Evaluate
\frac{65}{18}\approx 3.611111111
Factor
\frac{5 \cdot 13}{2 \cdot 3 ^ {2}} = 3\frac{11}{18} = 3.611111111111111
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\begin{array}{l}\phantom{180)}\phantom{1}\\180\overline{)650}\\\end{array}
Use the 1^{st} digit 6 from dividend 650
\begin{array}{l}\phantom{180)}0\phantom{2}\\180\overline{)650}\\\end{array}
Since 6 is less than 180, use the next digit 5 from dividend 650 and add 0 to the quotient
\begin{array}{l}\phantom{180)}0\phantom{3}\\180\overline{)650}\\\end{array}
Use the 2^{nd} digit 5 from dividend 650
\begin{array}{l}\phantom{180)}00\phantom{4}\\180\overline{)650}\\\end{array}
Since 65 is less than 180, use the next digit 0 from dividend 650 and add 0 to the quotient
\begin{array}{l}\phantom{180)}00\phantom{5}\\180\overline{)650}\\\end{array}
Use the 3^{rd} digit 0 from dividend 650
\begin{array}{l}\phantom{180)}003\phantom{6}\\180\overline{)650}\\\phantom{180)}\underline{\phantom{}540\phantom{}}\\\phantom{180)}110\\\end{array}
Find closest multiple of 180 to 650. We see that 3 \times 180 = 540 is the nearest. Now subtract 540 from 650 to get reminder 110. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }110
Since 110 is less than 180, stop the division. The reminder is 110. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}