this post was submitted on 07 Dec 2023
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8Γ·2(2+2) comes out to 16, not 1.
Saw it posted on Instagram or Facebook or somewhere and all of the top comments were saying 1. Any comment saying 16 had tons of comments ironically telling that person to go back to first grade and calling them stupid.
Let's see.
8Γ·2Γ(2+2) = 8Γ·2Γ4
At this point, you solve it left to right because division and multiplication are on the same level. BODMAS and PEMDAS were created by teachers to make it easier to remember, but ultimately, they are on the same level, meaning you solve it left-to-right, so....
8Γ·2Γ4 = 4Γ4 = 16.
So yes, it does equal 16.
Under pemdas divisor operators must literally be completed after multiplication. They are not of equal priority unless you restructure the problem to be of multiplication form, which requires making assumptions about the intent of the expression.
Okay, let me put it in other words: Pemdas and bodmas are bullshit. They are made up to help you memorise the order of operations. Multiplication and division are on the same level, so you do them linearly aka left to right.
Pemdas and bodmas are not bullshit, they are a standard to disambiguate expression communication. They are order of operations. Multiplication and division are not on the same level, they are distinct operations which form the identity when combined with a multiplication.
Similarly, log(x) and e^x are not the same operation, but form identity when composited.
Formulations of division in algebra allow it to be at the same priority as multiplication by restructuring it as multiplication, but that requires formulating the expression a particular way. The Γ· operator however is strictly division. That's its purpose. It's not a fantastic operator for common usage because of this.
There are valid orders of operations, such as depmas which I just made up which would make the above expression extremely ambiguous. Completely mathematically valid, order of ops is an established convention, not mathematical fact.
This comment is the epitome of being confidently wrong on the internet.
For one misinterpretation? Are you sure about that?
There was 3 misinterpretations - see my reply to them.
I made a hashtag for people #LoudlyNotUnderstandingThings :-)
No, they're not.
Yes, they are.
In other words, they are the inverse operation of each other - welcome to why they have the same precedence.
It's a mathematical fact.
Not literally. It's only a mnemonic, not the actual rules.
Yes, they are. Binary operators have equal precedence, and unary operators have equal precedence.
And both you and people arguing that it's 1 would be wrong.
This problem is stated ambiguously and implied multiplication sign between 2 and ( is often interpreted as having priority. This is all matter of convention.
I see what you're getting at but the issue isn't really the assumed multiplication symbol and it's priority. It's the fact that when there is implicit multiplication present in an algebraic expression, and really best practice for any math above algebra, you should never use the 'Γ·' symbol. You need to represent the division as a numerator and denominator which gets rid of any ambiguity since the problem will explicitly show whether (2+2) is modifying the numerator or denominator. Honestly after 7th grade I can't say I ever saw a 'Γ·' being used and I guess this is why.
That said, I'll die on a hill that this is 16.
Rest in peace
Under normal interpretations of pemdas this is simply wrong, but it's ok. Left to right only applies very last, meaning the divisor operator must literally come after 2(4).
This isn't really one of the ambiguous ones but it's fair to consider it unclear.
Pemdas puts division and multiplication on the same level, so 34/22 is 12 not 3. Implicit multiplication is also multiplication. It's a question of convention, but by default, it's 16.
https://en.m.wikipedia.org/wiki/Order_of_operations
There's no such thing as implicit multiplication. The answer is 1.
I don't know what you're on about with your distributive law thing. That just states that
a*(b + c) = a*b + a*c, and has literally no relation to notation.And "math is never ambiguous" is a very bold claim, and certainly doesn't hold for mathematical notation. For some simple exanples, see here: https://math.stackexchange.com/questions/1024280/most-ambiguous-and-inconsistent-phrases-and-notations-in-maths#1024302
No, The Distributive Law states that a(b+c)=(ab+ac), and that you must expand before you simplify.
Examples by people who simply don't remember all the rules of Maths. Did you read the answers?
Please learn some math before making more blatantly incorrect statements. Quoting yourself as a source is... an interesting thing to do.
https://en.m.wikipedia.org/wiki/Distributive_property
I did read the answers, try doing that yourself.
That is incorrect. Multiplication does NOT have presedence of division, they are equal. So it's left to right, which means division comes first.
Which brings you to a yet further ambiguous expression. I maintain that's a poor choice.
#MathsIsNeverAmbiguous if you follow all the rules of Maths (there's a lot of people here who aren't).
Back in gradeschool I was always taught that in Pemdas, the parenthesis are assumed to be there in 8Γ·(2Γ(2+2)) where as 8Γ·2Γ(2+2) would be 16, 8Γ·2(2+2) is the above and equals 1.
Not quite. It's true you resolve what's inside the parentheses first, giving you. 8Γ·2(4) or 8Γ·2x4.
Now this is what gets most people. Even though Multiplication technically comes before Division the Acronym PEMDAS, that's really just to make it sound correct phonetically. Really they have equal priority in the order of operations and the appropriate way to resolve the problem is to work from left to right solving each multiplication or division sign as you encounter them. Giving you 16. Same for addition and subtraction.
So basically the true order of operations is:
Source: Mechanical Engineering degree so an unfortunate amount of my life spent in math and physics classes.
Absolutely, its all seen as equal so it has to go left to right However as I said in the beginning the way I was taught atleast, is when you see 2(2+2) and not 2Γ(2+2) you assume that 2(2+2) actually means (2Γ(2+2 )) and so must do it together.
That's basically what I was taught, too.
Edit to add: Ha, I just realized how similar our usernames are. Neat! :)
2(4) is not exactly same as 2x4.
Correct! It's exactly the same as (2x4).