Evaluate
\frac{125}{18}\approx 6.944444444
Factor
\frac{5 ^ {3}}{2 \cdot 3 ^ {2}} = 6\frac{17}{18} = 6.944444444444445
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\begin{array}{l}\phantom{18)}\phantom{1}\\18\overline{)125}\\\end{array}
Use the 1^{st} digit 1 from dividend 125
\begin{array}{l}\phantom{18)}0\phantom{2}\\18\overline{)125}\\\end{array}
Since 1 is less than 18, use the next digit 2 from dividend 125 and add 0 to the quotient
\begin{array}{l}\phantom{18)}0\phantom{3}\\18\overline{)125}\\\end{array}
Use the 2^{nd} digit 2 from dividend 125
\begin{array}{l}\phantom{18)}00\phantom{4}\\18\overline{)125}\\\end{array}
Since 12 is less than 18, use the next digit 5 from dividend 125 and add 0 to the quotient
\begin{array}{l}\phantom{18)}00\phantom{5}\\18\overline{)125}\\\end{array}
Use the 3^{rd} digit 5 from dividend 125
\begin{array}{l}\phantom{18)}006\phantom{6}\\18\overline{)125}\\\phantom{18)}\underline{\phantom{}108\phantom{}}\\\phantom{18)9}17\\\end{array}
Find closest multiple of 18 to 125. We see that 6 \times 18 = 108 is the nearest. Now subtract 108 from 125 to get reminder 17. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }17
Since 17 is less than 18, stop the division. The reminder is 17. 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}