Evaluate
\frac{228}{107}\approx 2.130841121
Factor
\frac{2 ^ {2} \cdot 3 \cdot 19}{107} = 2\frac{14}{107} = 2.130841121495327
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\begin{array}{l}\phantom{107)}\phantom{1}\\107\overline{)228}\\\end{array}
Use the 1^{st} digit 2 from dividend 228
\begin{array}{l}\phantom{107)}0\phantom{2}\\107\overline{)228}\\\end{array}
Since 2 is less than 107, use the next digit 2 from dividend 228 and add 0 to the quotient
\begin{array}{l}\phantom{107)}0\phantom{3}\\107\overline{)228}\\\end{array}
Use the 2^{nd} digit 2 from dividend 228
\begin{array}{l}\phantom{107)}00\phantom{4}\\107\overline{)228}\\\end{array}
Since 22 is less than 107, use the next digit 8 from dividend 228 and add 0 to the quotient
\begin{array}{l}\phantom{107)}00\phantom{5}\\107\overline{)228}\\\end{array}
Use the 3^{rd} digit 8 from dividend 228
\begin{array}{l}\phantom{107)}002\phantom{6}\\107\overline{)228}\\\phantom{107)}\underline{\phantom{}214\phantom{}}\\\phantom{107)9}14\\\end{array}
Find closest multiple of 107 to 228. We see that 2 \times 107 = 214 is the nearest. Now subtract 214 from 228 to get reminder 14. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }14
Since 14 is less than 107, stop the division. The reminder is 14. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
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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}