Evaluate
\frac{140}{27}\approx 5.185185185
Factor
\frac{2 ^ {2} \cdot 5 \cdot 7}{3 ^ {3}} = 5\frac{5}{27} = 5.185185185185185
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\begin{array}{l}\phantom{54)}\phantom{1}\\54\overline{)280}\\\end{array}
Use the 1^{st} digit 2 from dividend 280
\begin{array}{l}\phantom{54)}0\phantom{2}\\54\overline{)280}\\\end{array}
Since 2 is less than 54, use the next digit 8 from dividend 280 and add 0 to the quotient
\begin{array}{l}\phantom{54)}0\phantom{3}\\54\overline{)280}\\\end{array}
Use the 2^{nd} digit 8 from dividend 280
\begin{array}{l}\phantom{54)}00\phantom{4}\\54\overline{)280}\\\end{array}
Since 28 is less than 54, use the next digit 0 from dividend 280 and add 0 to the quotient
\begin{array}{l}\phantom{54)}00\phantom{5}\\54\overline{)280}\\\end{array}
Use the 3^{rd} digit 0 from dividend 280
\begin{array}{l}\phantom{54)}005\phantom{6}\\54\overline{)280}\\\phantom{54)}\underline{\phantom{}270\phantom{}}\\\phantom{54)9}10\\\end{array}
Find closest multiple of 54 to 280. We see that 5 \times 54 = 270 is the nearest. Now subtract 270 from 280 to get reminder 10. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }10
Since 10 is less than 54, stop the division. The reminder is 10. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}