Evaluate
\frac{4}{3}\approx 1.333333333
Factor
\frac{2 ^ {2}}{3} = 1\frac{1}{3} = 1.3333333333333333
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\begin{array}{l}\phantom{81)}\phantom{1}\\81\overline{)108}\\\end{array}
Use the 1^{st} digit 1 from dividend 108
\begin{array}{l}\phantom{81)}0\phantom{2}\\81\overline{)108}\\\end{array}
Since 1 is less than 81, use the next digit 0 from dividend 108 and add 0 to the quotient
\begin{array}{l}\phantom{81)}0\phantom{3}\\81\overline{)108}\\\end{array}
Use the 2^{nd} digit 0 from dividend 108
\begin{array}{l}\phantom{81)}00\phantom{4}\\81\overline{)108}\\\end{array}
Since 10 is less than 81, use the next digit 8 from dividend 108 and add 0 to the quotient
\begin{array}{l}\phantom{81)}00\phantom{5}\\81\overline{)108}\\\end{array}
Use the 3^{rd} digit 8 from dividend 108
\begin{array}{l}\phantom{81)}001\phantom{6}\\81\overline{)108}\\\phantom{81)}\underline{\phantom{9}81\phantom{}}\\\phantom{81)9}27\\\end{array}
Find closest multiple of 81 to 108. We see that 1 \times 81 = 81 is the nearest. Now subtract 81 from 108 to get reminder 27. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }27
Since 27 is less than 81, stop the division. The reminder is 27. 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}