Evaluate
\frac{19}{6}\approx 3.166666667
Factor
\frac{19}{2 \cdot 3} = 3\frac{1}{6} = 3.1666666666666665
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\begin{array}{l}\phantom{120)}\phantom{1}\\120\overline{)380}\\\end{array}
Use the 1^{st} digit 3 from dividend 380
\begin{array}{l}\phantom{120)}0\phantom{2}\\120\overline{)380}\\\end{array}
Since 3 is less than 120, use the next digit 8 from dividend 380 and add 0 to the quotient
\begin{array}{l}\phantom{120)}0\phantom{3}\\120\overline{)380}\\\end{array}
Use the 2^{nd} digit 8 from dividend 380
\begin{array}{l}\phantom{120)}00\phantom{4}\\120\overline{)380}\\\end{array}
Since 38 is less than 120, use the next digit 0 from dividend 380 and add 0 to the quotient
\begin{array}{l}\phantom{120)}00\phantom{5}\\120\overline{)380}\\\end{array}
Use the 3^{rd} digit 0 from dividend 380
\begin{array}{l}\phantom{120)}003\phantom{6}\\120\overline{)380}\\\phantom{120)}\underline{\phantom{}360\phantom{}}\\\phantom{120)9}20\\\end{array}
Find closest multiple of 120 to 380. We see that 3 \times 120 = 360 is the nearest. Now subtract 360 from 380 to get reminder 20. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }20
Since 20 is less than 120, stop the division. The reminder is 20. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}