💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @ SmartmanApps @programming.dev

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22

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591

Joined

2 yr. ago

which clearly states that the distributive property is a generalization of the distributive law

Let me say again, people calling a Koala a Koala bear doesn't mean it actually is a bear. Stop reading wikipedia and pick up a Maths textbook.

You seem to be under the impression that the distributive law and distributive property are completely different statements

It's not an impression, it's in Year 7 Maths textbooks.

this certainly is not 7th year material

And yet it appears in every Year 7 textbook I've ever seen.

Looks like we're done here.

If you read the wikipedia article

...which isn't a Maths textbook!

also stating the distributive law, literally in the first sentence

Except what it states is the Distributive property, not The Distributive Law. If I call a Koala a Koala Bear, that doesn't mean it's a bear - it just means I used the wrong name. And again, not a Maths textbook - whoever wrote that demonstrably doesn't know the difference between the property and the law.

This is something you learn in elementary school

No it isn't. This is a year 7 topic. In Primary School they are only given bracketed terms without a coefficient (thus don't need to know The Distributive Law).

be assured that I am sufficiently qualified

No, I'm not assured of that when you're quoting wikipedia instead of Maths textbooks, and don't know the difference between The Distributive Property and The Distributive Law, nor know which grade this is taught to.

Wikipedia is not intrinsically less accurate than maths textbooks

BWAHAHAHAHA! You know how many wrong things I've seen in there? And I'm not even talking about Maths! Ever heard of edit wars? Whatever ends up on the page is whatever the admin believes. Wikipedia is "like an encyclopedia" in the same way that Madonna is like a virgin.

but you are misunderstanding them

And yet you have failed to point out how/why/where. In all of your comments here, you haven't even addressed The Distributive Law at all.

Whether you write it as a(b+c) = ab + ac or as a*(b+c) = ab + ac is insubstantial

And neither of those examples is about The Distributive Law - they are both to do with The Distributive Property (and you wrote the first one wrong anyway - it's a(b+c)=(ab+ac). Premature removal of brackets is how many people end up with the wrong answer).

If I write f^{-1}(x), without context, you have literally no way of knowing whether I am talking about a multiplicative or a functional inverse, which means that it is ambiguous

The inverse of the function is f(x)^-1. i.e. the negative exponent applies to the whole function, not just the x (since f(x) is a single term).

Correct! 2(2+2) is a single term - subject to The Distributive Law - and 2x(2+2) is 2 terms. Those who added a multiply sign there have effectively flipped the (2+2) from being in the denominator to being in the numerator, hence the wrong answer.

But it's not called "implicit multiplication" - it's Terms and/or The Distributive Law which applies (and they're 2 separate rules, so you cannot lump them together as a single rule).

2-(2-2)

But you broke the rule of left-associativity there. You can go right to left provided you keep each number with the sign to it's left (and you didn't do that when you separated the first 2 in brackets from it's minus sign).

I’ve never had anyone tell me operations with the same priority can be done either way, it’s always been left to right

It's left to right within each operator. You can do multiplication first and division next, or the other way around, as long as you do each operator left to right. Having said that, you also can do the whole group of equal precedence operators left to right - because you're still preserving left to right for each of the two operators - so you can do multiplication and division left to right at the same time, because they have equal precedence.

Having said that, it's an actual rule for division, but optional for the rest. The actual rule is you have to preserve left-associativity - i.e. a number is associated with the sign to the left of it - and going left to right is an easy way to do that.

8÷2(2+2)=8×(1/2)×(2+2)

No, that's wrong. 2(2+2) is a single term, and thus entirely in the denominator. When you separated the coefficient you flipped the (2+2) into the numerator, hence the wrong answer. You must never add multiplication signs where there are none.

8 / 2 * (2 + 2)

That's not the same as 8 / 2 (2 + 2). In the original question, 2(2+2) is a single term in the denominator, when you added the multiply you separated it and thus flipped the (2+2) to be in the numerator, hence the wrong answer.

Turns out I’m wrong, but I haven’t been told how or why. I’m willing to learn if people actually tell me

Well, I don't know what you said originally, so I don't know what it is you were told was wrong - 1 or 16? 😂 The correct answer is 1.

Anyhow, I have an order of operations thread which covers literally everything there is to know about it (including covering all the common mistakes and false claims made by some). It includes textbook references, historical Maths documents, worked examples, proofs, memes, the works! I'm a high school Maths teacher/tutor - I've taught this topic many times.

Sharp as well.

Everything I know is a lie

...including the comment you just replied to. Here is a thread with actual textbook references, historical Maths documents, worked examples, proofs, the works.

the problem with your logic is that it’s using rules designed for primary school

Actually The Distributive Law is taught in Year 7. The Primary School rule, which doesn't include brackets with coefficients, is only the intermediate step.

many decades ago. Not a rigorous mathematical convention

It's an actual rule which is centuries old.

mathematicians frequently use juxtaposition to indicate multiplication

It's not multiplication - it's either The Distributive Law or Terms, which are 2 separate rules.

an operation that doesn’t get used in primary school

Yes, as I said it's taught in Year 7.

8/2(2+2) = 8/2(4)

Then you do your exponents

You haven't finished Brackets yet! The next step is...

8/(2x4)=8/8

This is straight from the textbook

Not any textbook I've seen. Screenshot? Here's some actual textbooks

It's 1

M does not get priority over D

And M refers literally to multiplication signs, of which there are none, and Brackets has priority over everything.

8/2(2+2) =8/(2x2+2x2) =8/8 =1

Yes correct! I just had someone else here claim you couldn't do it with RPN - took me no time at all to show he was wrong about that! 😂

you could solve for the parentheses by multiplying 2+2 by two, giving you 8/8 quicker and still yielding 1. I’m now having more doubts about my math capabilities

No, that's the correct way to do it, as per The Distributive Law.

both are right

No, only 1 is right. If you get 16 then you did division before finishing solving brackets.

8/2(4) - Parentheses

8/8 - Multiplication

Correct steps, but wrong names. Where you said "multiplication" is actually still parentheses - that first step isn't finished until you have removed them (which isn't until after you have distributed and simplified, which you did do correctly).

Modern phone apps seem to be notorious for getting order of operations wrong

Yes, I know, and as a Maths teacher I am well and truly sick of hearing "but Google says...", and so I wrote this thread to try and get developers to fix their damn calculators.

an actual PEMDAS Solver

I looked and it's actually wrong. With the exception of MathGPT, I haven't found any e-calcs which do it correctly.

Old school calculator is wrong

No, it's right. The e-calculator is wrong.

the order of operations existed at the previous turn of the century, and should operate correctly on every digital calculator ever made

Yes, they should - welcome to what happens when programmers don't bother checking their Maths is correct when writing a calculator app (hence why I wrote the thread I linked to above).