## Question about best rational approximations.

Hey,

I have a quick question about best rational approximations of irrational numbers using continued fractions etc. (Continued fraction - Wikipedia, the free encyclopedia) Suppose we have a real number $x$, and we know that some rational number $\frac{a}{b}$ is a best approximation of $x$, in other word a convergent of the continued fraction of $x$.

Now suppose some other ration number $\frac{a'}{b'}$ is such that $x<\frac{a'}{b'}<\frac{a}{b}$. We then know for sure that $b, but is $\frac{a'}{b'}$ necessarily a best approximation of $x$ as well? It seems to me like this would be true, but I can't think of any good reason why.