What is 5-5x5+5?

Feek said:
[applying the usual left-to-right interpretation, which results in the answer being 5]
Now can someone explain to me in simple terms how the answer can be anything different?
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Because enough people with enough power decided that the usual idea of interpreting things directionally (usually but not always left to right) should be partially ignored sometimes for maths because reasons.

It's as arbitrary as that. There is no good reason. It might be different in the future. It's not "the rules of mathematics". It's a wholly arbitrary standard of writing that doesn't conform to the usual standards of writing.

Feek said:
I have maths A level and genuinely, the first time I ever heard of this bodmas thing was on these forums.
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Same here. I vaguely recall there being something else when I was younger, but I forget the details.
 
Angilion said:
Because enough people with enough power decided that the usual idea of interpreting things directionally (usually but not always left to right) should be partially ignored sometimes for maths because reasons.

It's as arbitrary as that. There is no good reason. It might be different in the future. It's not "the rules of mathematics". It's a wholly arbitrary standard of writing that doesn't conform to the usual standards of writing.
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It is correct to point out it is by convention, simply because people have said it should be. It isn't completely arbitrary though and there is some benefit to putting multiplication at a higher precedence - the purpose of having these conventions is to remove the need for parentheses, make things less verbose/clunky, by giving multiplication a higher precedence you've lessened the need for parentheses - think about writing out a higher-order polynomial for example etc...

So yes a deliberate choice has been made but that choice isn't completely devoid of reason, it is practical too.
 
dowie said:
It is correct to point out it is by convention, simply because people have said it should be. It isn't completely arbitrary though and there is some benefit to putting multiplication at a higher precedence - the purpose of having these conventions is to remove the need for parentheses, make things less verbose/clunky, by giving multiplication a higher precedence you've lessened the need for parentheses - think about writing out a higher-order polynomial for example etc...

So yes a deliberate choice has been made but that choice isn't completely devoid of reason, it is practical too.
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Fair point. It's less practical for simpler maths, but having a single standard for all written maths has its own very practical benefits.
 
dowie said:
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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Of course is by convention that you know where to put the brackets. It's not the BODMAS convention though. All you need to know is that you put brackets around everything which isn't addition or subtraction.
So, take 2x^2
Put brackets around the multiplication:
(2 x x^2)
Now or brackets around the powers:
(2 x (x^2))

Or, put brackets around the power first:
2 x (x^2)
Then around the multiplication:
(2 x (x^2))

Both give the same answer. You need to know some rules/conventions for how to add brackets but you don't need to know the order of operations to do it.

The fact that there are many people using that method and not failing at maths proves that you're wrong and BODMAS is not the only way to solve it.
 
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touch said:
Put brackets around the multiplication:
(2 x x^2)
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Why have you put brackets around the whole thing and *not* (2 x x)^2? How do you know? That's the question I think. (A dot is often used in maths to replace the multiplication sign and thus avoid confusion with the algebraic unknown x. So the above equation can be shown as (2.x)^2, which is a little less confusing.)

I think you're doing partial (and therefore incorrect except for trivial contrived examples) BODMAS. You say put brackets around everything that isn't addition or subtraction. So all you're doing is saying that BODM are all equal priority, which is incorrect.

touch said:
The fact that there are many people using that method and not failing at maths proves that you're wrong and BODMAS is not the only way to solve it.
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I think this thread shows that many people are failing at maths, and don't even realise it, which is a bit scary...
 
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Another method of notation rather than bracketing everything is to use a point or full stop as in 2.x^2 to seperate the multiplier 2 and the value raised to the power. When I used to write a lot of calculation by hand I often resorted to various ways to clarify my workings. Latterly I used TEDDS for Word to compose live calculations in documents and let the software do its worst. Usually it understood my intentions and rubbish in, rubbish out was avoided.
 
nightwish said:
I think you're doing partial (and therefore incorrect except for trivial contrived examples) BODMAS. You say put brackets around everything that isn't addition or subtraction. So all you're doing is saying that BODM are all equal priority, which is incorrect.
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It doesn't really make BODM equal priority, because when you add brackets around something like the x^2 that's always going to be the innermost bracket which will get evaluated first.
It doesn't change the order things will be evaluated, it's just another process to get to the same order (and therefor same result) without needing to actually know the order of operations.
 
touch said:
Of course is by convention that you know where to put the brackets. It's not the BODMAS convention though. All you need to know is that you put brackets around everything which isn't addition or subtraction.
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Please read more carefully - I didn't ask you to put any brackets anywhere, you've given some bizarre reply where you've put some pointless brackets in?

touch said:
Both give the same answer. You need to know some rules/conventions for how to add brackets but you don't need to know the order of operations to do it.

