Evaluate
\frac{8}{3}\approx 2.666666667
Factor
\frac{2 ^ {3}}{3} = 2\frac{2}{3} = 2.6666666666666665
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\begin{array}{l}\phantom{30)}\phantom{1}\\30\overline{)80}\\\end{array}
Use the 1^{st} digit 8 from dividend 80
\begin{array}{l}\phantom{30)}0\phantom{2}\\30\overline{)80}\\\end{array}
Since 8 is less than 30, use the next digit 0 from dividend 80 and add 0 to the quotient
\begin{array}{l}\phantom{30)}0\phantom{3}\\30\overline{)80}\\\end{array}
Use the 2^{nd} digit 0 from dividend 80
\begin{array}{l}\phantom{30)}02\phantom{4}\\30\overline{)80}\\\phantom{30)}\underline{\phantom{}60\phantom{}}\\\phantom{30)}20\\\end{array}
Find closest multiple of 30 to 80. We see that 2 \times 30 = 60 is the nearest. Now subtract 60 from 80 to get reminder 20. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }20
Since 20 is less than 30, stop the division. The reminder is 20. 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}