Evaluate
\frac{96}{85}\approx 1.129411765
Factor
\frac{2 ^ {5} \cdot 3}{5 \cdot 17} = 1\frac{11}{85} = 1.1294117647058823
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\begin{array}{l}\phantom{85)}\phantom{1}\\85\overline{)96}\\\end{array}
Use the 1^{st} digit 9 from dividend 96
\begin{array}{l}\phantom{85)}0\phantom{2}\\85\overline{)96}\\\end{array}
Since 9 is less than 85, use the next digit 6 from dividend 96 and add 0 to the quotient
\begin{array}{l}\phantom{85)}0\phantom{3}\\85\overline{)96}\\\end{array}
Use the 2^{nd} digit 6 from dividend 96
\begin{array}{l}\phantom{85)}01\phantom{4}\\85\overline{)96}\\\phantom{85)}\underline{\phantom{}85\phantom{}}\\\phantom{85)}11\\\end{array}
Find closest multiple of 85 to 96. We see that 1 \times 85 = 85 is the nearest. Now subtract 85 from 96 to get reminder 11. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }11
Since 11 is less than 85, stop the division. The reminder is 11. The topmost line 01 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}