Evaluate
\frac{3}{2}=1.5
Factor
\frac{3}{2} = 1\frac{1}{2} = 1.5
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\begin{array}{l}\phantom{22)}\phantom{1}\\22\overline{)33}\\\end{array}
Use the 1^{st} digit 3 from dividend 33
\begin{array}{l}\phantom{22)}0\phantom{2}\\22\overline{)33}\\\end{array}
Since 3 is less than 22, use the next digit 3 from dividend 33 and add 0 to the quotient
\begin{array}{l}\phantom{22)}0\phantom{3}\\22\overline{)33}\\\end{array}
Use the 2^{nd} digit 3 from dividend 33
\begin{array}{l}\phantom{22)}01\phantom{4}\\22\overline{)33}\\\phantom{22)}\underline{\phantom{}22\phantom{}}\\\phantom{22)}11\\\end{array}
Find closest multiple of 22 to 33. We see that 1 \times 22 = 22 is the nearest. Now subtract 22 from 33 to get reminder 11. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }11
Since 11 is less than 22, stop the division. The reminder is 11. 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}