Evaluate
\frac{30}{7}\approx 4.285714286
Factor
\frac{2 \cdot 3 \cdot 5}{7} = 4\frac{2}{7} = 4.285714285714286
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\begin{array}{l}\phantom{21)}\phantom{1}\\21\overline{)90}\\\end{array}
Use the 1^{st} digit 9 from dividend 90
\begin{array}{l}\phantom{21)}0\phantom{2}\\21\overline{)90}\\\end{array}
Since 9 is less than 21, use the next digit 0 from dividend 90 and add 0 to the quotient
\begin{array}{l}\phantom{21)}0\phantom{3}\\21\overline{)90}\\\end{array}
Use the 2^{nd} digit 0 from dividend 90
\begin{array}{l}\phantom{21)}04\phantom{4}\\21\overline{)90}\\\phantom{21)}\underline{\phantom{}84\phantom{}}\\\phantom{21)9}6\\\end{array}
Find closest multiple of 21 to 90. We see that 4 \times 21 = 84 is the nearest. Now subtract 84 from 90 to get reminder 6. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }6
Since 6 is less than 21, stop the division. The reminder is 6. 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}