How many times - stop putting * or x signs where they are not stated.
Y(b + c) = (Yb + Yc)
Y times (b + c) = Y * (b +c) = Y x (b +c)
The * or times sign means that the Y never goes inside the bracket, Y next to a bracket without an other operator means that the Y is part of the bracket (e.g. it is a factorial, etc.)
Completely wrong...
Y * (b +c) = Y x (b +c) = (Yb + Yc)
Looks like the Y just ended up in those brackets.
Feel free of course to provide links to any authoritative works backing up your claims though...
You honestly think the presence or absence of those parentheses (they are not brackets) in the expanded expression is significant? Please do not grow up to become a bridge builder. :eek:
There is NO difference here. You are looking at an isolated expression in which that brackets now have no meaning. You can put them back or remove them at will.
If it is (Yb +Yc), how come you get an answer of 288 to the original question?
Because in the original question Y = 48/2 Not 2
And I did not come to an answer of 288 Google and several other programming languages did. I'm arguing that they applied to only rules applicable to arrive at their answer...
Just so I'm clear, have we got as far as a broad concensus that the debate hinges on whether 48/2(12) = 48/2*12 ? Are most people happy that the thing on the right =288 ?
Congratulations everyone who has contributed to this meme. You have found a fundamental flaw in the use of BODMAS, BIDMAS, PEDMAS, etc. Can we now move on with our lives?
48 / 2(9+3) = 288
48 / x(9+3) = 2 when x = 2
Please bare in mind that these two solutions are man made. There is no mathematical law written into our physical universe that says we have to do notation this way. It is just how we do it.
Has anyone ever seen ab written as axb in a maths book, except perhaps when first explaining that ab means a times b?
Has anyone ever seen a(b+c) written as ax(b+c) in a maths book?
Has anyone ever seen two numbers multiplied together without a multiplication sign, perhaps written as (2)(3)?
I think not.
There are no such things as explicit and implicit multiplication. There is just multiplication, and according to the convention when it comes to the right of division in the same term it is done after the division.
From a scientific engineering background I'd state the answer is 2
6 x 10^5 is actually meaning 6 followed by 5 zeroes, or 600000 (It's scientific notation for extremely large numbers, for instance the speed of light is approximately 300000000 m/s, or 3 x 10^8 m/s - self-evident here that you can't split the 3 and the 10^8 as separate numbers, it's one entity)
Therefore it is 600000/300000 which is 2.
However, because the original question is ambiguous, it could also mean 6 x (10^5/3) x 10^5, to be unambiguous it would need to be written as
6 * 10^5
3 * 10^5
Wrong. The normal rules of expression evaluation still apply. Now if you had used the alternative scientific notation as commonly adopted on calculators and computers of 6E5 / 3E5 then the answer would indeed be 2.
Congratulations everyone who has contributed to this meme. You have found a fundamental flaw in the use of BODMAS, BIDMAS, PEDMAS, etc. Can we now move on with our lives?
48 / 2(9+3) = 288
48 / x(9+3) = 2 when x = 2
Please bare in mind that these two solutions are man made. There is no mathematical law written into our physical universe that says we have to do notation this way. It is just how we do it.
Wrong. The normal rules of expression evaluation still apply. Now if you had used the alternative scientific notation as commonly adopted on calculators and computers of 6E6 / 3E6 then the answer would indeed be 2.
Ah, but En or EXPn is simply shorthand for "x 10^n". Where did you get your new rule that applies only to calculators?
[And why have you multiplied my original exponents by 10?!]
Comments
What is the difference between the implied and explicit multiplier operand again?
No
Y * (b + c) = Y * b + Y * c - no brackets.
Y * (b +c) = Y x (b +c) = (Yb + Yc)
Looks like the Y just ended up in those brackets.
Feel free of course to provide links to any authoritative works backing up your claims though...
I did an Engineering degree, which is very maths intensive and have faced much tougher questions than that.
But I couldn't give you an answer that I could 100% believe was correct without clarification.
Depending on your interpretation of mathematical rules, both answers could be deemed right.
It doesn't - it is Yb + Yc without the brackets. If it is (Yb +Yc), how come your answer to the original question was 288 ?
There is NO difference here. You are looking at an isolated expression in which that brackets now have no meaning. You can put them back or remove them at will.
Because in the original question Y = 48/2 Not 2
And I did not come to an answer of 288 Google and several other programming languages did. I'm arguing that they applied to only rules applicable to arrive at their answer...
So, anyway - where do we all stand on 100/2π ?
Do we have a circle or a TARDIS?
You know, I don't think I have ever seen 2*π or 3*π. Its always 2π or 3π. Neither have I seen (2π) or (3π).
I call circle
disclaimer - just because I havn't seen it doesn't mean it doesn't exist. I'm using the Black Swan defense
48 / 2(9+3) = 288
48 / x(9+3) = 2 when x = 2
Please bare in mind that these two solutions are man made. There is no mathematical law written into our physical universe that says we have to do notation this way. It is just how we do it.
Has anyone ever seen a(b+c) written as ax(b+c) in a maths book?
Has anyone ever seen two numbers multiplied together without a multiplication sign, perhaps written as (2)(3)?
I think not.
There are no such things as explicit and implicit multiplication. There is just multiplication, and according to the convention when it comes to the right of division in the same term it is done after the division.
6 x 10^5 / 3 x 10^5
Start with the powers:
=6 x 100,000 / 3 x 100,000
Then left to right:
=600,000 / 3 x 100,000
=200,000 x 100,000
=20,000,000,000
(=2^10 if you prefer that way of expressing it)
EDIT: The final line above is incorrect and should read 2 x 10^10)
From a scientific engineering background I'd state the answer is 2
6 x 10^5 is actually meaning 6 followed by 5 zeroes, or 600000 (It's scientific notation for extremely large numbers, for instance the speed of light is approximately 300000000 m/s, or 3 x 10^8 m/s - self-evident here that you can't split the 3 and the 10^8 as separate numbers, it's one entity)
Therefore it is 600000/300000 which is 2.
However, because the original question is ambiguous, it could also mean 6 x (10^5/3) x 10^5, to be unambiguous it would need to be written as
6 * 10^5
3 * 10^5
2^10 is 1024.
20,000,000,000 would be 2 x 10 ^ 10.
Tricky stuff this mathematical notation...
It's 'bear in mind'.
3 x 10 ^ 8 isn't one entity, it's three separate numbers and two separate operations.
[And why have you multiplied my original exponents by 10?!]
(I miscounted the zeroes earlier but it makes no difference to the argument)