Something about the way this thread was written was kind of confusing,
Ok, sorry about that. I’m more than happy to update it if you want to give me some constructive feedback on what was confusing about it. Note though that this was the 3rd part in the series, and maybe you didn’t go back and read the previous 2 parts? They start here
Is it just that the terminology is wrong? Or am I missing something?
Yes and yes. :-) The 2 actual rules of Maths that apply here are Terms and The Distributive Law. These are 2 different rules of Maths - neither of which is “multiplication” - and so when lumping them together as “implicit multiplication” you end up with unpredictable, and usually wrong, answers. The only way to always get the right answer is to follow the actual rules of Maths.
a x b, a*b, ab, and a(b) are all acceptable notations to describe the operation “multiply a and b.”
No, they’re not. The first two are multiplications, the second two are Terms. Note that a Term is a product, the result of a multiplication. In the mnemonics, “Multiplication”" refers literally to multiplication signs, and nothing else.
Ok, sorry about that. I’m more than happy to update it if you want to give me some constructive feedback on what was confusing about it. Note though that this was the 3rd part in the series, and maybe you didn’t go back and read the previous 2 parts? They start here
NP. I’m not really great at giving writing advice, so can’t really help there. Something about it just didn’t click when I read it. The extra context you linked did help a bit.
As far as the issue: After reading it I think it does just seem to be a matter of terminology mixed with problems that arise with when you need to write math expressions inline in text. If you can write things out on paper or use a markdown language, it’s really easy to see how a fractional expression is structured.
8
2(1+3)
is a lot easier to read than 8/2(1+3) even if they technically are meant to be evaluated the same. There’s no room for confusion.
And as for distributive law vs multiplication, maybe this is just taking for granted a thing that I learned a long time ago, but to me they’re just the same thing in practice. When I see a(x+1) I know that in order to multiply these I need to distribute. And if we fill in the algebraic symbols for numbers, you don’t even need to distribute to get the answer since you can just evaluate the parentheses then use the result to multiply by the outside.
Conversely, if I was factoring something, I would need to do division.
ax + a
a
= x+1, thus: a(x+1)
I think we’re basically talking about the same thing, I’m just being a bit lose with the terminology.
And while we’re at it, the best way to make sure there’s no misunderstanding is to just use parenthesis for EVERYTHING! I’m mostly kidding, this can rapidly get unreadable once you nest more than a few parens, although for these toy expressions, it would have the desired effect.
(8)/(2(1+3)) is obviously different than (8/2)(1+3)
Ok, sorry about that. I’m more than happy to update it if you want to give me some constructive feedback on what was confusing about it. Note though that this was the 3rd part in the series, and maybe you didn’t go back and read the previous 2 parts? They start here
Yes and yes. :-) The 2 actual rules of Maths that apply here are Terms and The Distributive Law. These are 2 different rules of Maths - neither of which is “multiplication” - and so when lumping them together as “implicit multiplication” you end up with unpredictable, and usually wrong, answers. The only way to always get the right answer is to follow the actual rules of Maths.
No, they’re not. The first two are multiplications, the second two are Terms. Note that a Term is a product, the result of a multiplication. In the mnemonics, “Multiplication”" refers literally to multiplication signs, and nothing else.
NP. I’m not really great at giving writing advice, so can’t really help there. Something about it just didn’t click when I read it. The extra context you linked did help a bit.
As far as the issue: After reading it I think it does just seem to be a matter of terminology mixed with problems that arise with when you need to write math expressions inline in text. If you can write things out on paper or use a markdown language, it’s really easy to see how a fractional expression is structured.
8
2(1+3)
is a lot easier to read than 8/2(1+3) even if they technically are meant to be evaluated the same. There’s no room for confusion.
And as for distributive law vs multiplication, maybe this is just taking for granted a thing that I learned a long time ago, but to me they’re just the same thing in practice. When I see a(x+1) I know that in order to multiply these I need to distribute. And if we fill in the algebraic symbols for numbers, you don’t even need to distribute to get the answer since you can just evaluate the parentheses then use the result to multiply by the outside.
Conversely, if I was factoring something, I would need to do division.
ax + a
a
= x+1, thus: a(x+1)
I think we’re basically talking about the same thing, I’m just being a bit lose with the terminology.
And while we’re at it, the best way to make sure there’s no misunderstanding is to just use parenthesis for EVERYTHING! I’m mostly kidding, this can rapidly get unreadable once you nest more than a few parens, although for these toy expressions, it would have the desired effect.
(8)/(2(1+3)) is obviously different than (8/2)(1+3)