Evaluate
\frac{508}{185}\approx 2.745945946
Factor
\frac{2 ^ {2} \cdot 127}{5 \cdot 37} = 2\frac{138}{185} = 2.745945945945946
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\begin{array}{l}\phantom{555)}\phantom{1}\\555\overline{)1524}\\\end{array}
Use the 1^{st} digit 1 from dividend 1524
\begin{array}{l}\phantom{555)}0\phantom{2}\\555\overline{)1524}\\\end{array}
Since 1 is less than 555, use the next digit 5 from dividend 1524 and add 0 to the quotient
\begin{array}{l}\phantom{555)}0\phantom{3}\\555\overline{)1524}\\\end{array}
Use the 2^{nd} digit 5 from dividend 1524
\begin{array}{l}\phantom{555)}00\phantom{4}\\555\overline{)1524}\\\end{array}
Since 15 is less than 555, use the next digit 2 from dividend 1524 and add 0 to the quotient
\begin{array}{l}\phantom{555)}00\phantom{5}\\555\overline{)1524}\\\end{array}
Use the 3^{rd} digit 2 from dividend 1524
\begin{array}{l}\phantom{555)}000\phantom{6}\\555\overline{)1524}\\\end{array}
Since 152 is less than 555, use the next digit 4 from dividend 1524 and add 0 to the quotient
\begin{array}{l}\phantom{555)}000\phantom{7}\\555\overline{)1524}\\\end{array}
Use the 4^{th} digit 4 from dividend 1524
\begin{array}{l}\phantom{555)}0002\phantom{8}\\555\overline{)1524}\\\phantom{555)}\underline{\phantom{}1110\phantom{}}\\\phantom{555)9}414\\\end{array}
Find closest multiple of 555 to 1524. We see that 2 \times 555 = 1110 is the nearest. Now subtract 1110 from 1524 to get reminder 414. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }414
Since 414 is less than 555, stop the division. The reminder is 414. The topmost line 0002 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}