Evaluate
\frac{108}{13}\approx 8.307692308
Factor
\frac{2 ^ {2} \cdot 3 ^ {3}}{13} = 8\frac{4}{13} = 8.307692307692308
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\begin{array}{l}\phantom{78)}\phantom{1}\\78\overline{)648}\\\end{array}
Use the 1^{st} digit 6 from dividend 648
\begin{array}{l}\phantom{78)}0\phantom{2}\\78\overline{)648}\\\end{array}
Since 6 is less than 78, use the next digit 4 from dividend 648 and add 0 to the quotient
\begin{array}{l}\phantom{78)}0\phantom{3}\\78\overline{)648}\\\end{array}
Use the 2^{nd} digit 4 from dividend 648
\begin{array}{l}\phantom{78)}00\phantom{4}\\78\overline{)648}\\\end{array}
Since 64 is less than 78, use the next digit 8 from dividend 648 and add 0 to the quotient
\begin{array}{l}\phantom{78)}00\phantom{5}\\78\overline{)648}\\\end{array}
Use the 3^{rd} digit 8 from dividend 648
\begin{array}{l}\phantom{78)}008\phantom{6}\\78\overline{)648}\\\phantom{78)}\underline{\phantom{}624\phantom{}}\\\phantom{78)9}24\\\end{array}
Find closest multiple of 78 to 648. We see that 8 \times 78 = 624 is the nearest. Now subtract 624 from 648 to get reminder 24. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }24
Since 24 is less than 78, stop the division. The reminder is 24. The topmost line 008 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8.
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}