Evaluate
\frac{27}{4}=6.75
Factor
\frac{3 ^ {3}}{2 ^ {2}} = 6\frac{3}{4} = 6.75
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\begin{array}{l}\phantom{20)}\phantom{1}\\20\overline{)135}\\\end{array}
Use the 1^{st} digit 1 from dividend 135
\begin{array}{l}\phantom{20)}0\phantom{2}\\20\overline{)135}\\\end{array}
Since 1 is less than 20, use the next digit 3 from dividend 135 and add 0 to the quotient
\begin{array}{l}\phantom{20)}0\phantom{3}\\20\overline{)135}\\\end{array}
Use the 2^{nd} digit 3 from dividend 135
\begin{array}{l}\phantom{20)}00\phantom{4}\\20\overline{)135}\\\end{array}
Since 13 is less than 20, use the next digit 5 from dividend 135 and add 0 to the quotient
\begin{array}{l}\phantom{20)}00\phantom{5}\\20\overline{)135}\\\end{array}
Use the 3^{rd} digit 5 from dividend 135
\begin{array}{l}\phantom{20)}006\phantom{6}\\20\overline{)135}\\\phantom{20)}\underline{\phantom{}120\phantom{}}\\\phantom{20)9}15\\\end{array}
Find closest multiple of 20 to 135. We see that 6 \times 20 = 120 is the nearest. Now subtract 120 from 135 to get reminder 15. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }15
Since 15 is less than 20, stop the division. The reminder is 15. The topmost line 006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}