Evaluate
\frac{3}{2}=1.5
Factor
\frac{3}{2} = 1\frac{1}{2} = 1.5
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\begin{array}{l}\phantom{180)}\phantom{1}\\180\overline{)270}\\\end{array}
Use the 1^{st} digit 2 from dividend 270
\begin{array}{l}\phantom{180)}0\phantom{2}\\180\overline{)270}\\\end{array}
Since 2 is less than 180, use the next digit 7 from dividend 270 and add 0 to the quotient
\begin{array}{l}\phantom{180)}0\phantom{3}\\180\overline{)270}\\\end{array}
Use the 2^{nd} digit 7 from dividend 270
\begin{array}{l}\phantom{180)}00\phantom{4}\\180\overline{)270}\\\end{array}
Since 27 is less than 180, use the next digit 0 from dividend 270 and add 0 to the quotient
\begin{array}{l}\phantom{180)}00\phantom{5}\\180\overline{)270}\\\end{array}
Use the 3^{rd} digit 0 from dividend 270
\begin{array}{l}\phantom{180)}001\phantom{6}\\180\overline{)270}\\\phantom{180)}\underline{\phantom{}180\phantom{}}\\\phantom{180)9}90\\\end{array}
Find closest multiple of 180 to 270. We see that 1 \times 180 = 180 is the nearest. Now subtract 180 from 270 to get reminder 90. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }90
Since 90 is less than 180, stop the division. The reminder is 90. The topmost line 001 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}