Evaluate
\frac{140}{9}\approx 15.555555556
Factor
\frac{2 ^ {2} \cdot 5 \cdot 7}{3 ^ {2}} = 15\frac{5}{9} = 15.555555555555555
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\begin{array}{l}\phantom{27)}\phantom{1}\\27\overline{)420}\\\end{array}
Use the 1^{st} digit 4 from dividend 420
\begin{array}{l}\phantom{27)}0\phantom{2}\\27\overline{)420}\\\end{array}
Since 4 is less than 27, use the next digit 2 from dividend 420 and add 0 to the quotient
\begin{array}{l}\phantom{27)}0\phantom{3}\\27\overline{)420}\\\end{array}
Use the 2^{nd} digit 2 from dividend 420
\begin{array}{l}\phantom{27)}01\phantom{4}\\27\overline{)420}\\\phantom{27)}\underline{\phantom{}27\phantom{9}}\\\phantom{27)}15\\\end{array}
Find closest multiple of 27 to 42. We see that 1 \times 27 = 27 is the nearest. Now subtract 27 from 42 to get reminder 15. Add 1 to quotient.
\begin{array}{l}\phantom{27)}01\phantom{5}\\27\overline{)420}\\\phantom{27)}\underline{\phantom{}27\phantom{9}}\\\phantom{27)}150\\\end{array}
Use the 3^{rd} digit 0 from dividend 420
\begin{array}{l}\phantom{27)}015\phantom{6}\\27\overline{)420}\\\phantom{27)}\underline{\phantom{}27\phantom{9}}\\\phantom{27)}150\\\phantom{27)}\underline{\phantom{}135\phantom{}}\\\phantom{27)9}15\\\end{array}
Find closest multiple of 27 to 150. We see that 5 \times 27 = 135 is the nearest. Now subtract 135 from 150 to get reminder 15. Add 5 to quotient.
\text{Quotient: }15 \text{Reminder: }15
Since 15 is less than 27, stop the division. The reminder is 15. The topmost line 015 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 15.
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}