Every time I see the US notation for the long division I am momentarily taken aback by its topsy-turviness. Why write the dividend and divisor in the swapped order, divisor being to the left of the dividend? Why write the answer at the top? Why not keep the natural "dividend / divisor" order and then write the answer to the right? Just like this:
? No wonder school students struggle with it so much: it's the most subtle arithmetic algorithm on its own, and adding frivolous notational convolutions only complicates things further. "Start by swapping the numbers, and write the divisor to the left of the dividend"— no, don't start with that, this step is completely unnecessary. Well, I guess it could be worse: they could've put the answer on the bottom, and made chain of subtractions go up, now that would be trippy (look up the "galley division method", I am not making this up).
Every time I see the US notation for the long division I am momentarily taken aback by its topsy-turviness. Why write the dividend and divisor in the swapped order, divisor being to the left of the dividend? Why write the answer at the top? Why not keep the natural "dividend / divisor" order and then write the answer to the right? Just like this:
? No wonder school students struggle with it so much: it's the most subtle arithmetic algorithm on its own, and adding frivolous notational convolutions only complicates things further. "Start by swapping the numbers, and write the divisor to the left of the dividend"— no, don't start with that, this step is completely unnecessary. Well, I guess it could be worse: they could've put the answer on the bottom, and made chain of subtractions go up, now that would be trippy (look up the "galley division method", I am not making this up).because if put the divisor to the left, you can easily zero extend, and get the decimal place of the quotient for free.
you say "natural order" but its obviously arbitrary, not natural. the divides predicate has the opposite order for example