You don’t do multiplication before division, they’re equal operations, so you go left to right. 8 x 0.5 (2 + 2) is the same from a mathematical point of view.
Parenthesis comes first, do everything in each of them as though they were a whole equation to themselves.
8/2(2+2) = 8/2(4)
Then you do your exponents. The equation doesn’t have any, so we can go ahead and skip those.
Multiplication and division are the same operation, just flipped around, so you go left to right and do those as you come across them. A number next to a parenthesis means multiplication, so to simplify:
8/2(4) = 8/2x4
8/2x4 = 4x4
4x4 = 16
Addition and subtraction don’t have any weird effects on the outcomes of each other, so you go left to right and do them as they come up. This equation has no more addition or subtraction to do, so we can consider what we have left our answer.
Therefore: 8/2(2+2)=16
This is straight from the textbook. You are wrong, and so are your purpose-built calculators.
You can do this without needing to replace by using a backslash. 1*2 comes from 1\*2.
Anyway, the problem with your logic is that it’s using rules designed for primary school by one random primary school teacher many decades ago. Not a rigorous mathematical convention.
In real maths, mathematicians frequently use juxtaposition to indicate multiplication at a higher priority than division. Rather than BIDMAS, something like BIJMDAS might work. But that isn’t as catchy, and more to the point: it requires understanding of an operation that doesn’t get used in primary school, so would be silly to put in to a mnemonic designed to aid probably school children.
…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
Anyway, I’m the time that is relevant here is when you’ve done the various relevant mathematical tools, but haven’t yet been exposed to multiplication by juxtaposition. Which I’m fairly sure for me at least was in year 6.
It’s an actual rule which is centuries old.
No, the idea of specifically codifying BIDMAS comes from the early 1900s.
I don’t know why you’re going throughout this thread over multiple hours spamming out your nonsense, but it’s wrong. BIDMAS is a convention, and a very useful one, but only because we instinctively know juxtaposition actually comes before explicit multiplication or division, and a rigid primary school application of BIDMAS will lead you to the wrong answer.
Thankfully, I think you know that last part. Because I think that’s what you mean when you keep saying “it’s called terms”. But that, too, is wrong. It’s used in terms, for sure. y = 2x2 + 91/2)x - 4 contains three terms, the x2 term is 2x2, etc. But if I then changed the constant term to be 4(2 - 3×5) + 1, all of that would still only be the one term. Terms and multiplication by juxtaposition can work together, but fundamentally refer to entirely different aspects of mathematics. Juxtaposition is a notational thing, while terms are a fundamental aspect of the equation itself.
Oh really? My apologies then. I’ve only ever heard Year 7 called high school or middle school, never primary school. What country is that in?
multiplication by juxtaposition. Which I’m fairly sure for me at least was in year 6
I’ve seen some Year 6 classes do some pre-algebra (like “what number goes in this box to make this true”), but Year 7 is when it’s properly first taught. Every textbook I’ve ever seen it in has been Year 7 (and Year 8, as revision).
Also, it’s not “multiplication by juxtaposition”, since it’s not multiplication - it’s The Distributive Law - which is Distribution - and/or Terms - which is a product, which is the result of a multiplication.
No, the idea of specifically codifying BIDMAS comes from the early 1900s
The order of operations rules are older than that - we can see in Lennes’ letter (1917) that all the textbooks were already using it then, and Cajori says - in 1928 - that the order of operations rules are at least 300 years old (which now makes them at least 400 years old).
If you’re talking about when was the mnemonic BIDMAS made up, that I don’t know, but the mnemonics are only ways to remember the rules anyway, not the actual rules.
I don’t know why you’re going throughout this thread
I’m a Maths teacher, that’s what we do. :-)
a rigid primary school application of BIDMAS will lead you to the wrong answer
Only if the bracketed term has a coefficient (welcome to how Texas Instruments gets the wrong answer), which is never the case in Primary School questions - that’s taught in Year 7 (when we teach The Distributive Law).
juxtaposition actually comes before explicit multiplication… I think that’s what you mean when you keep saying “it’s called terms”
Terms come before operators, and we never call it juxtaposition, because The Distributive Law is also what people are calling “strong juxtaposition” (and/or “implicit multiplication”), but is a separate rule, so to lump 2 different rules together under 1 name is where a lot of people end up going wrong. There’s a Youtube where the woman gets confused by a calculator’s behaviour and she says “sometimes it obeys juxtaposition and sometimes it doesn’t” (cos she lumped those 2 rules together), and I for one can see clear as day the issue is it’s obeying Terms but not obeying The Distributive Law (but she lumped them together and doesn’t understand these are 2 separate behaviours).
