Evaluate
\frac{54}{31}\approx 1.741935484
Factor
\frac{2 \cdot 3 ^ {3}}{31} = 1\frac{23}{31} = 1.7419354838709677
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\begin{array}{l}\phantom{31)}\phantom{1}\\31\overline{)54}\\\end{array}
Use the 1^{st} digit 5 from dividend 54
\begin{array}{l}\phantom{31)}0\phantom{2}\\31\overline{)54}\\\end{array}
Since 5 is less than 31, use the next digit 4 from dividend 54 and add 0 to the quotient
\begin{array}{l}\phantom{31)}0\phantom{3}\\31\overline{)54}\\\end{array}
Use the 2^{nd} digit 4 from dividend 54
\begin{array}{l}\phantom{31)}01\phantom{4}\\31\overline{)54}\\\phantom{31)}\underline{\phantom{}31\phantom{}}\\\phantom{31)}23\\\end{array}
Find closest multiple of 31 to 54. We see that 1 \times 31 = 31 is the nearest. Now subtract 31 from 54 to get reminder 23. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }23
Since 23 is less than 31, stop the division. The reminder is 23. 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}