Evaluate
\frac{17}{3}\approx 5.666666667
Factor
\frac{17}{3} = 5\frac{2}{3} = 5.666666666666667
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\begin{array}{l}\phantom{18)}\phantom{1}\\18\overline{)102}\\\end{array}
Use the 1^{st} digit 1 from dividend 102
\begin{array}{l}\phantom{18)}0\phantom{2}\\18\overline{)102}\\\end{array}
Since 1 is less than 18, use the next digit 0 from dividend 102 and add 0 to the quotient
\begin{array}{l}\phantom{18)}0\phantom{3}\\18\overline{)102}\\\end{array}
Use the 2^{nd} digit 0 from dividend 102
\begin{array}{l}\phantom{18)}00\phantom{4}\\18\overline{)102}\\\end{array}
Since 10 is less than 18, use the next digit 2 from dividend 102 and add 0 to the quotient
\begin{array}{l}\phantom{18)}00\phantom{5}\\18\overline{)102}\\\end{array}
Use the 3^{rd} digit 2 from dividend 102
\begin{array}{l}\phantom{18)}005\phantom{6}\\18\overline{)102}\\\phantom{18)}\underline{\phantom{9}90\phantom{}}\\\phantom{18)9}12\\\end{array}
Find closest multiple of 18 to 102. We see that 5 \times 18 = 90 is the nearest. Now subtract 90 from 102 to get reminder 12. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }12
Since 12 is less than 18, stop the division. The reminder is 12. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}