Evaluate
\frac{27}{19}\approx 1.421052632
Factor
\frac{3 ^ {3}}{19} = 1\frac{8}{19} = 1.4210526315789473
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\begin{array}{l}\phantom{38)}\phantom{1}\\38\overline{)54}\\\end{array}
Use the 1^{st} digit 5 from dividend 54
\begin{array}{l}\phantom{38)}0\phantom{2}\\38\overline{)54}\\\end{array}
Since 5 is less than 38, use the next digit 4 from dividend 54 and add 0 to the quotient
\begin{array}{l}\phantom{38)}0\phantom{3}\\38\overline{)54}\\\end{array}
Use the 2^{nd} digit 4 from dividend 54
\begin{array}{l}\phantom{38)}01\phantom{4}\\38\overline{)54}\\\phantom{38)}\underline{\phantom{}38\phantom{}}\\\phantom{38)}16\\\end{array}
Find closest multiple of 38 to 54. We see that 1 \times 38 = 38 is the nearest. Now subtract 38 from 54 to get reminder 16. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }16
Since 16 is less than 38, stop the division. The reminder is 16. 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}