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{24)}\phantom{1}\\24\overline{)162}\\\end{array}
Use the 1^{st} digit 1 from dividend 162
\begin{array}{l}\phantom{24)}0\phantom{2}\\24\overline{)162}\\\end{array}
Since 1 is less than 24, use the next digit 6 from dividend 162 and add 0 to the quotient
\begin{array}{l}\phantom{24)}0\phantom{3}\\24\overline{)162}\\\end{array}
Use the 2^{nd} digit 6 from dividend 162
\begin{array}{l}\phantom{24)}00\phantom{4}\\24\overline{)162}\\\end{array}
Since 16 is less than 24, use the next digit 2 from dividend 162 and add 0 to the quotient
\begin{array}{l}\phantom{24)}00\phantom{5}\\24\overline{)162}\\\end{array}
Use the 3^{rd} digit 2 from dividend 162
\begin{array}{l}\phantom{24)}006\phantom{6}\\24\overline{)162}\\\phantom{24)}\underline{\phantom{}144\phantom{}}\\\phantom{24)9}18\\\end{array}
Find closest multiple of 24 to 162. We see that 6 \times 24 = 144 is the nearest. Now subtract 144 from 162 to get reminder 18. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }18
Since 18 is less than 24, stop the division. The reminder is 18. 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}