Evaluate
\frac{65}{36}\approx 1.805555556
Factor
\frac{5 \cdot 13}{2 ^ {2} \cdot 3 ^ {2}} = 1\frac{29}{36} = 1.8055555555555556
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\begin{array}{l}\phantom{180)}\phantom{1}\\180\overline{)325}\\\end{array}
Use the 1^{st} digit 3 from dividend 325
\begin{array}{l}\phantom{180)}0\phantom{2}\\180\overline{)325}\\\end{array}
Since 3 is less than 180, use the next digit 2 from dividend 325 and add 0 to the quotient
\begin{array}{l}\phantom{180)}0\phantom{3}\\180\overline{)325}\\\end{array}
Use the 2^{nd} digit 2 from dividend 325
\begin{array}{l}\phantom{180)}00\phantom{4}\\180\overline{)325}\\\end{array}
Since 32 is less than 180, use the next digit 5 from dividend 325 and add 0 to the quotient
\begin{array}{l}\phantom{180)}00\phantom{5}\\180\overline{)325}\\\end{array}
Use the 3^{rd} digit 5 from dividend 325
\begin{array}{l}\phantom{180)}001\phantom{6}\\180\overline{)325}\\\phantom{180)}\underline{\phantom{}180\phantom{}}\\\phantom{180)}145\\\end{array}
Find closest multiple of 180 to 325. We see that 1 \times 180 = 180 is the nearest. Now subtract 180 from 325 to get reminder 145. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }145
Since 145 is less than 180, stop the division. The reminder is 145. The topmost line 001 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}