Evaluate
\frac{14}{3}\approx 4.666666667
Factor
\frac{2 \cdot 7}{3} = 4\frac{2}{3} = 4.666666666666667
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\begin{array}{l}\phantom{18)}\phantom{1}\\18\overline{)84}\\\end{array}
Use the 1^{st} digit 8 from dividend 84
\begin{array}{l}\phantom{18)}0\phantom{2}\\18\overline{)84}\\\end{array}
Since 8 is less than 18, use the next digit 4 from dividend 84 and add 0 to the quotient
\begin{array}{l}\phantom{18)}0\phantom{3}\\18\overline{)84}\\\end{array}
Use the 2^{nd} digit 4 from dividend 84
\begin{array}{l}\phantom{18)}04\phantom{4}\\18\overline{)84}\\\phantom{18)}\underline{\phantom{}72\phantom{}}\\\phantom{18)}12\\\end{array}
Find closest multiple of 18 to 84. We see that 4 \times 18 = 72 is the nearest. Now subtract 72 from 84 to get reminder 12. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }12
Since 12 is less than 18, stop the division. The reminder is 12. The topmost line 04 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}