Evaluate
\frac{12}{5}=2.4
Factor
\frac{2 ^ {2} \cdot 3}{5} = 2\frac{2}{5} = 2.4
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\begin{array}{l}\phantom{45)}\phantom{1}\\45\overline{)108}\\\end{array}
Use the 1^{st} digit 1 from dividend 108
\begin{array}{l}\phantom{45)}0\phantom{2}\\45\overline{)108}\\\end{array}
Since 1 is less than 45, use the next digit 0 from dividend 108 and add 0 to the quotient
\begin{array}{l}\phantom{45)}0\phantom{3}\\45\overline{)108}\\\end{array}
Use the 2^{nd} digit 0 from dividend 108
\begin{array}{l}\phantom{45)}00\phantom{4}\\45\overline{)108}\\\end{array}
Since 10 is less than 45, use the next digit 8 from dividend 108 and add 0 to the quotient
\begin{array}{l}\phantom{45)}00\phantom{5}\\45\overline{)108}\\\end{array}
Use the 3^{rd} digit 8 from dividend 108
\begin{array}{l}\phantom{45)}002\phantom{6}\\45\overline{)108}\\\phantom{45)}\underline{\phantom{9}90\phantom{}}\\\phantom{45)9}18\\\end{array}
Find closest multiple of 45 to 108. We see that 2 \times 45 = 90 is the nearest. Now subtract 90 from 108 to get reminder 18. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }18
Since 18 is less than 45, stop the division. The reminder is 18. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}