Evaluate
\frac{90}{7}\approx 12.857142857
Factor
\frac{2 \cdot 3 ^ {2} \cdot 5}{7} = 12\frac{6}{7} = 12.857142857142858
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\begin{array}{l}\phantom{63)}\phantom{1}\\63\overline{)810}\\\end{array}
Use the 1^{st} digit 8 from dividend 810
\begin{array}{l}\phantom{63)}0\phantom{2}\\63\overline{)810}\\\end{array}
Since 8 is less than 63, use the next digit 1 from dividend 810 and add 0 to the quotient
\begin{array}{l}\phantom{63)}0\phantom{3}\\63\overline{)810}\\\end{array}
Use the 2^{nd} digit 1 from dividend 810
\begin{array}{l}\phantom{63)}01\phantom{4}\\63\overline{)810}\\\phantom{63)}\underline{\phantom{}63\phantom{9}}\\\phantom{63)}18\\\end{array}
Find closest multiple of 63 to 81. We see that 1 \times 63 = 63 is the nearest. Now subtract 63 from 81 to get reminder 18. Add 1 to quotient.
\begin{array}{l}\phantom{63)}01\phantom{5}\\63\overline{)810}\\\phantom{63)}\underline{\phantom{}63\phantom{9}}\\\phantom{63)}180\\\end{array}
Use the 3^{rd} digit 0 from dividend 810
\begin{array}{l}\phantom{63)}012\phantom{6}\\63\overline{)810}\\\phantom{63)}\underline{\phantom{}63\phantom{9}}\\\phantom{63)}180\\\phantom{63)}\underline{\phantom{}126\phantom{}}\\\phantom{63)9}54\\\end{array}
Find closest multiple of 63 to 180. We see that 2 \times 63 = 126 is the nearest. Now subtract 126 from 180 to get reminder 54. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }54
Since 54 is less than 63, stop the division. The reminder is 54. The topmost line 012 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 12.
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}