My Math Forum Is there a name for this? Can it be expressed algebraically?

 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 February 9th, 2016, 11:55 AM #1 Newbie   Joined: Feb 2016 From: London Posts: 2 Thanks: 0 Is there a name for this? Can it be expressed algebraically? I'm not sure if this has a name but: 6420 / 420 = 15.285714285714285714285714285714 420 / 15.285714285714285714285714285714 = 27.476635514018691588785046728972 27.476635514018691588785046728972 / 420 = 0.06542056074766355140186915887851 420 / 0.06542056074766355140186915887851 = 6419.9999999 or 6420 Another example: 5000 / 200 = 25 200 / 25 = 8 8 / 200 = 0.04 200 / 0.04 = 5000 Is there a name for this?
 February 9th, 2016, 02:46 PM #2 Senior Member   Joined: Jul 2014 From: भारत Posts: 1,178 Thanks: 230 Division.
 February 9th, 2016, 03:07 PM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,305 Thanks: 2443 Math Focus: Mainly analysis and algebra $${a \over b}=c \\ {b \over c}={b \over {a \over b}}= {b^2 \over a} \\ {{b^2 \over a} \over b}={b \over a} \\ {b \over {b \over a}}=a$$ So it's just a pattern of division that works for any non-zero $a$ and $b$. Thanks from dude24760
 February 10th, 2016, 03:31 AM #4 Newbie   Joined: Feb 2016 From: London Posts: 2 Thanks: 0 Just wanted to say, I know it's division (obviously), but I wanted to know if repeatedly dividing like this, and ending up with the number you started with, I was wondering if this kind of pattern had a name. Thanks anyway.

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