Knowing the price of 1Kg of Potatoes, the street-side vegetable seller in my home town in India only needs to know how much to charge me for 3/4 Kg.  He doesn't really care how innovations in mathematics resulted in fractional multiplication.  This can be extended to the teaching of basic maths.  Students who show an interest or an aptitude for grasping the finer and more insightful details can go on to read up on it, or ask their professors.<p>What we really need is professors knowledgeable enough to answer these questions or point the student to the right texts.