Well, you're right so long as 1/3 = 2/6. This is a mathematical equivalence... Fractions are a 2d projective space: they are pairs (n, d) where (mn, md) is equ

Well, you're right so long as 1/3 = 2/6. This is a mathematical equivalence... Fractions are a 2d projective space: they are pairs (n, d) where (mn, md) is equivalent to (n, d). The suggested operation is totally fine if you are working in ambient (that is, non-projective) space... ie, if you continually keep track of the 'size' of the thing being measured. The equivalence operation is hard to master, and makes the arithmetic complicated.