Translation of "fraction" in a sentence I'm having difficulty translating the following sentence into Chinese:


  A fraction q of the population is smart.


I was tempted to translate this as 


  百分之 q 的人口是聪明的。


But strictly speaking this is not correct, because fraction as a mathematical terminology means 分数 in Chinese (as in a / b for some natural numbers a and b), which is not necessarily a percentage. 

Using the literal Chinese translation of fraction doesn't read well:


  分数 q 的人口是聪明的。


I'm hoping to get help on a better translation of the sentence. Thank you!



EDIT

From the comments it's clear to me that the English sentence to be translated, taken on its own, may be open to multiple interpretations. I hope the following context will clarify its meaning. 

The intended meaning of "A fraction q of the population is smart" is that 


  The total number of smart people is q * N


given that the population size is N. To put this in full context, the original sentence I am to translate is related to calculating a conditional probability using Bayes' rule:


  Suppose p% of the population is educated, and a fraction q of the educated is smart. Suppose further that a fraction r of the uneducated is smart as well. What is the probability that a randomly selected educated person is smart?


Replacing the algebra notations with numbers, the above could have read:


  Suppose 73% of the population is educated, and 4/7 of the educated is smart. Suppose further that 2/3 of the uneducated is smart as well. What is the probability that a randomly selected educated person is smart?
Suppose 73% of the population is educated, and 4/7 of the educated is smart. Suppose further that 2/3 of the uneducated is smart as well. What is the probability that a randomly selected educated person is smart?
假设73%的人口受过教育，而受过教育的人当中4/7是聪明的。进一步假设2/3没受过教育的人也是聪明的。随机抽取一个受过教育的人是聪明的概率是多少？

&quot;(Ratio q) + of + X&quot; can be translated as

(在)X(当)中q. &quot;(在)受过教育的人(当)中4/7是聪明的&quot;. And &quot;其中4/7是聪明的&quot; sounds more concise – though IMO it can't be applied to this example because it's a little ambiguous.
qX. &quot;4/7受过教育的人是聪明的&quot;. Sometimes for the subtle fluency, when X doesn't contain &quot;的&quot;, it would be better to say  &quot;q的X&quot; instead, such as &quot;4/7的农民&quot;, &quot;30%的学生&quot;.
X的q. It sounds a little colloquial and a little awkward for this example because there're two close &quot;的&quot;s: &quot;受过教育的人的4/7是聪明的&quot;.

(Ratio q) above can be replaced by a percentage &quot;p%&quot; too. Either &quot;(在)受过教育的人(当)中50%是聪明的&quot; or
&quot;(在)受过教育的人(当)中p%是聪明的&quot; (p% as a variable) is fine.
However, if you have to use &quot;ratio q&quot; as a variable, it has to be &quot;比例q&quot; or &quot;比率q&quot;, and a &quot;有&quot; would be necessary: &quot;受过教育的人中有比率q是聪明的&quot;. Though maybe not everyone consider it clear enough - &quot;比率q的X&quot; and &quot;X的比率q&quot; patterns are even worse.
PS: I don't see the point of this math problem. If we just randomly select a person within the educated, i.e. P(smart|educated), then, isn't the answer a trivial 4/7? Have I missed anything? :/