2 + 3 * 4 = 14 using the order of operations [parenthesis, multiplication, addition].
2 + (3 * 4) = 14 using the order of operations [parenthesis, addition, multiplication].
There, two different orders of operation, the same answer.
But they’re the same order of operations - you didn’t do multiplication last in the second example, you did it first, because it was inside brackets.
In terms of BEDMAS…
2+3x4=2+12=14 M A
2+(3x4)=2+12=14 B A
Same order of operations rules! This is what I keep saying to you - there’s no way around it! We didn’t choose it, it’s a law of nature. The only thing we chose is how to write it. It’s the same with the Laws of Physics - they are laws of nature, and we just chose how to write them.
You changed my equation, so of course it is going to be wrong
No, I didn’t. I simply substituted addition for multiplication, as per the definition of multiplication as shorthand for addition, which in the previous comment you weren’t contesting. Analogy, if you wrote 2, and I substituted 1+1, then that doesn’t change the answer because 1+1=2. In the same way, 4x10=4+4+4+4+4+4+4+4+4+4
You said…
does 3 + 4 * 10 + 7 equal 77
And so I did the Maths. We know, by definition 4x10=4+4+4+4+4+4+4+4+4+4, therefore I can swap those around with each other and it doesn’t change the answer. So…
3+4+4+4+4+4+4+4+4+4+4+7=50, which does not equal 77! The answer is wrong, because the answer is, you know, wrong.
If I changed your 2 + 3 * 4 to (2 + 3) * 4, then then your answer would be 20 and that would be “wrong”.
No, because adding brackets around addition does change the answer, because now you’re doing the addition first, because it’s inside brackets. (2+3)x4 does equal 20, and 2+3x4 does equal 14 - they are 2 different equations, and have different answers. You changed the answer when you added the brackets to say “do this addition first instead of the multiplication”.
right answer is 14 because that is what the order of operations give us
NO, because that’s what arithmetic gives us - nothing to do with order of operations.
Here it is on a number line (no order of operations involved at all)…
And now, since we already know that the answer is 14, we can deduce the order of operations rules needed to make it so… which is multiplication before addition, and that is because multiplication is a shorthand form of addition! There are no other order of operations rules which work, only this works.
No, they’re not the same order of operations. If I left out the parentheses the answer would have been 20 instead of 14. Stop assuming my example are incorrect or I have made some kind of error.
Listen I have to bow out of this conversation. I haven’t found any of your arguments relevant let alone convincing. And every time you reply, you seem to intentionally miss any point that I’m making while being snarky and insulting. It’s extremely frustrating to me.
Seriously, I don’t know if this is sunken cost fallacy issue that you’re having. Or if you’re some kind of AI designed to maximize my frustration.
I’m sorry I have to end this conversation, but there other things I’d like to focus on in my life.
If I left out the parentheses the answer would have been 20 instead of 14
Did you get that answer from the Windows calculator? That’s a bug in “Standard” mode. You need to put it in Scientific mode to get the right answer (I guess no-one has noticed that the “standard” mode is wrong, cos no-one uses it usually).
they’re not the same order of operations. If I left out the parentheses the answer would have been 20 instead of 14
No it wouldn’t. B E D M A S. I even showed you on the number line why it’s 14 (which you’ve ignored). No wonder you don’t understand what I’m talking about if you think the answer is 20.
Stop assuming my example are incorrect or I have made some kind of error
There’s no assumption - I’m a Maths teacher. If you think the answer is 20 then you did make an error.
you’re some kind of AI designed to maximize my frustration
No, just trying to show you how Maths works. Some other people thanked me.
But they’re the same order of operations - you didn’t do multiplication last in the second example, you did it first, because it was inside brackets.
In terms of BEDMAS…
2+3x4=2+12=14 M A
2+(3x4)=2+12=14 B A
Same order of operations rules! This is what I keep saying to you - there’s no way around it! We didn’t choose it, it’s a law of nature. The only thing we chose is how to write it. It’s the same with the Laws of Physics - they are laws of nature, and we just chose how to write them.
No, I didn’t. I simply substituted addition for multiplication, as per the definition of multiplication as shorthand for addition, which in the previous comment you weren’t contesting. Analogy, if you wrote 2, and I substituted 1+1, then that doesn’t change the answer because 1+1=2. In the same way, 4x10=4+4+4+4+4+4+4+4+4+4
You said…
And so I did the Maths. We know, by definition 4x10=4+4+4+4+4+4+4+4+4+4, therefore I can swap those around with each other and it doesn’t change the answer. So…
3+4+4+4+4+4+4+4+4+4+4+7=50, which does not equal 77! The answer is wrong, because the answer is, you know, wrong.
No, because adding brackets around addition does change the answer, because now you’re doing the addition first, because it’s inside brackets. (2+3)x4 does equal 20, and 2+3x4 does equal 14 - they are 2 different equations, and have different answers. You changed the answer when you added the brackets to say “do this addition first instead of the multiplication”.
NO, because that’s what arithmetic gives us - nothing to do with order of operations.
Here it is on a number line (no order of operations involved at all)…
And now, since we already know that the answer is 14, we can deduce the order of operations rules needed to make it so… which is multiplication before addition, and that is because multiplication is a shorthand form of addition! There are no other order of operations rules which work, only this works.
No, they’re not the same order of operations. If I left out the parentheses the answer would have been 20 instead of 14. Stop assuming my example are incorrect or I have made some kind of error.
Listen I have to bow out of this conversation. I haven’t found any of your arguments relevant let alone convincing. And every time you reply, you seem to intentionally miss any point that I’m making while being snarky and insulting. It’s extremely frustrating to me.
Seriously, I don’t know if this is sunken cost fallacy issue that you’re having. Or if you’re some kind of AI designed to maximize my frustration.
I’m sorry I have to end this conversation, but there other things I’d like to focus on in my life.
I wish you well.
Did you get that answer from the Windows calculator? That’s a bug in “Standard” mode. You need to put it in Scientific mode to get the right answer (I guess no-one has noticed that the “standard” mode is wrong, cos no-one uses it usually).
No it wouldn’t. B E D M A S. I even showed you on the number line why it’s 14 (which you’ve ignored). No wonder you don’t understand what I’m talking about if you think the answer is 20.
There’s no assumption - I’m a Maths teacher. If you think the answer is 20 then you did make an error.
No, just trying to show you how Maths works. Some other people thanked me.