Evaluate
\frac{40}{19}\approx 2.105263158
Factor
\frac{2 ^ {3} \cdot 5}{19} = 2\frac{2}{19} = 2.1052631578947367
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\begin{array}{l}\phantom{285)}\phantom{1}\\285\overline{)600}\\\end{array}
Use the 1^{st} digit 6 from dividend 600
\begin{array}{l}\phantom{285)}0\phantom{2}\\285\overline{)600}\\\end{array}
Since 6 is less than 285, use the next digit 0 from dividend 600 and add 0 to the quotient
\begin{array}{l}\phantom{285)}0\phantom{3}\\285\overline{)600}\\\end{array}
Use the 2^{nd} digit 0 from dividend 600
\begin{array}{l}\phantom{285)}00\phantom{4}\\285\overline{)600}\\\end{array}
Since 60 is less than 285, use the next digit 0 from dividend 600 and add 0 to the quotient
\begin{array}{l}\phantom{285)}00\phantom{5}\\285\overline{)600}\\\end{array}
Use the 3^{rd} digit 0 from dividend 600
\begin{array}{l}\phantom{285)}002\phantom{6}\\285\overline{)600}\\\phantom{285)}\underline{\phantom{}570\phantom{}}\\\phantom{285)9}30\\\end{array}
Find closest multiple of 285 to 600. We see that 2 \times 285 = 570 is the nearest. Now subtract 570 from 600 to get reminder 30. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }30
Since 30 is less than 285, stop the division. The reminder is 30. 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}