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  • in reply to: Elementary Mathematical Equation #2179735

    @ujm thanks for the post, I was pleasantly surprised to enjoy it. You are either aware of the pitfalls in this and testing us, or were genuinely intrigued by the debate it can potentially engender.

    I’d like to post (what I believe is) *the* definitive answer. So no other answers need be given following this. Only your thanks, and praises are necessary.

    8÷2(2+2) = ?
    This question seems simple-enough. And anyone who proudly quotes their “PEMDAS” or “BODMAS” will quickly lament those whom they think don’t even know that much.
    But, to such a potentially over-confident person, there are two potential pitfalls that one needs to be aware of:

    Pitfall #1: PEMDAS doesn’t mean PEMDAS
    Just because the “M” is written before the “D” (or vice versa for BODMAS (which proves this point)), doesn’t necessarily mean that M[ultiplication] is performed before D[ivision]. They, in fact, hold equal priority, and so those two operations must be executed from left to right.
    So in 8/2*4, you do the division first.

    Pitfall #2: 10y doesn’t mean 10*y
    In 8÷2(2+2), there is no symbol given for the multiplication, just the juxtaposition of the “2” to the parentheses. By convention that is, and usually can, be regarded as a shorthand for multiplication. So when we see 10y in a formula, we can rightly treat it as 10*y. But, since these two are co-dependent they should more correctly be written with parentheses around them, so 10y is really (10*y) within parenthesis. This would make a difference to something like this example: 20/10y = 20/(10*y).

    So too in the problem given, 8÷2(2+2), it is natural to want to treat this as 8÷(2*4).
    BUT, strictly speaking, there is only this juxtaposition between a constant coefficient and a variable, never a constant and another constant.
    So, the 2(2+2) of the question is just 2×4 – without parentheses – and not (2×4) – as a single unit.

    So, in summary:
    8÷2(2+2) is more rightly:
    8÷2*(2+2), which =
    And since PEMDAS doesn’t mean “M” before “D”, but rather apply them left-to-right, it =

    That said, the faulty is really in the question; it was technically incorrect to write 2(2+2) without a symbol between them. So if someone went along with the questioner’s mistake at treated it as 8÷(2*4) and said the answer is 1, I would fault the questioner, not the one giving the answer. (Unless they made a mistake in Pitfall #1, in which case I would blame their school teacher.)

    Now that I have given the definitive answer to this question, I would like to also state, for the record, that Trump isn’t as bad as some people think. Even his middos aren’t as despicable as some believe. Those that do think so are the kind of idiots who are swayed by headlines and can’t read the body of an article, or certainly can’t divorce themselves from their pre-conceived perceptions formed upon reading the misleading headlines. He absolutely didn’t lead and insurrection, not that J6 was anything remotely close to an insurrection. And those on this forum who are quick to criticize the frum yidden, are low-lives, descendants of Lavan haRosha.

    Wishing you all a chag kasher v’sameach.

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