Evaluate
\frac{89}{82}\approx 1.085365854
Factor
\frac{89}{2 \cdot 41} = 1\frac{7}{82} = 1.0853658536585367
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\begin{array}{l}\phantom{82)}\phantom{1}\\82\overline{)89}\\\end{array}
Use the 1^{st} digit 8 from dividend 89
\begin{array}{l}\phantom{82)}0\phantom{2}\\82\overline{)89}\\\end{array}
Since 8 is less than 82, use the next digit 9 from dividend 89 and add 0 to the quotient
\begin{array}{l}\phantom{82)}0\phantom{3}\\82\overline{)89}\\\end{array}
Use the 2^{nd} digit 9 from dividend 89
\begin{array}{l}\phantom{82)}01\phantom{4}\\82\overline{)89}\\\phantom{82)}\underline{\phantom{}82\phantom{}}\\\phantom{82)9}7\\\end{array}
Find closest multiple of 82 to 89. We see that 1 \times 82 = 82 is the nearest. Now subtract 82 from 89 to get reminder 7. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }7
Since 7 is less than 82, stop the division. The reminder is 7. 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}