Evaluate
\frac{19}{5}=3.8
Factor
\frac{19}{5} = 3\frac{4}{5} = 3.8
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\begin{array}{l}\phantom{15)}\phantom{1}\\15\overline{)57}\\\end{array}
Use the 1^{st} digit 5 from dividend 57
\begin{array}{l}\phantom{15)}0\phantom{2}\\15\overline{)57}\\\end{array}
Since 5 is less than 15, use the next digit 7 from dividend 57 and add 0 to the quotient
\begin{array}{l}\phantom{15)}0\phantom{3}\\15\overline{)57}\\\end{array}
Use the 2^{nd} digit 7 from dividend 57
\begin{array}{l}\phantom{15)}03\phantom{4}\\15\overline{)57}\\\phantom{15)}\underline{\phantom{}45\phantom{}}\\\phantom{15)}12\\\end{array}
Find closest multiple of 15 to 57. We see that 3 \times 15 = 45 is the nearest. Now subtract 45 from 57 to get reminder 12. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }12
Since 12 is less than 15, stop the division. The reminder is 12. The topmost line 03 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}