Evaluate
\frac{17}{6}\approx 2.833333333
Factor
\frac{17}{2 \cdot 3} = 2\frac{5}{6} = 2.8333333333333335
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\begin{array}{l}\phantom{12)}\phantom{1}\\12\overline{)34}\\\end{array}
Use the 1^{st} digit 3 from dividend 34
\begin{array}{l}\phantom{12)}0\phantom{2}\\12\overline{)34}\\\end{array}
Since 3 is less than 12, use the next digit 4 from dividend 34 and add 0 to the quotient
\begin{array}{l}\phantom{12)}0\phantom{3}\\12\overline{)34}\\\end{array}
Use the 2^{nd} digit 4 from dividend 34
\begin{array}{l}\phantom{12)}02\phantom{4}\\12\overline{)34}\\\phantom{12)}\underline{\phantom{}24\phantom{}}\\\phantom{12)}10\\\end{array}
Find closest multiple of 12 to 34. We see that 2 \times 12 = 24 is the nearest. Now subtract 24 from 34 to get reminder 10. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }10
Since 10 is less than 12, stop the division. The reminder is 10. 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}