Terms and multiplication by juxtaposition can work together
But that’s my point, there’s no such thing as “multiplication by juxtaposition”. A Term is a product, which is the result of a multiplication.
If a=2 and b=3 then…
axb=2x3 - 2 terms
ab=6 - 1 term
In the mnemonics “Multiplication” refers literally to multiplication signs, and nothing else. The Distributive Law is done as part of solving Brackets, and there’s nothing that needs doing with Terms, since they’re already simplified (unless you’ve been given some values for the pronumerals, in which case you can substitute in the values, but see above for the correct way to do this with ab, though you could also do (2x3), but absolutely never 2x3, cos then you just broke up the term, and get the wrong answer - brackets can’t be removed unless there is only 1 term left inside. People writing 2(3)=2x3 are making the same mistake).
Multiplication and division are same level just as addition and subtraction are same level. So it would be worked multiplication and division in order from left to right.
In PEMDAS M does not get priority over D so the equation has to be executed in order: 8/2=4, 4*4=16. You would be correct if all PEMDAS were a priority list., but it is not.
My public school education on pemdas is that for multiplication/division and addition/subtraction, you do them on order from left to right. Doing it that way gets me 16, which I believe to be right, but I’m also very bad at math. The way you had explained is also technically correct, if you do the multiplication out of order. Now that I think about it, 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, both are right, but I know that’s wrong, I just don’t know why
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.
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.
Agree completely. Old school calculator is wrong, but why? Pemdas wasn’t really big in school curriculums until around the turn of the century, but the order of operations existed at the previous turn of the century, and should operate correctly on every digital calculator ever made…
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).
Think of it like this: if you wrote it as a fraction instead of using the divide symbol, the implicit multiplication would only make sense if both were in the denominator.
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Nope. It’s PEMDAS at work.
8/2(2+2)
8/2(4) - Parentheses
8/8 - Multiplication
1 - Division
Modern phone apps seem to be notorious for getting order of operations wrong. I’ve never had this issue with a dedicated calculator.
Edit: my petard has been hoisted
You don’t do multiplication before division, they’re equal operations, so you go left to right. 8 x 0.5 (2 + 2) is the same from a mathematical point of view.
I’ve always been taught that + and - were interchangeable with each other for pemdas, as well as * and /. So the hierarchy is
Actively wrong.
PE(MD)(AS).
Parenthesis comes first, do everything in each of them as though they were a whole equation to themselves.
8/2(2+2) = 8/2(4)
Then you do your exponents. The equation doesn’t have any, so we can go ahead and skip those.
Multiplication and division are the same operation, just flipped around, so you go left to right and do those as you come across them. A number next to a parenthesis means multiplication, so to simplify:
8/2(4) = 8/2x4
8/2x4 = 4x4
4x4 = 16
Addition and subtraction don’t have any weird effects on the outcomes of each other, so you go left to right and do them as they come up. This equation has no more addition or subtraction to do, so we can consider what we have left our answer.
Therefore: 8/2(2+2)=16
This is straight from the textbook. You are wrong, and so are your purpose-built calculators.
EDIT: Replaced * with x to avoid italicising.
You can do this without needing to replace by using a backslash. 1*2 comes from
1\*2.Anyway, the problem with your logic is that it’s using rules designed for primary school by one random primary school teacher many decades ago. Not a rigorous mathematical convention.
In real maths, mathematicians frequently use juxtaposition to indicate multiplication at a higher priority than division. Rather than BIDMAS, something like BIJMDAS might work. But that isn’t as catchy, and more to the point: it requires understanding of an operation that doesn’t get used in primary school, so would be silly to put in to a mnemonic designed to aid probably school children.
Just looked it up. Everything I know is a lie. Thank you, kind stranger on the internet. I’m going to go have an existential crisis, now.
…including the comment you just replied to. Here is a thread with actual textbook references, historical Maths documents, worked examples, proofs, the works.
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.
It’s an actual rule which is centuries old.
It’s not multiplication - it’s either The Distributive Law or Terms, which are 2 separate rules.
Yes, as I said it’s taught in Year 7.
When I was in school, year 7 was primary school.
Anyway, I’m the time that is relevant here is when you’ve done the various relevant mathematical tools, but haven’t yet been exposed to multiplication by juxtaposition. Which I’m fairly sure for me at least was in year 6.
No, the idea of specifically codifying BIDMAS comes from the early 1900s.
I don’t know why you’re going throughout this thread over multiple hours spamming out your nonsense, but it’s wrong. BIDMAS is a convention, and a very useful one, but only because we instinctively know juxtaposition actually comes before explicit multiplication or division, and a rigid primary school application of BIDMAS will lead you to the wrong answer.
