Evaluate
\frac{20}{9}\approx 2.222222222
Factor
\frac{2 ^ {2} \cdot 5}{3 ^ {2}} = 2\frac{2}{9} = 2.2222222222222223
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\begin{array}{l}\phantom{270)}\phantom{1}\\270\overline{)600}\\\end{array}
Use the 1^{st} digit 6 from dividend 600
\begin{array}{l}\phantom{270)}0\phantom{2}\\270\overline{)600}\\\end{array}
Since 6 is less than 270, use the next digit 0 from dividend 600 and add 0 to the quotient
\begin{array}{l}\phantom{270)}0\phantom{3}\\270\overline{)600}\\\end{array}
Use the 2^{nd} digit 0 from dividend 600
\begin{array}{l}\phantom{270)}00\phantom{4}\\270\overline{)600}\\\end{array}
Since 60 is less than 270, use the next digit 0 from dividend 600 and add 0 to the quotient
\begin{array}{l}\phantom{270)}00\phantom{5}\\270\overline{)600}\\\end{array}
Use the 3^{rd} digit 0 from dividend 600
\begin{array}{l}\phantom{270)}002\phantom{6}\\270\overline{)600}\\\phantom{270)}\underline{\phantom{}540\phantom{}}\\\phantom{270)9}60\\\end{array}
Find closest multiple of 270 to 600. We see that 2 \times 270 = 540 is the nearest. Now subtract 540 from 600 to get reminder 60. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }60
Since 60 is less than 270, stop the division. The reminder is 60. The topmost line 002 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}