Evaluate
\frac{37}{17}\approx 2.176470588
Factor
\frac{37}{17} = 2\frac{3}{17} = 2.176470588235294
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\begin{array}{l}\phantom{17)}\phantom{1}\\17\overline{)37}\\\end{array}
Use the 1^{st} digit 3 from dividend 37
\begin{array}{l}\phantom{17)}0\phantom{2}\\17\overline{)37}\\\end{array}
Since 3 is less than 17, use the next digit 7 from dividend 37 and add 0 to the quotient
\begin{array}{l}\phantom{17)}0\phantom{3}\\17\overline{)37}\\\end{array}
Use the 2^{nd} digit 7 from dividend 37
\begin{array}{l}\phantom{17)}02\phantom{4}\\17\overline{)37}\\\phantom{17)}\underline{\phantom{}34\phantom{}}\\\phantom{17)9}3\\\end{array}
Find closest multiple of 17 to 37. We see that 2 \times 17 = 34 is the nearest. Now subtract 34 from 37 to get reminder 3. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }3
Since 3 is less than 17, stop the division. The reminder is 3. The topmost line 02 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}