Comment by ndriscoll

Don't we still teach kids that e.g. 3/4=6/8, that they need to make a common denominator to add, and that they should cross multiply to check equality? I suppose we don't teach zero divisors, but otherwise, jargon aside, I'd be hard pressed to explain how we don't teach kids that fractions are members of ZxZ* mod (ad-bc).

Lies to children are like... time-reversal symmetry.