Submitted by **TheManNamedPeterPan** t3_z8c5vf
in **explainlikeimfive**

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**orangezeroalpha**
t1_iybjwhl wrote

Reply to comment by **BurnOutBrighter6** in **ELI5 why we first multiply, then add** by **TheManNamedPeterPan**

If parentheses are used most of this confusion immediately evaporates. A person can still remember how to do math decades after forgetting the "order of operations."

If someone wanted the answer to 1+2x4+3 I'd ask them why they wrote it out in a way that is so easy for typical humans to misinterpret.

May not be helpful, but my point is, avoid needless confusion if possible. One does this with parentheses. I'm not sure I can think of an example other than a math class where it would be advantageous to avoid parentheses. Long live parentheses.

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**DecentChanceOfLousy**
t1_iyc04yn wrote

Parentheses very quickly become unreadable when you have too many of them.

3(5x^3+2)^2 becomes 3*(((5*(x^3))+2)^2) without order of operations to do the implicit grouping for you. It's not incomprehensible, but it's much harder to read. Longer equations would be awful.

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**Cypher1388**
t1_iyc76hc wrote

I live in excel for work... Color coded parentheses ftw

... Seriously though, I probably use more than I need to, but they reduce ambiguity to a point that any loss of immediate readability is a sacrifice worth making imo

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**the_running_stache**
t1_iyc8r0r wrote

As a financial engineer, I write a lot of mathematical code. I, too, use more parentheses than I need to, but they reduce ambiguity to the next person reading the code. Long love parentheses!

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**DecentChanceOfLousy**
t1_iydvi3w wrote

Yup. Programming languages or technical formulas end up having so many parenthesis that most editors support color coding or matched pair highlighting so you can sort out which is which. And you'd need more if every operation had to have parenthesis around it to clarify which order it's supposed to be done in. If you kept the left-to-right convention (despite throwing other conventions which are no more arbitrary away), you could reorder some things to remove a bit of the confusion. But it wouldn't help nearly as much as every symbol having an order of operations so you skip as many parenthesis as possible while remaining unambiguous.

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**[deleted]**
t1_iyc7x79 wrote

[removed]

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**PobreCositaFea_**
t1_iyc9ded wrote

In maths you use this: [ ] and this: { } as second and third parentheses. It´s not so confusing then.

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**MoobooMagoo**
t1_iyc0zud wrote

You're not wrong, but most of the confusion with order of operations happens at the multiplication -> addition level. At least in my experience. Like 5x^2 is really obvious what it's supposed to be to most people (if you're using actual super script, anyway).

Although that said, I understand that this very well may be because once you start doing more complicated math that actually requires a lot of parentheses and exponents and stuff you've already used the order of operations so many times it starts to become second nature, so it might just be that those are more obvious because the people that are encountering them are already well practiced.

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**SirX86**
t1_iyc20rc wrote

>Like 5x^2 is really obvious what it's supposed to be to most people

In the spirit of the original question, you could argue: why is it obvious that 5x² means 5*(x²) and not (5*x)²?

Indeed people often get confused over -x²: is that (-1)*(x²) or (-1*x)²?

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**SupaFugDup**
t1_iyc6y57 wrote

Just to be sure, it is -1(x²) right?

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**-Revelation-**
t1_iyc9brh wrote

it is

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**Kalirren**
t1_iycayo7 wrote

And the answer to the "why" is because exponentiation distributes over multiplication, and not the other way around, just like multiplication distributes over addition.

xy^(2) = x*(y^2) = x*y^2 != (x*y)^2 = (xy)^(2) = x^(2)y^(2)

x*(y^2) != (x*y) ^ (x*2)

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**No-Eggplant-5396**
t1_iyed1g0 wrote

Convention. It's like the alphabet. The alphabet isn't required to be in ABC ordering by a fundamental force of nature but rather just some particular ordering for better communication.

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**DecentChanceOfLousy**
t1_iyc1nqo wrote

That is, indeed, the whole point. You practice them so that they become second nature when you do more complicated math.

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**ohyonghao**
t1_iybrk08 wrote

While taking a course in Group Theory for my mathematics degree, the author of the book declared that parenthesis are unnecessary and redundant.

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**shotsallover**
t1_iybt4f5 wrote

That must have been a fun passing grade to earn.

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**TwiNighty**
t1_iyc2of0 wrote

Because in a group, we are only dealing with a single associative binary operation, in which case parenthesis are indeed unnecessary.

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**orangezeroalpha**
t1_iybtvaa wrote

I feel for you.

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**yogert909**
t1_iybunl4 wrote

I still write parentheses when I don’t need to sometimes, but as I get more comfortable with order of operations it does make things simpler not to have all the nested parentheses in complicated equations.

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