Evaluate
\frac{16}{9}\approx 1.777777778
Factor
\frac{2 ^ {4}}{3 ^ {2}} = 1\frac{7}{9} = 1.7777777777777777
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\begin{array}{l}\phantom{54)}\phantom{1}\\54\overline{)96}\\\end{array}
Use the 1^{st} digit 9 from dividend 96
\begin{array}{l}\phantom{54)}0\phantom{2}\\54\overline{)96}\\\end{array}
Since 9 is less than 54, use the next digit 6 from dividend 96 and add 0 to the quotient
\begin{array}{l}\phantom{54)}0\phantom{3}\\54\overline{)96}\\\end{array}
Use the 2^{nd} digit 6 from dividend 96
\begin{array}{l}\phantom{54)}01\phantom{4}\\54\overline{)96}\\\phantom{54)}\underline{\phantom{}54\phantom{}}\\\phantom{54)}42\\\end{array}
Find closest multiple of 54 to 96. We see that 1 \times 54 = 54 is the nearest. Now subtract 54 from 96 to get reminder 42. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }42
Since 42 is less than 54, stop the division. The reminder is 42. 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}