Evaluate
\frac{27}{10}=2.7
Factor
\frac{3 ^ {3}}{2 \cdot 5} = 2\frac{7}{10} = 2.7
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\begin{array}{l}\phantom{20)}\phantom{1}\\20\overline{)54}\\\end{array}
Use the 1^{st} digit 5 from dividend 54
\begin{array}{l}\phantom{20)}0\phantom{2}\\20\overline{)54}\\\end{array}
Since 5 is less than 20, use the next digit 4 from dividend 54 and add 0 to the quotient
\begin{array}{l}\phantom{20)}0\phantom{3}\\20\overline{)54}\\\end{array}
Use the 2^{nd} digit 4 from dividend 54
\begin{array}{l}\phantom{20)}02\phantom{4}\\20\overline{)54}\\\phantom{20)}\underline{\phantom{}40\phantom{}}\\\phantom{20)}14\\\end{array}
Find closest multiple of 20 to 54. We see that 2 \times 20 = 40 is the nearest. Now subtract 40 from 54 to get reminder 14. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }14
Since 14 is less than 20, stop the division. The reminder is 14. 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}