Evaluate
\frac{18}{7}\approx 2.571428571
Factor
\frac{2 \cdot 3 ^ {2}}{7} = 2\frac{4}{7} = 2.5714285714285716
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\begin{array}{l}\phantom{21)}\phantom{1}\\21\overline{)54}\\\end{array}
Use the 1^{st} digit 5 from dividend 54
\begin{array}{l}\phantom{21)}0\phantom{2}\\21\overline{)54}\\\end{array}
Since 5 is less than 21, use the next digit 4 from dividend 54 and add 0 to the quotient
\begin{array}{l}\phantom{21)}0\phantom{3}\\21\overline{)54}\\\end{array}
Use the 2^{nd} digit 4 from dividend 54
\begin{array}{l}\phantom{21)}02\phantom{4}\\21\overline{)54}\\\phantom{21)}\underline{\phantom{}42\phantom{}}\\\phantom{21)}12\\\end{array}
Find closest multiple of 21 to 54. We see that 2 \times 21 = 42 is the nearest. Now subtract 42 from 54 to get reminder 12. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }12
Since 12 is less than 21, stop the division. The reminder is 12. The topmost line 02 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}