Evaluate
\frac{9}{8}=1.125
Factor
\frac{3 ^ {2}}{2 ^ {3}} = 1\frac{1}{8} = 1.125
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\begin{array}{l}\phantom{72)}\phantom{1}\\72\overline{)81}\\\end{array}
Use the 1^{st} digit 8 from dividend 81
\begin{array}{l}\phantom{72)}0\phantom{2}\\72\overline{)81}\\\end{array}
Since 8 is less than 72, use the next digit 1 from dividend 81 and add 0 to the quotient
\begin{array}{l}\phantom{72)}0\phantom{3}\\72\overline{)81}\\\end{array}
Use the 2^{nd} digit 1 from dividend 81
\begin{array}{l}\phantom{72)}01\phantom{4}\\72\overline{)81}\\\phantom{72)}\underline{\phantom{}72\phantom{}}\\\phantom{72)9}9\\\end{array}
Find closest multiple of 72 to 81. We see that 1 \times 72 = 72 is the nearest. Now subtract 72 from 81 to get reminder 9. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }9
Since 9 is less than 72, stop the division. The reminder is 9. 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}