Evaluate
\frac{54}{7}\approx 7.714285714
Factor
\frac{2 \cdot 3 ^ {3}}{7} = 7\frac{5}{7} = 7.714285714285714
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\begin{array}{l}\phantom{21)}\phantom{1}\\21\overline{)162}\\\end{array}
Use the 1^{st} digit 1 from dividend 162
\begin{array}{l}\phantom{21)}0\phantom{2}\\21\overline{)162}\\\end{array}
Since 1 is less than 21, use the next digit 6 from dividend 162 and add 0 to the quotient
\begin{array}{l}\phantom{21)}0\phantom{3}\\21\overline{)162}\\\end{array}
Use the 2^{nd} digit 6 from dividend 162
\begin{array}{l}\phantom{21)}00\phantom{4}\\21\overline{)162}\\\end{array}
Since 16 is less than 21, use the next digit 2 from dividend 162 and add 0 to the quotient
\begin{array}{l}\phantom{21)}00\phantom{5}\\21\overline{)162}\\\end{array}
Use the 3^{rd} digit 2 from dividend 162
\begin{array}{l}\phantom{21)}007\phantom{6}\\21\overline{)162}\\\phantom{21)}\underline{\phantom{}147\phantom{}}\\\phantom{21)9}15\\\end{array}
Find closest multiple of 21 to 162. We see that 7 \times 21 = 147 is the nearest. Now subtract 147 from 162 to get reminder 15. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }15
Since 15 is less than 21, stop the division. The reminder is 15. The topmost line 007 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 7.
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}