Is this the most elementary colloquium topic you have ever seen? You may be surprised.
What method might someone choose for determining whether or not two fractions are equal, and is it valid? There are several possibilities that are a priori varyingly credible or conclusive.
Not wanting to spill the beans for audience participation, I maintain there is a very delicate mathematical issue here, something powerful but sufficiently subtle that it tends early to become invisible to a mathematician, by assuming intuitive second nature. For others it remains entirely outside conscious awareness, despite perhaps being used occasionally in practice without question.
Gauss, Euler, and Euclid all shed light on the question. So is the biggest secret of fractions too complicated for school or street? Quick, does 23/67 equal 33/97, and why?