Evaluate
\frac{5}{3}\approx 1.666666667
Factor
\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667
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\begin{array}{l}\phantom{108)}\phantom{1}\\108\overline{)180}\\\end{array}
Use the 1^{st} digit 1 from dividend 180
\begin{array}{l}\phantom{108)}0\phantom{2}\\108\overline{)180}\\\end{array}
Since 1 is less than 108, use the next digit 8 from dividend 180 and add 0 to the quotient
\begin{array}{l}\phantom{108)}0\phantom{3}\\108\overline{)180}\\\end{array}
Use the 2^{nd} digit 8 from dividend 180
\begin{array}{l}\phantom{108)}00\phantom{4}\\108\overline{)180}\\\end{array}
Since 18 is less than 108, use the next digit 0 from dividend 180 and add 0 to the quotient
\begin{array}{l}\phantom{108)}00\phantom{5}\\108\overline{)180}\\\end{array}
Use the 3^{rd} digit 0 from dividend 180
\begin{array}{l}\phantom{108)}001\phantom{6}\\108\overline{)180}\\\phantom{108)}\underline{\phantom{}108\phantom{}}\\\phantom{108)9}72\\\end{array}
Find closest multiple of 108 to 180. We see that 1 \times 108 = 108 is the nearest. Now subtract 108 from 180 to get reminder 72. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }72
Since 72 is less than 108, stop the division. The reminder is 72. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}