He explains that it was a "triumph of Greek mathematics" to prove that multiplying the top and bottom of a fraction is how you multiply two fractions. That is, we accept as true that you can multiply fractions this way, but we kind of just got lucky that it does work that way. Proving that it always works is non-trivial, but that is totally glossed over in math classes, doing a disservice to students.
This is in context of dividing two fractions where kids are taught an arbitrary rule too early in their studies and it turns them off to math overall because it's become a class of memorizing arbitrary procedures instead of learning concepts.
(That's all my summary of that segment with a little reading between the lines, not my personal view of it. Or it might be later, but have to consider it more.)
This is in context of dividing two fractions where kids are taught an arbitrary rule too early in their studies and it turns them off to math overall because it's become a class of memorizing arbitrary procedures instead of learning concepts.
(That's all my summary of that segment with a little reading between the lines, not my personal view of it. Or it might be later, but have to consider it more.)