Evaluate
\frac{140}{81}\approx 1.728395062
Factor
\frac{2 ^ {2} \cdot 5 \cdot 7}{3 ^ {4}} = 1\frac{59}{81} = 1.728395061728395
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\begin{array}{l}\phantom{81)}\phantom{1}\\81\overline{)140}\\\end{array}
Use the 1^{st} digit 1 from dividend 140
\begin{array}{l}\phantom{81)}0\phantom{2}\\81\overline{)140}\\\end{array}
Since 1 is less than 81, use the next digit 4 from dividend 140 and add 0 to the quotient
\begin{array}{l}\phantom{81)}0\phantom{3}\\81\overline{)140}\\\end{array}
Use the 2^{nd} digit 4 from dividend 140
\begin{array}{l}\phantom{81)}00\phantom{4}\\81\overline{)140}\\\end{array}
Since 14 is less than 81, use the next digit 0 from dividend 140 and add 0 to the quotient
\begin{array}{l}\phantom{81)}00\phantom{5}\\81\overline{)140}\\\end{array}
Use the 3^{rd} digit 0 from dividend 140
\begin{array}{l}\phantom{81)}001\phantom{6}\\81\overline{)140}\\\phantom{81)}\underline{\phantom{9}81\phantom{}}\\\phantom{81)9}59\\\end{array}
Find closest multiple of 81 to 140. We see that 1 \times 81 = 81 is the nearest. Now subtract 81 from 140 to get reminder 59. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }59
Since 59 is less than 81, stop the division. The reminder is 59. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}