Evaluate
\frac{3}{2}=1.5
Factor
\frac{3}{2} = 1\frac{1}{2} = 1.5
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\begin{array}{l}\phantom{60)}\phantom{1}\\60\overline{)90}\\\end{array}
Use the 1^{st} digit 9 from dividend 90
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)90}\\\end{array}
Since 9 is less than 60, use the next digit 0 from dividend 90 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)90}\\\end{array}
Use the 2^{nd} digit 0 from dividend 90
\begin{array}{l}\phantom{60)}01\phantom{4}\\60\overline{)90}\\\phantom{60)}\underline{\phantom{}60\phantom{}}\\\phantom{60)}30\\\end{array}
Find closest multiple of 60 to 90. We see that 1 \times 60 = 60 is the nearest. Now subtract 60 from 90 to get reminder 30. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }30
Since 30 is less than 60, stop the division. The reminder is 30. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}