Evaluate
\frac{529}{27}\approx 19.592592593
Factor
\frac{23 ^ {2}}{3 ^ {3}} = 19\frac{16}{27} = 19.59259259259259
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\begin{array}{l}\phantom{27)}\phantom{1}\\27\overline{)529}\\\end{array}
Use the 1^{st} digit 5 from dividend 529
\begin{array}{l}\phantom{27)}0\phantom{2}\\27\overline{)529}\\\end{array}
Since 5 is less than 27, use the next digit 2 from dividend 529 and add 0 to the quotient
\begin{array}{l}\phantom{27)}0\phantom{3}\\27\overline{)529}\\\end{array}
Use the 2^{nd} digit 2 from dividend 529
\begin{array}{l}\phantom{27)}01\phantom{4}\\27\overline{)529}\\\phantom{27)}\underline{\phantom{}27\phantom{9}}\\\phantom{27)}25\\\end{array}
Find closest multiple of 27 to 52. We see that 1 \times 27 = 27 is the nearest. Now subtract 27 from 52 to get reminder 25. Add 1 to quotient.
\begin{array}{l}\phantom{27)}01\phantom{5}\\27\overline{)529}\\\phantom{27)}\underline{\phantom{}27\phantom{9}}\\\phantom{27)}259\\\end{array}
Use the 3^{rd} digit 9 from dividend 529
\begin{array}{l}\phantom{27)}019\phantom{6}\\27\overline{)529}\\\phantom{27)}\underline{\phantom{}27\phantom{9}}\\\phantom{27)}259\\\phantom{27)}\underline{\phantom{}243\phantom{}}\\\phantom{27)9}16\\\end{array}
Find closest multiple of 27 to 259. We see that 9 \times 27 = 243 is the nearest. Now subtract 243 from 259 to get reminder 16. Add 9 to quotient.
\text{Quotient: }19 \text{Reminder: }16
Since 16 is less than 27, stop the division. The reminder is 16. The topmost line 019 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 19.
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}