Evaluate
\frac{111}{17}\approx 6.529411765
Factor
\frac{3 \cdot 37}{17} = 6\frac{9}{17} = 6.529411764705882
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\begin{array}{l}\phantom{17)}\phantom{1}\\17\overline{)111}\\\end{array}
Use the 1^{st} digit 1 from dividend 111
\begin{array}{l}\phantom{17)}0\phantom{2}\\17\overline{)111}\\\end{array}
Since 1 is less than 17, use the next digit 1 from dividend 111 and add 0 to the quotient
\begin{array}{l}\phantom{17)}0\phantom{3}\\17\overline{)111}\\\end{array}
Use the 2^{nd} digit 1 from dividend 111
\begin{array}{l}\phantom{17)}00\phantom{4}\\17\overline{)111}\\\end{array}
Since 11 is less than 17, use the next digit 1 from dividend 111 and add 0 to the quotient
\begin{array}{l}\phantom{17)}00\phantom{5}\\17\overline{)111}\\\end{array}
Use the 3^{rd} digit 1 from dividend 111
\begin{array}{l}\phantom{17)}006\phantom{6}\\17\overline{)111}\\\phantom{17)}\underline{\phantom{}102\phantom{}}\\\phantom{17)99}9\\\end{array}
Find closest multiple of 17 to 111. We see that 6 \times 17 = 102 is the nearest. Now subtract 102 from 111 to get reminder 9. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }9
Since 9 is less than 17, stop the division. The reminder is 9. The topmost line 006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}