Evaluate
\frac{155}{54}\approx 2.87037037
Factor
\frac{5 \cdot 31}{2 \cdot 3 ^ {3}} = 2\frac{47}{54} = 2.8703703703703702
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\begin{array}{l}\phantom{54)}\phantom{1}\\54\overline{)155}\\\end{array}
Use the 1^{st} digit 1 from dividend 155
\begin{array}{l}\phantom{54)}0\phantom{2}\\54\overline{)155}\\\end{array}
Since 1 is less than 54, use the next digit 5 from dividend 155 and add 0 to the quotient
\begin{array}{l}\phantom{54)}0\phantom{3}\\54\overline{)155}\\\end{array}
Use the 2^{nd} digit 5 from dividend 155
\begin{array}{l}\phantom{54)}00\phantom{4}\\54\overline{)155}\\\end{array}
Since 15 is less than 54, use the next digit 5 from dividend 155 and add 0 to the quotient
\begin{array}{l}\phantom{54)}00\phantom{5}\\54\overline{)155}\\\end{array}
Use the 3^{rd} digit 5 from dividend 155
\begin{array}{l}\phantom{54)}002\phantom{6}\\54\overline{)155}\\\phantom{54)}\underline{\phantom{}108\phantom{}}\\\phantom{54)9}47\\\end{array}
Find closest multiple of 54 to 155. We see that 2 \times 54 = 108 is the nearest. Now subtract 108 from 155 to get reminder 47. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }47
Since 47 is less than 54, stop the division. The reminder is 47. The topmost line 002 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}