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Alright settle down it's only a commercial.
What is 5-5x5+5?
- Thread starter Lysander
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I know, I saw you mention that there was no acronym, the point is that the order of operations still matters regardless of whether you learned an acronym at school, the answer is still -15. This isn't some brand new concept. You did ask for someone to explain why it is -15, the maths hasn't changed here.
Edit - the acronyms have existed since the late 1800s so you might have simply forgotten but more importantly the order of operations has been there for well over a century whether your teacher taught an acronym or not.
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As he must recognise to some degree, as that's what tells him to do brackets first and not just do left-to-right regardless
As he must recognise to some degree, as that's what tells him to do brackets first and not just do left-to-right regardless
Well yeah, and I doubt anyone can find an example of a textbook from the past 50 years where literally everything was bracketed, it would be pointlessly verbose. Even if we are to assume some erratic, crazy maths teacher who has taught a class that only brackets matter and then stuck them around everything.
I think people just tend to forget the basics or don't pay attention to these things, why say 2x^2 is read as 2(x^2) and not (2x)^2 etc... the conventions have been there for a few centuries and the mnemonics for over 100 years:
http://www.math.ucdenver.edu/~jloats/Student pdfs/4_Order of OperationsSass.pdf
If you know 2x^2 is read as 2(x^2) then you don't need to know the order of operations to solve it. (As long as you know brackets need to be solved first).
You'd only need to know the order to solve it if you didn't know that 2x^2 implied 2(x^2).
It's the order of operations that means we know to read 2x^2 as 2(x^2) and not (2x)^2, because they are what tells us indices have a higher precedent than multiplication
I'm starting to feel like there must be some Inception style 'wind up within a wind up' posts going on hereLOL wat?
How do you know it is to be read as 2(x^2) in the first place?
Quite possibly, though there have been threads like this before with some spectacularly bad takes.
LOL wat?
How do you know it is to be read as 2(x^2) in the first place?
Because you've learnt that way.
You need to know various rules to understand maths. You don't specifically need to know the order of operations.
Interpreting how to put the brackets into it is essentially doing the same thing as defining the order, just with a slightly different process.
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insert video of george carlin explaining half the people are dumber than average but some are full of it and some are nuts.
Yes, you've learned.... which order to perform the operations!
Well, you do in this case, the rules in question literally are which order to perform operations....
It literally is defining the order of those operations... that's the point!
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He's referring to a different problem where there is some implied multiplication before a set of parentheses and division on the same line, that's where there are differing conventions. See also page 2 of the link at the bottom of post #104.
It isn't really a dilemma these days as we don't generally use typewriters or printers that need to keep everything on one line so don't have much need for this symbol: ÷ or a forward slash / rather we can use a horizontal line to separate the numerator and denominator.
Nope... if 2x^2 was (2x)^2 (i.e. multiplication had precedence over exponents) then that wouldn't (by definition) be equivalent to 4x^2 it would, however, be 4(x^2)... since 4x^2 (with multiplication at a higher precedence), would be (4x) * (4x) so 16(x^2)... best that you keep up yourself
The precedence of operations is entirely arbitrary and by convention, it's not something you can make an argument for one way or another beyond simply people deciding it is so.
No. If you learn how to correctly add the brackets then you don't need to know the order of operations.
Add brackets around anything which isn't addition or subtraction. It doesn't matter which order you add the brackets. Using 1 + 2x^2 as an example, you can start with bracketing the multiplication first:
1 + (2 x x^2)
1 + (2 x (x^2))
Or you can start with bracketing the power first:
1 + 2(x^2)
1 + (2 x (x^2))
You get the same result both ways and then you don't need to know the order of operations to calculate the answer either - just calculate innermost bracket first and work out.
BODMAS is a simpler way to do it because it can get complicated with multiple nested brackets but your wrong to say that's the only way it can be done.
Wat???
There are no brackets in the example I gave! I used brackets in the explanation of that example to illustrate the difference in the way it could be interpreted depending on what priority is given to the order of those operations!
No, this is just plain wrong. I'll try a longer explanation.
The example I gave was: 2x^2
Now read it carefully and note there is no addition or subtraction there, there are no brackets...
By convention, it is read as 2(x^2) and not (2x)^2 - i.e. in order to read it correctly, you need to know that the convention is that the exponents have higher precedence than multiplication!
You don't get the same result both ways, this can be shown quite easily:
suppose x = 3
2(3^2) = 18
(2*3)^2 = 36
Those results are not the same!
So again, in order to write 2x^2 without using brackets and have what you mean understood by others there needs to be a convention re: whether the exponent or the multiplication comes first i.e. an order for those operations.... We have these conventions because sticking brackets around everything becomes pointlessly verbose and even then when using brackets, you at least need to know that brackets have higher precedence than everything else!
If you don't believe me then explain how you know that 2x^2 is read as 2(x^2) and not (2x)^2 other than by convention?
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