Growing by Denominators
Find the smallest fraction, which will triple in size, when you add its denominator to its numerator and its denominator.
Find the smallest fraction which will quadruple when the same process is applied.
Find the smallest fraction which will quadruple when the same process is applied.
posted by Zaux at
6:41 AM
6 Comments:
Not sure if they're the smallest?
1/5 > 6/10 =3/5
1/7 > 8/14 =4/7
but they work!
regards, Curtis
good work Curtis
forgot the equation:
fraction x/y
3(x/y) = x+y/2y
thus 3x/y = x+y/2y
thus 6x/2y = x+y/2y
thus 6x = x+y
thus 5x = y
if x=1.....y=5
hence 1/5
n(x/y)= x+y/2y
(2n-1)x = y
so for 19 times fraction is 1/37
I think!!
regards, Curtis
Let n/d be the fraction.
Then require (n+d)/(d+d) = 3n/d
=> n+d = 6n => d = 5n => n/d = 1/5
and (n+d)/(d+d) = 6n/10n = 3/5 = 3*(1/5)
This post has been removed by the author.
.. sorry Curtis, I've only just realised that's what you did. If you'd written 3(x/y) = (x+y)/(2y) I wouldn't have posted.
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