Evaluate
\frac{45}{8}=5.625
Factor
\frac{3 ^ {2} \cdot 5}{2 ^ {3}} = 5\frac{5}{8} = 5.625
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\begin{array}{l}\phantom{32)}\phantom{1}\\32\overline{)180}\\\end{array}
Use the 1^{st} digit 1 from dividend 180
\begin{array}{l}\phantom{32)}0\phantom{2}\\32\overline{)180}\\\end{array}
Since 1 is less than 32, use the next digit 8 from dividend 180 and add 0 to the quotient
\begin{array}{l}\phantom{32)}0\phantom{3}\\32\overline{)180}\\\end{array}
Use the 2^{nd} digit 8 from dividend 180
\begin{array}{l}\phantom{32)}00\phantom{4}\\32\overline{)180}\\\end{array}
Since 18 is less than 32, use the next digit 0 from dividend 180 and add 0 to the quotient
\begin{array}{l}\phantom{32)}00\phantom{5}\\32\overline{)180}\\\end{array}
Use the 3^{rd} digit 0 from dividend 180
\begin{array}{l}\phantom{32)}005\phantom{6}\\32\overline{)180}\\\phantom{32)}\underline{\phantom{}160\phantom{}}\\\phantom{32)9}20\\\end{array}
Find closest multiple of 32 to 180. We see that 5 \times 32 = 160 is the nearest. Now subtract 160 from 180 to get reminder 20. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }20
Since 20 is less than 32, stop the division. The reminder is 20. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}