Thankfully, I think you know that last part. Because I think that’s what you mean when you keep saying “it’s called terms”. But that, too, is wrong. It’s used in terms, for sure. y = 2x2 + 91/2)x - 4 contains three terms, the x2 term is 2x2, etc. But if I then changed the constant term to be 4(2 - 3×5) + 1, all of that would still only be the one term. Terms and multiplication by juxtaposition can work together, but fundamentally refer to entirely different aspects of mathematics. Juxtaposition is a notational thing, while terms are a fundamental aspect of the equation itself.
Oh really? My apologies then. I’ve only ever heard Year 7 called high school or middle school, never primary school. What country is that in?
I’ve seen some Year 6 classes do some pre-algebra (like “what number goes in this box to make this true”), but Year 7 is when it’s properly first taught. Every textbook I’ve ever seen it in has been Year 7 (and Year 8, as revision).
Also, it’s not “multiplication by juxtaposition”, since it’s not multiplication - it’s The Distributive Law - which is Distribution - and/or Terms - which is a product, which is the result of a multiplication.
The order of operations rules are older than that - we can see in Lennes’ letter (1917) that all the textbooks were already using it then, and Cajori says - in 1928 - that the order of operations rules are at least 300 years old (which now makes them at least 400 years old).
If you’re talking about when was the mnemonic BIDMAS made up, that I don’t know, but the mnemonics are only ways to remember the rules anyway, not the actual rules.
I’m a Maths teacher, that’s what we do. :-)
Only if the bracketed term has a coefficient (welcome to how Texas Instruments gets the wrong answer), which is never the case in Primary School questions - that’s taught in Year 7 (when we teach The Distributive Law).
Terms come before operators, and we never call it juxtaposition, because The Distributive Law is also what people are calling “strong juxtaposition” (and/or “implicit multiplication”), but is a separate rule, so to lump 2 different rules together under 1 name is where a lot of people end up going wrong. There’s a Youtube where the woman gets confused by a calculator’s behaviour and she says “sometimes it obeys juxtaposition and sometimes it doesn’t” (cos she lumped those 2 rules together), and I for one can see clear as day the issue is it’s obeying Terms but not obeying The Distributive Law (but she lumped them together and doesn’t understand these are 2 separate behaviours).
But that’s my point, there’s no such thing as “multiplication by juxtaposition”. A Term is a product, which is the result of a multiplication.
If a=2 and b=3 then…
axb=2x3 - 2 terms
ab=6 - 1 term
In the mnemonics “Multiplication” refers literally to multiplication signs, and nothing else. The Distributive Law is done as part of solving Brackets, and there’s nothing that needs doing with Terms, since they’re already simplified (unless you’ve been given some values for the pronumerals, in which case you can substitute in the values, but see above for the correct way to do this with ab, though you could also do (2x3), but absolutely never 2x3, cos then you just broke up the term, and get the wrong answer - brackets can’t be removed unless there is only 1 term left inside. People writing 2(3)=2x3 are making the same mistake).
You haven’t finished Brackets yet! The next step is…
8/(2x4)=8/8
Not any textbook I’ve seen. Screenshot? Here’s some actual textbooks
Child, this thread is literally four months old. Get a life.
Yeah, didn’t think that came from any textbook.
Multiplication and division are same level just as addition and subtraction are same level. So it would be worked multiplication and division in order from left to right.
In PEMDAS M does not get priority over D so the equation has to be executed in order: 8/2=4, 4*4=16. You would be correct if all PEMDAS were a priority list., but it is not.
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
My public school education on pemdas is that for multiplication/division and addition/subtraction, you do them on order from left to right. Doing it that way gets me 16, which I believe to be right, but I’m also very bad at math. The way you had explained is also technically correct, if you do the multiplication out of order. Now that I think about it, 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, both are right, but I know that’s wrong, I just don’t know why
No, that’s the correct way to do it, as per The Distributive Law.
No, only 1 is right. If you get 16 then you did division before finishing solving brackets.
just requires using the proper calculator:
2 2 + 2 * 8 / .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! 😂
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).
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.
Agree completely. Old school calculator is wrong, but why? Pemdas wasn’t really big in school curriculums until around the turn of the century, but the order of operations existed at the previous turn of the century, and should operate correctly on every digital calculator ever made…
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The ad filled app sucks for sure, but it is correct in this case.
There’s 4 levels to PEMDAS, not 6.
Also,
an actual PEMDAS Solver:
https://www.symbolab.com/solver/step-by-step/8\div2(2%2B2)?or=input
I looked and it’s actually wrong. With the exception of MathGPT, I haven’t found any e-calcs which do it correctly.
No, it’s right. The e-calculator is wrong.
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).
Think of it like this: if you wrote it as a fraction instead of using the divide symbol, the implicit multiplication would only make sense if both were in the denominator.