Evaluate
\frac{321}{40}=8.025
Factor
\frac{3 \cdot 107}{2 ^ {3} \cdot 5} = 8\frac{1}{40} = 8.025
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\begin{array}{l}\phantom{80)}\phantom{1}\\80\overline{)642}\\\end{array}
Use the 1^{st} digit 6 from dividend 642
\begin{array}{l}\phantom{80)}0\phantom{2}\\80\overline{)642}\\\end{array}
Since 6 is less than 80, use the next digit 4 from dividend 642 and add 0 to the quotient
\begin{array}{l}\phantom{80)}0\phantom{3}\\80\overline{)642}\\\end{array}
Use the 2^{nd} digit 4 from dividend 642
\begin{array}{l}\phantom{80)}00\phantom{4}\\80\overline{)642}\\\end{array}
Since 64 is less than 80, use the next digit 2 from dividend 642 and add 0 to the quotient
\begin{array}{l}\phantom{80)}00\phantom{5}\\80\overline{)642}\\\end{array}
Use the 3^{rd} digit 2 from dividend 642
\begin{array}{l}\phantom{80)}008\phantom{6}\\80\overline{)642}\\\phantom{80)}\underline{\phantom{}640\phantom{}}\\\phantom{80)99}2\\\end{array}
Find closest multiple of 80 to 642. We see that 8 \times 80 = 640 is the nearest. Now subtract 640 from 642 to get reminder 2. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }2
Since 2 is less than 80, stop the division. The reminder is 2. 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}