Evaluate
\frac{27}{11}\approx 2.454545455
Factor
\frac{3 ^ {3}}{11} = 2\frac{5}{11} = 2.4545454545454546
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\begin{array}{l}\phantom{22)}\phantom{1}\\22\overline{)54}\\\end{array}
Use the 1^{st} digit 5 from dividend 54
\begin{array}{l}\phantom{22)}0\phantom{2}\\22\overline{)54}\\\end{array}
Since 5 is less than 22, use the next digit 4 from dividend 54 and add 0 to the quotient
\begin{array}{l}\phantom{22)}0\phantom{3}\\22\overline{)54}\\\end{array}
Use the 2^{nd} digit 4 from dividend 54
\begin{array}{l}\phantom{22)}02\phantom{4}\\22\overline{)54}\\\phantom{22)}\underline{\phantom{}44\phantom{}}\\\phantom{22)}10\\\end{array}
Find closest multiple of 22 to 54. We see that 2 \times 22 = 44 is the nearest. Now subtract 44 from 54 to get reminder 10. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }10
Since 10 is less than 22, stop the division. The reminder is 10. The topmost line 02 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}