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{50)}\phantom{1}\\50\overline{)135}\\\end{array}
Use the 1^{st} digit 1 from dividend 135
\begin{array}{l}\phantom{50)}0\phantom{2}\\50\overline{)135}\\\end{array}
Since 1 is less than 50, use the next digit 3 from dividend 135 and add 0 to the quotient
\begin{array}{l}\phantom{50)}0\phantom{3}\\50\overline{)135}\\\end{array}
Use the 2^{nd} digit 3 from dividend 135
\begin{array}{l}\phantom{50)}00\phantom{4}\\50\overline{)135}\\\end{array}
Since 13 is less than 50, use the next digit 5 from dividend 135 and add 0 to the quotient
\begin{array}{l}\phantom{50)}00\phantom{5}\\50\overline{)135}\\\end{array}
Use the 3^{rd} digit 5 from dividend 135
\begin{array}{l}\phantom{50)}002\phantom{6}\\50\overline{)135}\\\phantom{50)}\underline{\phantom{}100\phantom{}}\\\phantom{50)9}35\\\end{array}
Find closest multiple of 50 to 135. We see that 2 \times 50 = 100 is the nearest. Now subtract 100 from 135 to get reminder 35. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }35
Since 35 is less than 50, stop the division. The reminder is 35. 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}