Question

The least possible fraction that is greater than 1/2 ?? The least possible fraction that is greater than 1/2 ?? @Mathematics

Answer 1

You want the smallest fraction p/q such that
p/q > 1/2?

Answer 2

11/20

Answer 3

I ask because there is no smallest fraction
1/2 < 51/100 < 11/20

But then
1/2 < 501/1000 < 51/100

But then
1/2 < 5001/10000 < 501/1000 < 51/100 < 11/20

Answer 4

Given any fraction greater than 1/2, you can always find another fraction between them.

Answer 5

..for example, the fraction half way between them:
\[ \frac{1}{2} \left( \frac{p}{q} + \frac{1}{2} \right) =\frac{1}{2} \frac{ 2p + q}{ 2q } = \frac{ 2p + q}{ 4q } \]

So suppose you started with 11/20.
The fraction half way between 1/2 and 11/20 (p = 11, q = 20) is
\[ \frac{1}{2} \left( \frac{11}{20} + \frac{1}{2} \right) = \frac{22 + 20}{80} = \frac{21}{40} \]