Evaluate
\frac{55}{36}\approx 1.527777778
Factor
\frac{5 \cdot 11}{2 ^ {2} \cdot 3 ^ {2}} = 1\frac{19}{36} = 1.5277777777777777
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\begin{array}{l}\phantom{36)}\phantom{1}\\36\overline{)55}\\\end{array}
Use the 1^{st} digit 5 from dividend 55
\begin{array}{l}\phantom{36)}0\phantom{2}\\36\overline{)55}\\\end{array}
Since 5 is less than 36, use the next digit 5 from dividend 55 and add 0 to the quotient
\begin{array}{l}\phantom{36)}0\phantom{3}\\36\overline{)55}\\\end{array}
Use the 2^{nd} digit 5 from dividend 55
\begin{array}{l}\phantom{36)}01\phantom{4}\\36\overline{)55}\\\phantom{36)}\underline{\phantom{}36\phantom{}}\\\phantom{36)}19\\\end{array}
Find closest multiple of 36 to 55. We see that 1 \times 36 = 36 is the nearest. Now subtract 36 from 55 to get reminder 19. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }19
Since 19 is less than 36, stop the division. The reminder is 19. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}