Evaluate
\frac{110}{9}\approx 12.222222222
Factor
\frac{2 \cdot 5 \cdot 11}{3 ^ {2}} = 12\frac{2}{9} = 12.222222222222221
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\begin{array}{l}\phantom{45)}\phantom{1}\\45\overline{)550}\\\end{array}
Use the 1^{st} digit 5 from dividend 550
\begin{array}{l}\phantom{45)}0\phantom{2}\\45\overline{)550}\\\end{array}
Since 5 is less than 45, use the next digit 5 from dividend 550 and add 0 to the quotient
\begin{array}{l}\phantom{45)}0\phantom{3}\\45\overline{)550}\\\end{array}
Use the 2^{nd} digit 5 from dividend 550
\begin{array}{l}\phantom{45)}01\phantom{4}\\45\overline{)550}\\\phantom{45)}\underline{\phantom{}45\phantom{9}}\\\phantom{45)}10\\\end{array}
Find closest multiple of 45 to 55. We see that 1 \times 45 = 45 is the nearest. Now subtract 45 from 55 to get reminder 10. Add 1 to quotient.
\begin{array}{l}\phantom{45)}01\phantom{5}\\45\overline{)550}\\\phantom{45)}\underline{\phantom{}45\phantom{9}}\\\phantom{45)}100\\\end{array}
Use the 3^{rd} digit 0 from dividend 550
\begin{array}{l}\phantom{45)}012\phantom{6}\\45\overline{)550}\\\phantom{45)}\underline{\phantom{}45\phantom{9}}\\\phantom{45)}100\\\phantom{45)}\underline{\phantom{9}90\phantom{}}\\\phantom{45)9}10\\\end{array}
Find closest multiple of 45 to 100. We see that 2 \times 45 = 90 is the nearest. Now subtract 90 from 100 to get reminder 10. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }10
Since 10 is less than 45, stop the division. The reminder is 10. The topmost line 012 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 12.
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}