Evaluate
\frac{250}{111}\approx 2.252252252
Factor
\frac{2 \cdot 5 ^ {3}}{3 \cdot 37} = 2\frac{28}{111} = 2.2522522522522523
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\begin{array}{l}\phantom{222)}\phantom{1}\\222\overline{)500}\\\end{array}
Use the 1^{st} digit 5 from dividend 500
\begin{array}{l}\phantom{222)}0\phantom{2}\\222\overline{)500}\\\end{array}
Since 5 is less than 222, use the next digit 0 from dividend 500 and add 0 to the quotient
\begin{array}{l}\phantom{222)}0\phantom{3}\\222\overline{)500}\\\end{array}
Use the 2^{nd} digit 0 from dividend 500
\begin{array}{l}\phantom{222)}00\phantom{4}\\222\overline{)500}\\\end{array}
Since 50 is less than 222, use the next digit 0 from dividend 500 and add 0 to the quotient
\begin{array}{l}\phantom{222)}00\phantom{5}\\222\overline{)500}\\\end{array}
Use the 3^{rd} digit 0 from dividend 500
\begin{array}{l}\phantom{222)}002\phantom{6}\\222\overline{)500}\\\phantom{222)}\underline{\phantom{}444\phantom{}}\\\phantom{222)9}56\\\end{array}
Find closest multiple of 222 to 500. We see that 2 \times 222 = 444 is the nearest. Now subtract 444 from 500 to get reminder 56. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }56
Since 56 is less than 222, stop the division. The reminder is 56. 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}