💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱

  • 137 Posts
  • 187 Comments
Joined 11 months ago
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Cake day: November 25th, 2023

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  • I would have got 1 by doing 2(2+2) = 8 first. Not because of bracket but because of “implied multiplication.”

    Yeah, right answer but wrong reason. There’s no such thing as implicit multiplication.

    What I am learning here: 8÷2(2+2) is not same as 8÷2×(2+2)

    Correct, and that’s because of Terms - 8÷2(2+2) is 2 terms, with the (2+2) in the denominator, but 8÷2×(2+2) is 3 terms, with the (2+2) in the numerator… hence why people get the wrong answer when they add an extra multiply in.

    number next bracket is not the same as normal multiplication in rule book

    Right, because it’s not “multiplication” at all (only applies literally to multiplication signs), it’s a coefficient of a bracketed term, which means we have to apply The Distributive Law as part of solving Brackets.

    ÷ & × have right of way rule with whoever is left most wins

    Yeah, the actual rule is Left associativity, and going left to right is the easy way to obey that.


  • multiple always happens first. But apparently it’s what’s left side first

    Multiplication and division are equal precedence (and done left to right) if that’s what you’re talking about, but the issue is that a(b+c) isn’t “multiplication” at all, it’s a bracketed term with a coefficient which is therefore subject to The Distributive Law, and is solved as part of solving Brackets, which is always first. Multiplication refers literally to multiplication signs, of which there are none in the original question. A Term is a product, which is the result of a multiplication, not something which is to be multiplied.

    If a=2 and b=3, then…

    axb=2x3 - 2 terms

    ab=6 - 1 term



  • inside radicals

    I had to look up what that meant (should’ve done that the first time - sorry) - have never heard that before, must be a local terminology.

    So, square roots (or other roots) can be expressed as an exponent - e.g. the square root of 2 is the same as 2 to the power ½ - so that’s covered by “E”, exponents! (or I for Index, or O for to the Order of, depending on your area)

    I appreciate your mention of the importance of teaching the difference between operators and terms

    Thank you.

    My pedagogical background is in the sciences and I’m much better at doing math than teaching it

    Oh god, welcome to why I have so many people argue with me, a Maths teacher, about it. There’s a whole bunch of Youtubes and blogs out there by Physics majors. I’m like “OMG, why are you trusting someone with a Physics major over someone with a Maths major - god help me”.

    I would like if math classes (in my area) did more explicitly teach the difference between terms and operators

    So what area are you in? A country will do. You said PEMDAS so I’m guessing the U.S.? I’ve heard via Youtubes/blogs that indeed there is more confusion with what is taught there, but I ended up Googling for U.S. textbooks, and found the same thing being taught in the textbook, so I’m not sure where this “that’s not what they teach in the U.S.” is coming from (why I was Googling for U.S. textbooks in the first place). Is the standard of teachers there actually worse than elsewhere? Or is it perhaps (possibly more likely) that there’s just more U.S. people posting, therefore more people who’ve forgotten the actual rules, and are just (as I’ve seen many times) they’re just blaming it on what they were taught (which I’ve usually found isn’t true at all).


  • Ok, that’s a start. In your simple example they are all equal, but they aren’t all the same.

    yn+y - 2 terms

    y(n+1) - 1 term

    y×(n +1) - 2 terms

    To see the difference, now precede it with a division, like in the original question…

    1÷yn+y=(1/yn)+y

    1÷y(n+1)=1/(yn+y)

    1÷y×(n +1)=(n +1)/y

    Note that in the last one, compared to the second one, the (n+1) is now in the numerator instead of in the denominator. Welcome to why having the (2+2) in the numerator gives the wrong answer.