Evaluate
\frac{85}{16}=5.3125
Factor
\frac{5 \cdot 17}{2 ^ {4}} = 5\frac{5}{16} = 5.3125
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\begin{array}{l}\phantom{16)}\phantom{1}\\16\overline{)85}\\\end{array}
Use the 1^{st} digit 8 from dividend 85
\begin{array}{l}\phantom{16)}0\phantom{2}\\16\overline{)85}\\\end{array}
Since 8 is less than 16, use the next digit 5 from dividend 85 and add 0 to the quotient
\begin{array}{l}\phantom{16)}0\phantom{3}\\16\overline{)85}\\\end{array}
Use the 2^{nd} digit 5 from dividend 85
\begin{array}{l}\phantom{16)}05\phantom{4}\\16\overline{)85}\\\phantom{16)}\underline{\phantom{}80\phantom{}}\\\phantom{16)9}5\\\end{array}
Find closest multiple of 16 to 85. We see that 5 \times 16 = 80 is the nearest. Now subtract 80 from 85 to get reminder 5. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }5
Since 5 is less than 16, stop the division. The reminder is 5. The topmost line 05 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}