Evaluate
\frac{81}{5}=16.2
Factor
\frac{3 ^ {4}}{5} = 16\frac{1}{5} = 16.2
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\begin{array}{l}\phantom{20)}\phantom{1}\\20\overline{)324}\\\end{array}
Use the 1^{st} digit 3 from dividend 324
\begin{array}{l}\phantom{20)}0\phantom{2}\\20\overline{)324}\\\end{array}
Since 3 is less than 20, use the next digit 2 from dividend 324 and add 0 to the quotient
\begin{array}{l}\phantom{20)}0\phantom{3}\\20\overline{)324}\\\end{array}
Use the 2^{nd} digit 2 from dividend 324
\begin{array}{l}\phantom{20)}01\phantom{4}\\20\overline{)324}\\\phantom{20)}\underline{\phantom{}20\phantom{9}}\\\phantom{20)}12\\\end{array}
Find closest multiple of 20 to 32. We see that 1 \times 20 = 20 is the nearest. Now subtract 20 from 32 to get reminder 12. Add 1 to quotient.
\begin{array}{l}\phantom{20)}01\phantom{5}\\20\overline{)324}\\\phantom{20)}\underline{\phantom{}20\phantom{9}}\\\phantom{20)}124\\\end{array}
Use the 3^{rd} digit 4 from dividend 324
\begin{array}{l}\phantom{20)}016\phantom{6}\\20\overline{)324}\\\phantom{20)}\underline{\phantom{}20\phantom{9}}\\\phantom{20)}124\\\phantom{20)}\underline{\phantom{}120\phantom{}}\\\phantom{20)99}4\\\end{array}
Find closest multiple of 20 to 124. We see that 6 \times 20 = 120 is the nearest. Now subtract 120 from 124 to get reminder 4. Add 6 to quotient.
\text{Quotient: }16 \text{Reminder: }4
Since 4 is less than 20, stop the division. The reminder is 4. The topmost line 016 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 16.
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}