Evaluate
\frac{80}{9}\approx 8.888888889
Factor
\frac{2 ^ {4} \cdot 5}{3 ^ {2}} = 8\frac{8}{9} = 8.88888888888889
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\begin{array}{l}\phantom{27)}\phantom{1}\\27\overline{)240}\\\end{array}
Use the 1^{st} digit 2 from dividend 240
\begin{array}{l}\phantom{27)}0\phantom{2}\\27\overline{)240}\\\end{array}
Since 2 is less than 27, use the next digit 4 from dividend 240 and add 0 to the quotient
\begin{array}{l}\phantom{27)}0\phantom{3}\\27\overline{)240}\\\end{array}
Use the 2^{nd} digit 4 from dividend 240
\begin{array}{l}\phantom{27)}00\phantom{4}\\27\overline{)240}\\\end{array}
Since 24 is less than 27, use the next digit 0 from dividend 240 and add 0 to the quotient
\begin{array}{l}\phantom{27)}00\phantom{5}\\27\overline{)240}\\\end{array}
Use the 3^{rd} digit 0 from dividend 240
\begin{array}{l}\phantom{27)}008\phantom{6}\\27\overline{)240}\\\phantom{27)}\underline{\phantom{}216\phantom{}}\\\phantom{27)9}24\\\end{array}
Find closest multiple of 27 to 240. We see that 8 \times 27 = 216 is the nearest. Now subtract 216 from 240 to get reminder 24. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }24
Since 24 is less than 27, stop the division. The reminder is 24. The topmost line 008 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8.
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}