Evaluate
\frac{304}{9}\approx 33.777777778
Factor
\frac{2 ^ {4} \cdot 19}{3 ^ {2}} = 33\frac{7}{9} = 33.77777777777778
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\begin{array}{l}\phantom{27)}\phantom{1}\\27\overline{)912}\\\end{array}
Use the 1^{st} digit 9 from dividend 912
\begin{array}{l}\phantom{27)}0\phantom{2}\\27\overline{)912}\\\end{array}
Since 9 is less than 27, use the next digit 1 from dividend 912 and add 0 to the quotient
\begin{array}{l}\phantom{27)}0\phantom{3}\\27\overline{)912}\\\end{array}
Use the 2^{nd} digit 1 from dividend 912
\begin{array}{l}\phantom{27)}03\phantom{4}\\27\overline{)912}\\\phantom{27)}\underline{\phantom{}81\phantom{9}}\\\phantom{27)}10\\\end{array}
Find closest multiple of 27 to 91. We see that 3 \times 27 = 81 is the nearest. Now subtract 81 from 91 to get reminder 10. Add 3 to quotient.
\begin{array}{l}\phantom{27)}03\phantom{5}\\27\overline{)912}\\\phantom{27)}\underline{\phantom{}81\phantom{9}}\\\phantom{27)}102\\\end{array}
Use the 3^{rd} digit 2 from dividend 912
\begin{array}{l}\phantom{27)}033\phantom{6}\\27\overline{)912}\\\phantom{27)}\underline{\phantom{}81\phantom{9}}\\\phantom{27)}102\\\phantom{27)}\underline{\phantom{9}81\phantom{}}\\\phantom{27)9}21\\\end{array}
Find closest multiple of 27 to 102. We see that 3 \times 27 = 81 is the nearest. Now subtract 81 from 102 to get reminder 21. Add 3 to quotient.
\text{Quotient: }33 \text{Reminder: }21
Since 21 is less than 27, stop the division. The reminder is 21. The topmost line 033 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 33.
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}