Evaluate
\frac{32}{27}\approx 1.185185185
Factor
\frac{2 ^ {5}}{3 ^ {3}} = 1\frac{5}{27} = 1.1851851851851851
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\begin{array}{l}\phantom{162)}\phantom{1}\\162\overline{)192}\\\end{array}
Use the 1^{st} digit 1 from dividend 192
\begin{array}{l}\phantom{162)}0\phantom{2}\\162\overline{)192}\\\end{array}
Since 1 is less than 162, use the next digit 9 from dividend 192 and add 0 to the quotient
\begin{array}{l}\phantom{162)}0\phantom{3}\\162\overline{)192}\\\end{array}
Use the 2^{nd} digit 9 from dividend 192
\begin{array}{l}\phantom{162)}00\phantom{4}\\162\overline{)192}\\\end{array}
Since 19 is less than 162, use the next digit 2 from dividend 192 and add 0 to the quotient
\begin{array}{l}\phantom{162)}00\phantom{5}\\162\overline{)192}\\\end{array}
Use the 3^{rd} digit 2 from dividend 192
\begin{array}{l}\phantom{162)}001\phantom{6}\\162\overline{)192}\\\phantom{162)}\underline{\phantom{}162\phantom{}}\\\phantom{162)9}30\\\end{array}
Find closest multiple of 162 to 192. We see that 1 \times 162 = 162 is the nearest. Now subtract 162 from 192 to get reminder 30. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }30
Since 30 is less than 162, stop the division. The reminder is 30. 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}