I think the confusion is in the way it’s displayed. The notation in the comic is ambiguous, where the division is shown as a symbol, while the multiplication is implied with the brackets, so some people see the question as 8/(2*(2+2))=1, while others see it as 8/2*(2+2).
For the later, my understanding is that multiplication and division actually have equal priority and are solved left to right (rather than an explicit order as PEDMAS and BEDMAS seem to suggest). So the second interpretation would give 8/2*(2+2)=8/2*(4)=4*4=16
The reason this isn’t a problem more often is because
math questions should be written unambiguously, using symbols everywhere and fraction bars
in real life problems, there is a certain order in which you manipulate the numbers, and we can use correct notation (with an excessive number of brackets if needed) to keep it crystal clear
Also the (2+2) bit isn’t relevant to the confusion. We might as well replace it with 4 when discussing the problem. No one should be messing that bit up
I’ve heard it both ways that in PEMDAS, it’s really more like P,E,MD,AS. As in, when you reach the multiplication and division steps, it’s assumed you do them together in written order, followed by addition and subtraction after.
And like you said, the real-world measurement will actually end up dictating the order, but if this distinction needed to be made, you would separate as necessary with more parentheses.
No, literally all maths is commutative. In fact, you can arbitrarily substitute any number with another number and get the right answer. See?
4+4=8
5+3=8
9+1=8
Same for multiplication and sublimation. 5x2=8.
I could go on, but I’m pretty sure that I’ll injure myself.
But you’re literally wrong in this case. There are two different but valid ways of interpreting the equation that will result in different results. It’s written ambiguously on purpose.
I agree, which is why I don’t see why people are saying the answer is 16. You add in the parentheses, you multiply, then you divide. The answer is 1.
This left-to-right business linked below is complete nonsense when it comes to equations. That’s how westerners read books, but not how math is communicated. Am I that old? Like Mr. Incredible said, did they change math!?!
Who teaches orders of operation other than PEMDAS?
I think the confusion is in the way it’s displayed. The notation in the comic is ambiguous, where the division is shown as a symbol, while the multiplication is implied with the brackets, so some people see the question as
8/(2*(2+2))=1, while others see it as8/2*(2+2).For the later, my understanding is that multiplication and division actually have equal priority and are solved left to right (rather than an explicit order as PEDMAS and BEDMAS seem to suggest). So the second interpretation would give
8/2*(2+2)=8/2*(4)=4*4=16The reason this isn’t a problem more often is because
Also the (2+2) bit isn’t relevant to the confusion. We might as well replace it with 4 when discussing the problem. No one should be messing that bit upI’ve heard it both ways that in PEMDAS, it’s really more like P,E,MD,AS. As in, when you reach the multiplication and division steps, it’s assumed you do them together in written order, followed by addition and subtraction after.
And like you said, the real-world measurement will actually end up dictating the order, but if this distinction needed to be made, you would separate as necessary with more parentheses.
But also, all maths are commutative, so you can just mush all the numbers together using any means you desire and you’ll always get the right answer.
My math teachers all kicked me out because I was so advanced.
All maths is not communtative. Most of linear algebra and number systems above the complex numbers (i.e. quaternions and above) are not commutative.
But yes, all maths in most peoples everyday life is commutative.
Forgot my “/s,” but I’m happy to double down.
No, literally all maths is commutative. In fact, you can arbitrarily substitute any number with another number and get the right answer. See?
4+4=8
5+3=8
9+1=8
Same for multiplication and sublimation. 5x2=8.
I could go on, but I’m pretty sure that I’ll injure myself.
But you’re literally wrong in this case. There are two different but valid ways of interpreting the equation that will result in different results. It’s written ambiguously on purpose.
The parentheses are what make people accept the missing multiplication symbol.
Right, good point
We were taught BEDMAS in Canada which has the division and multiplication switched. Which still equals one.
Addition / subtraction and multiplication / division are interchangeable, so that’s still functionally identical in all aspects.
PEJMDAS. Juxtaposition is a distinct stage.
Edit: This makes it consistent with
I agree, which is why I don’t see why people are saying the answer is 16. You add in the parentheses, you multiply, then you divide. The answer is 1.
This left-to-right business linked below is complete nonsense when it comes to equations. That’s how westerners read books, but not how math is communicated. Am I that old? Like Mr. Incredible said, did they change math!?!