Evaluate
\frac{45}{16}=2.8125
Factor
\frac{3 ^ {2} \cdot 5}{2 ^ {4}} = 2\frac{13}{16} = 2.8125
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\begin{array}{l}\phantom{64)}\phantom{1}\\64\overline{)180}\\\end{array}
Use the 1^{st} digit 1 from dividend 180
\begin{array}{l}\phantom{64)}0\phantom{2}\\64\overline{)180}\\\end{array}
Since 1 is less than 64, use the next digit 8 from dividend 180 and add 0 to the quotient
\begin{array}{l}\phantom{64)}0\phantom{3}\\64\overline{)180}\\\end{array}
Use the 2^{nd} digit 8 from dividend 180
\begin{array}{l}\phantom{64)}00\phantom{4}\\64\overline{)180}\\\end{array}
Since 18 is less than 64, use the next digit 0 from dividend 180 and add 0 to the quotient
\begin{array}{l}\phantom{64)}00\phantom{5}\\64\overline{)180}\\\end{array}
Use the 3^{rd} digit 0 from dividend 180
\begin{array}{l}\phantom{64)}002\phantom{6}\\64\overline{)180}\\\phantom{64)}\underline{\phantom{}128\phantom{}}\\\phantom{64)9}52\\\end{array}
Find closest multiple of 64 to 180. We see that 2 \times 64 = 128 is the nearest. Now subtract 128 from 180 to get reminder 52. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }52
Since 52 is less than 64, stop the division. The reminder is 52. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}