Evaluate
\frac{117}{28}\approx 4.178571429
Factor
\frac{3 ^ {2} \cdot 13}{2 ^ {2} \cdot 7} = 4\frac{5}{28} = 4.178571428571429
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\begin{array}{l}\phantom{140)}\phantom{1}\\140\overline{)585}\\\end{array}
Use the 1^{st} digit 5 from dividend 585
\begin{array}{l}\phantom{140)}0\phantom{2}\\140\overline{)585}\\\end{array}
Since 5 is less than 140, use the next digit 8 from dividend 585 and add 0 to the quotient
\begin{array}{l}\phantom{140)}0\phantom{3}\\140\overline{)585}\\\end{array}
Use the 2^{nd} digit 8 from dividend 585
\begin{array}{l}\phantom{140)}00\phantom{4}\\140\overline{)585}\\\end{array}
Since 58 is less than 140, use the next digit 5 from dividend 585 and add 0 to the quotient
\begin{array}{l}\phantom{140)}00\phantom{5}\\140\overline{)585}\\\end{array}
Use the 3^{rd} digit 5 from dividend 585
\begin{array}{l}\phantom{140)}004\phantom{6}\\140\overline{)585}\\\phantom{140)}\underline{\phantom{}560\phantom{}}\\\phantom{140)9}25\\\end{array}
Find closest multiple of 140 to 585. We see that 4 \times 140 = 560 is the nearest. Now subtract 560 from 585 to get reminder 25. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }25
Since 25 is less than 140, stop the division. The reminder is 25. The topmost line 004 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}