Question

is 300 to 450 the same as 250 to 300

Answer 1

no

Answer 2

No, it's not equal.
Source: http://www.wolframalpha.com/input/?i=300^450+%3D+250^300
But if you don't have a super-calculator like wolfram alpha, you think the following,
You know that:
\[a < b \Rightarrow a ^{300} < b^{300} \Rightarrow a^{450} < b^{300}\]
Consider a= 250 and b=300

Answer 3

\(\bf \cfrac{300}{450}= \cfrac{250}{300}\qquad ?\)

what do you think?

Answer 4

jdoe0001, that's also false.
Source: http://www.wolframalpha.com/input/?i=%28300%2F450%29+%3D+%28250%2F300%29
You can check that by doing the following:
\[\frac{ 300 }{ 450 } \neq \frac{250}{300}\]
\[\frac{300}{450} \times \frac{300}{300} \neq \frac{250}{300} \times \frac{450}{450} \]
\[\frac{90000}{135000} \neq \frac{112500}{135000}\]