Evaluate
\frac{65}{12}\approx 5.416666667
Factor
\frac{5 \cdot 13}{2 ^ {2} \cdot 3} = 5\frac{5}{12} = 5.416666666666667
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\begin{array}{l}\phantom{36)}\phantom{1}\\36\overline{)195}\\\end{array}
Use the 1^{st} digit 1 from dividend 195
\begin{array}{l}\phantom{36)}0\phantom{2}\\36\overline{)195}\\\end{array}
Since 1 is less than 36, use the next digit 9 from dividend 195 and add 0 to the quotient
\begin{array}{l}\phantom{36)}0\phantom{3}\\36\overline{)195}\\\end{array}
Use the 2^{nd} digit 9 from dividend 195
\begin{array}{l}\phantom{36)}00\phantom{4}\\36\overline{)195}\\\end{array}
Since 19 is less than 36, use the next digit 5 from dividend 195 and add 0 to the quotient
\begin{array}{l}\phantom{36)}00\phantom{5}\\36\overline{)195}\\\end{array}
Use the 3^{rd} digit 5 from dividend 195
\begin{array}{l}\phantom{36)}005\phantom{6}\\36\overline{)195}\\\phantom{36)}\underline{\phantom{}180\phantom{}}\\\phantom{36)9}15\\\end{array}
Find closest multiple of 36 to 195. We see that 5 \times 36 = 180 is the nearest. Now subtract 180 from 195 to get reminder 15. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }15
Since 15 is less than 36, stop the division. The reminder is 15. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}