Evaluate
\frac{153}{55}\approx 2.781818182
Factor
\frac{3 ^ {2} \cdot 17}{5 \cdot 11} = 2\frac{43}{55} = 2.7818181818181817
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\begin{array}{l}\phantom{55)}\phantom{1}\\55\overline{)153}\\\end{array}
Use the 1^{st} digit 1 from dividend 153
\begin{array}{l}\phantom{55)}0\phantom{2}\\55\overline{)153}\\\end{array}
Since 1 is less than 55, use the next digit 5 from dividend 153 and add 0 to the quotient
\begin{array}{l}\phantom{55)}0\phantom{3}\\55\overline{)153}\\\end{array}
Use the 2^{nd} digit 5 from dividend 153
\begin{array}{l}\phantom{55)}00\phantom{4}\\55\overline{)153}\\\end{array}
Since 15 is less than 55, use the next digit 3 from dividend 153 and add 0 to the quotient
\begin{array}{l}\phantom{55)}00\phantom{5}\\55\overline{)153}\\\end{array}
Use the 3^{rd} digit 3 from dividend 153
\begin{array}{l}\phantom{55)}002\phantom{6}\\55\overline{)153}\\\phantom{55)}\underline{\phantom{}110\phantom{}}\\\phantom{55)9}43\\\end{array}
Find closest multiple of 55 to 153. We see that 2 \times 55 = 110 is the nearest. Now subtract 110 from 153 to get reminder 43. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }43
Since 43 is less than 55, stop the division. The reminder is 43. 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}