The fact that there are many people using that method and not failing at maths proves that you're wrong and BODMAS is not the only way to solve it.
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Nope...

Again the example I gave you was 2x^2 - there are no brackets in that example, there is no addition or subtraction the point being made is quite a simple one - you need to know the order of operations (i.e. that exponents have priority over multiplication) in order to correctly read that example as intended, that's all.

If you don't believe you need to know the order of operations then please explain how you can correctly read it with the exponent having priority over multiplication?

Do you not understand that (2x)^2 and 2(x^2) are different? i.e. if you gave priority to multiplication instead of exponents you could end up with a different answer?

Hagar said:
Another method of notation rather than bracketing everything is to use a point or full stop as in 2.x^2 to seperate the multiplier 2 and the value raised to the power.
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That doesn't change anything here - whether multiplication is implied or you've thrown in a . or a * the exponent still takes priority.
 
dowie said:
Again the example I gave you was 2x^2 - there are no brackets in that example
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It's fine to add extra brackets in to make a calculation clearer. It doesn't change the calculation.

dowie said:
Do you not understand that (2x)^2 and 2(x^2) are different? i.e. if you gave priority to multiplication instead of exponents you could end up with a different answer?
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No, you're doing it wrong. Look at my post again:

touch said:
So, take 2x^2
Put brackets around the multiplication:
(2 x x^2)
Now or brackets around the powers:
(2 x (x^2))

Or, put brackets around the power first:
2 x (x^2)
Then around the multiplication:
(2 x (x^2))
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The 2 lines in bold are arrived at using different orders of adding the brackets, because it doesn't matter which order you add the brackets.
Can you explain why you think these bold lines give different answers?
 
Any brackets rule that consistently gives you the same answer as BODMAS in *all* cases must be equivalent to BODMAS. If it does not, then it is incorrect.

What, exactly, is this brackets rule? Please define it precisely. I rather suspect the way it's being used here is the outcome of bad teaching plus poor understanding plus poor memory and can be debunked pretty easily if you can describe exactly what it is in the first place. If you cannot, well that tells it's own story...
 
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touch said:
So, take 2x^2
Put brackets around the multiplication:
(2 x x^2)
Now or brackets around the powers:
(2 x (x^2))

Or, put brackets around the power first:
2 x (x^2)
Then around the multiplication:
(2 x (x^2))
Click to expand...
The 2 lines in bold are arrived at using different orders of adding the brackets, because it doesn't matter which order you add the brackets.
Can you explain why you think these bold lines give different answers?
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Your lines in bold don't give different answers ergo I'm not sure what you think you're illustrating there, your outer set of brackets add nothing, all you've done in each case is to apply some brackets to the exponent term in order to give it priority.

The question was how do you know to prioritize the exponent term over multiplication i.e. how do you know to read: 2x^2 as 2(x^2) and not (2x)^2?

Do you not understand the question?

Let's say x is 3 then...

with the exponent given priority we'd have:
2(3^2) = 18

with multiplication given priority we'd have:
(2*3)^2 = 36

The point being made here is that you need to know that, by convention, we prioritize the exponent.

nightwish said:
Any brackets rule that consistently gives you the same answer as BODMAS in *all* cases must be equivalent to BODMAS. If it does not, then it is incorrect.

What, exactly, is this brackets rule? Please define it precisely. I rather suspect the way it's being used here is the outcome of bad teaching plus poor understanding plus poor memory and can be debunked pretty easily if you can describe exactly what it is in the first place. If you cannot, well that tells it's own story...
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I don't think he can, he's just put brackets around the exponent and some redundant set of brackets around the whole thing. He doesn't seem to realise that he's simply given priority to the exponent term, which is of course by convention as per the order of operations.
 
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dowie said:
That doesn't change anything here - whether multiplication is implied or you've thrown in a . or a * the exponent still takes priority.
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You are right. All notation does is to help the reader, reviewer or checker of the methodology and the results. It is also true that maths and algebra is taught so that mathematicians can converse using a common language and understand the workings using conventions and avoiding copious margin notes in the authors spoken language.
 
This is the ultimate irrelevant discussion :p

BUT it’s obvs -15.

We had a super heated version of this on here about 15 years ago, with a slightly different maths problem.
 
Nitefly said:
We had a super heated version of this on here about 15 years ago, with a slightly different maths problem.
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Big difference with that one, the question in the OP isn't controversial, it's just catching out a few people who have forgotten the basics and seems to have provoked some dodgy maths takes by some.

The one that you're thinking of is the one addressed in the youtube video posted above in #114, it involves implied multiplication and division in the same line and there are two ways of handling that implied multiplication - giving it higher precedence isn't something covered by BODMAS etc.. but is a convention that is sometimes adopted ergo it appears on facebook, twitter etc.. every so often and causes a bit bun fight.
 
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