Evaluate
\frac{845}{63}\approx 13.412698413
Factor
\frac{5 \cdot 13 ^ {2}}{3 ^ {2} \cdot 7} = 13\frac{26}{63} = 13.412698412698413
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\begin{array}{l}\phantom{63)}\phantom{1}\\63\overline{)845}\\\end{array}
Use the 1^{st} digit 8 from dividend 845
\begin{array}{l}\phantom{63)}0\phantom{2}\\63\overline{)845}\\\end{array}
Since 8 is less than 63, use the next digit 4 from dividend 845 and add 0 to the quotient
\begin{array}{l}\phantom{63)}0\phantom{3}\\63\overline{)845}\\\end{array}
Use the 2^{nd} digit 4 from dividend 845
\begin{array}{l}\phantom{63)}01\phantom{4}\\63\overline{)845}\\\phantom{63)}\underline{\phantom{}63\phantom{9}}\\\phantom{63)}21\\\end{array}
Find closest multiple of 63 to 84. We see that 1 \times 63 = 63 is the nearest. Now subtract 63 from 84 to get reminder 21. Add 1 to quotient.
\begin{array}{l}\phantom{63)}01\phantom{5}\\63\overline{)845}\\\phantom{63)}\underline{\phantom{}63\phantom{9}}\\\phantom{63)}215\\\end{array}
Use the 3^{rd} digit 5 from dividend 845
\begin{array}{l}\phantom{63)}013\phantom{6}\\63\overline{)845}\\\phantom{63)}\underline{\phantom{}63\phantom{9}}\\\phantom{63)}215\\\phantom{63)}\underline{\phantom{}189\phantom{}}\\\phantom{63)9}26\\\end{array}
Find closest multiple of 63 to 215. We see that 3 \times 63 = 189 is the nearest. Now subtract 189 from 215 to get reminder 26. Add 3 to quotient.
\text{Quotient: }13 \text{Reminder: }26
Since 26 is less than 63, stop the division. The reminder is 26. The topmost line 013 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 13.
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}