Evaluate
\frac{8}{5}=1.6
Factor
\frac{2 ^ {3}}{5} = 1\frac{3}{5} = 1.6
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\begin{array}{l}\phantom{320)}\phantom{1}\\320\overline{)512}\\\end{array}
Use the 1^{st} digit 5 from dividend 512
\begin{array}{l}\phantom{320)}0\phantom{2}\\320\overline{)512}\\\end{array}
Since 5 is less than 320, use the next digit 1 from dividend 512 and add 0 to the quotient
\begin{array}{l}\phantom{320)}0\phantom{3}\\320\overline{)512}\\\end{array}
Use the 2^{nd} digit 1 from dividend 512
\begin{array}{l}\phantom{320)}00\phantom{4}\\320\overline{)512}\\\end{array}
Since 51 is less than 320, use the next digit 2 from dividend 512 and add 0 to the quotient
\begin{array}{l}\phantom{320)}00\phantom{5}\\320\overline{)512}\\\end{array}
Use the 3^{rd} digit 2 from dividend 512
\begin{array}{l}\phantom{320)}001\phantom{6}\\320\overline{)512}\\\phantom{320)}\underline{\phantom{}320\phantom{}}\\\phantom{320)}192\\\end{array}
Find closest multiple of 320 to 512. We see that 1 \times 320 = 320 is the nearest. Now subtract 320 from 512 to get reminder 192. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }192
Since 192 is less than 320, stop the division. The reminder is 192. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}