Evaluate
\frac{85}{32}=2.65625
Factor
\frac{5 \cdot 17}{2 ^ {5}} = 2\frac{21}{32} = 2.65625
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\begin{array}{l}\phantom{192)}\phantom{1}\\192\overline{)510}\\\end{array}
Use the 1^{st} digit 5 from dividend 510
\begin{array}{l}\phantom{192)}0\phantom{2}\\192\overline{)510}\\\end{array}
Since 5 is less than 192, use the next digit 1 from dividend 510 and add 0 to the quotient
\begin{array}{l}\phantom{192)}0\phantom{3}\\192\overline{)510}\\\end{array}
Use the 2^{nd} digit 1 from dividend 510
\begin{array}{l}\phantom{192)}00\phantom{4}\\192\overline{)510}\\\end{array}
Since 51 is less than 192, use the next digit 0 from dividend 510 and add 0 to the quotient
\begin{array}{l}\phantom{192)}00\phantom{5}\\192\overline{)510}\\\end{array}
Use the 3^{rd} digit 0 from dividend 510
\begin{array}{l}\phantom{192)}002\phantom{6}\\192\overline{)510}\\\phantom{192)}\underline{\phantom{}384\phantom{}}\\\phantom{192)}126\\\end{array}
Find closest multiple of 192 to 510. We see that 2 \times 192 = 384 is the nearest. Now subtract 384 from 510 to get reminder 126. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }126
Since 126 is less than 192, stop the division. The reminder is 126. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}