Evaluate
\frac{89}{65}\approx 1.369230769
Factor
\frac{89}{5 \cdot 13} = 1\frac{24}{65} = 1.3692307692307693
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\begin{array}{l}\phantom{65)}\phantom{1}\\65\overline{)89}\\\end{array}
Use the 1^{st} digit 8 from dividend 89
\begin{array}{l}\phantom{65)}0\phantom{2}\\65\overline{)89}\\\end{array}
Since 8 is less than 65, use the next digit 9 from dividend 89 and add 0 to the quotient
\begin{array}{l}\phantom{65)}0\phantom{3}\\65\overline{)89}\\\end{array}
Use the 2^{nd} digit 9 from dividend 89
\begin{array}{l}\phantom{65)}01\phantom{4}\\65\overline{)89}\\\phantom{65)}\underline{\phantom{}65\phantom{}}\\\phantom{65)}24\\\end{array}
Find closest multiple of 65 to 89. We see that 1 \times 65 = 65 is the nearest. Now subtract 65 from 89 to get reminder 24. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }24
Since 24 is less than 65, stop the division. The reminder is 24. 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}