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>I have this 2-5/8 tile I need to split in half. Ok, 1-5/16. Contrast that with 2.625 / 2 = 1.3125.

The latter is much easier to think about IMO.

I find the latter more difficult because you’re carrying numbers to different places and have to reason about the whole number. In the former you can cheat by just halving (doubling, yeah it’s a little counterintuitive) the denominator (ignoring the integer in both examples, since that’s easy in both).

But I will grant you, converting between denominators makes my head hurt in the imperial system. Overall I do still think metric is easier as a whole.

Just double the denominator. Do you have .625/2=.3125 memorized?

No but half of 625 is very easy math (half of 600 is 300, half of 25 is 12.5) and it makes doing everything else so much easier.

That and in practice, tiles aren't found in dimensions of 26.25 cm, but 20, 25 or 30 cm.

Calculations with those numbers are trivial to make, and when they aren't trivial those numbers are also easier to type on a calculator than fractions.

It's "easy math" if you're trained to think and calculate in that way. Never assume something is universally easy because it comes easy to yourself.

not a convincing argument. Same can be said for the other side

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