Evaluate
\frac{7}{2}=3.5
Factor
\frac{7}{2} = 3\frac{1}{2} = 3.5
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\begin{array}{l}\phantom{12)}\phantom{1}\\12\overline{)42}\\\end{array}
Use the 1^{st} digit 4 from dividend 42
\begin{array}{l}\phantom{12)}0\phantom{2}\\12\overline{)42}\\\end{array}
Since 4 is less than 12, use the next digit 2 from dividend 42 and add 0 to the quotient
\begin{array}{l}\phantom{12)}0\phantom{3}\\12\overline{)42}\\\end{array}
Use the 2^{nd} digit 2 from dividend 42
\begin{array}{l}\phantom{12)}03\phantom{4}\\12\overline{)42}\\\phantom{12)}\underline{\phantom{}36\phantom{}}\\\phantom{12)9}6\\\end{array}
Find closest multiple of 12 to 42. We see that 3 \times 12 = 36 is the nearest. Now subtract 36 from 42 to get reminder 6. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }6
Since 6 is less than 12, stop the division. The reminder is 6. 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}