Evaluate
\frac{45}{4}=11.25
Factor
\frac{3 ^ {2} \cdot 5}{2 ^ {2}} = 11\frac{1}{4} = 11.25
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\begin{array}{l}\phantom{16)}\phantom{1}\\16\overline{)180}\\\end{array}
Use the 1^{st} digit 1 from dividend 180
\begin{array}{l}\phantom{16)}0\phantom{2}\\16\overline{)180}\\\end{array}
Since 1 is less than 16, use the next digit 8 from dividend 180 and add 0 to the quotient
\begin{array}{l}\phantom{16)}0\phantom{3}\\16\overline{)180}\\\end{array}
Use the 2^{nd} digit 8 from dividend 180
\begin{array}{l}\phantom{16)}01\phantom{4}\\16\overline{)180}\\\phantom{16)}\underline{\phantom{}16\phantom{9}}\\\phantom{16)9}2\\\end{array}
Find closest multiple of 16 to 18. We see that 1 \times 16 = 16 is the nearest. Now subtract 16 from 18 to get reminder 2. Add 1 to quotient.
\begin{array}{l}\phantom{16)}01\phantom{5}\\16\overline{)180}\\\phantom{16)}\underline{\phantom{}16\phantom{9}}\\\phantom{16)9}20\\\end{array}
Use the 3^{rd} digit 0 from dividend 180
\begin{array}{l}\phantom{16)}011\phantom{6}\\16\overline{)180}\\\phantom{16)}\underline{\phantom{}16\phantom{9}}\\\phantom{16)9}20\\\phantom{16)}\underline{\phantom{9}16\phantom{}}\\\phantom{16)99}4\\\end{array}
Find closest multiple of 16 to 20. We see that 1 \times 16 = 16 is the nearest. Now subtract 16 from 20 to get reminder 4. Add 1 to quotient.
\text{Quotient: }11 \text{Reminder: }4
Since 4 is less than 16, stop the division. The reminder is 4. The topmost line 011 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 11.
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}