529411
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\begin{array}{l}\phantom{17)}\phantom{1}\\17\overline{)30}\\\end{array}
Use the 1^{st} digit 3 from dividend 30
\begin{array}{l}\phantom{17)}0\phantom{2}\\17\overline{)30}\\\end{array}
Since 3 is less than 17, use the next digit 0 from dividend 30 and add 0 to the quotient
\begin{array}{l}\phantom{17)}0\phantom{3}\\17\overline{)30}\\\end{array}
Use the 2^{nd} digit 0 from dividend 30
\begin{array}{l}\phantom{17)}01\phantom{4}\\17\overline{)30}\\\phantom{17)}\underline{\phantom{}17\phantom{}}\\\phantom{17)}13\\\end{array}
Find closest multiple of 17 to 30. We see that 1 \times 17 = 17 is the nearest. Now subtract 17 from 30 to get reminder 13. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }13
Since 13 is less than 17, stop the division. The reminder is 13. The topmost line 01 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}