Evaluate
\frac{33}{32}=1.03125
Factor
\frac{3 \cdot 11}{2 ^ {5}} = 1\frac{1}{32} = 1.03125
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\begin{array}{l}\phantom{64)}\phantom{1}\\64\overline{)66}\\\end{array}
Use the 1^{st} digit 6 from dividend 66
\begin{array}{l}\phantom{64)}0\phantom{2}\\64\overline{)66}\\\end{array}
Since 6 is less than 64, use the next digit 6 from dividend 66 and add 0 to the quotient
\begin{array}{l}\phantom{64)}0\phantom{3}\\64\overline{)66}\\\end{array}
Use the 2^{nd} digit 6 from dividend 66
\begin{array}{l}\phantom{64)}01\phantom{4}\\64\overline{)66}\\\phantom{64)}\underline{\phantom{}64\phantom{}}\\\phantom{64)9}2\\\end{array}
Find closest multiple of 64 to 66. We see that 1 \times 64 = 64 is the nearest. Now subtract 64 from 66 to get reminder 2. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }2
Since 2 is less than 64, stop the division. The reminder is 2. 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}