48÷2(9+3) = ????
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(Warning: the following points are incredibly pedantic, but then again, so is this entire thread.)
It strikes me as amusing that a lot of people in this thread seem to be confusing a matter of notation for something that has to do with actual math.
Math is what it is because it corresponds to reality. That is why it produces correct answers, i.e. ones that also correspond with reality. Any deviation from those laws will produce incorrect results, i.e. ones that no longer correspond with reality. If all of the symbols were written differently, and different precedence rules were used, it would still be math, and it would still correspond with reality. It would probably be less convenient, though. Notation is what it is because having a uniformly accepted form of notation provides two advantages: lack of ambiguity in the intention of any written expression, and mental convenience, i.e. the written form corresponds with the ideas expressed.
The math problem in the OP is designed to highlight an issue of notation. It does not have anything to do with "omfg go learn the fundamental nature of math." The reason that any controversy at all exists is due to the fact that people have grown up learning slightly two different rulesets for notation. In my math classes, the idea that juxtaposition takes precedence was never stated, but it was always implicitly assumed. Why? Because it often makes notation easier and mote intuitive, which is the entire point of notation.
There is no debate about the fundamental concepts of math in this thread. It's a debate about which notation is more legitimate. The fact that people aren't drilling down to the core issue leads to a case of two different groups thinking: "I'm OBVIOUSLY right! It's math! It can only have one answer!" What it comes down to is: mathematical operations themselves can only have as single outcome, but notation is not an essential part of math; it's an artifact of presentation. The rules used for presentation are not unambiguous unless there is universal agreement about what constitutes proper notation.
It strikes me as amusing that a lot of people in this thread seem to be confusing a matter of notation for something that has to do with actual math.
Math is what it is because it corresponds to reality. That is why it produces correct answers, i.e. ones that also correspond with reality. Any deviation from those laws will produce incorrect results, i.e. ones that no longer correspond with reality. If all of the symbols were written differently, and different precedence rules were used, it would still be math, and it would still correspond with reality. It would probably be less convenient, though. Notation is what it is because having a uniformly accepted form of notation provides two advantages: lack of ambiguity in the intention of any written expression, and mental convenience, i.e. the written form corresponds with the ideas expressed.
The math problem in the OP is designed to highlight an issue of notation. It does not have anything to do with "omfg go learn the fundamental nature of math." The reason that any controversy at all exists is due to the fact that people have grown up learning slightly two different rulesets for notation. In my math classes, the idea that juxtaposition takes precedence was never stated, but it was always implicitly assumed. Why? Because it often makes notation easier and mote intuitive, which is the entire point of notation.
There is no debate about the fundamental concepts of math in this thread. It's a debate about which notation is more legitimate. The fact that people aren't drilling down to the core issue leads to a case of two different groups thinking: "I'm OBVIOUSLY right! It's math! It can only have one answer!" What it comes down to is: mathematical operations themselves can only have as single outcome, but notation is not an essential part of math; it's an artifact of presentation. The rules used for presentation are not unambiguous unless there is universal agreement about what constitutes proper notation.
ok fuck heads that keep saying juxtaposition
do you know what htat means?
Using juxtaposition for multiplication saves space when writing longer expressions.
collapses to
.
so fuckin 2(9+3) = 2 x (9+3)
and people who say
what about 48/2x where x = 9+3... what is 2x? 2 * x.... 48 / 2 * x = 288 x = 12
do you know what htat means?
Using juxtaposition for multiplication saves space when writing longer expressions.
so fuckin 2(9+3) = 2 x (9+3)
and people who say
what about 48/2x where x = 9+3... what is 2x? 2 * x.... 48 / 2 * x = 288 x = 12
ok fuck heads that keep saying juxtaposition
do you know what htat means?
Using juxtaposition for multiplication saves space when writing longer expressions.collapses to.
so fuckin 2(9+3) = 2 x (9+3)
and people who say
what about 48/2x where x = 9+3... what is 2x? 2 * x.... 48 / 2 * x = 288 x = 12
SO 4X/2X=2X^2 ? ITS NOT 4X/2X=2 ?
lolz
No the rules of algebra always applies, the answer to the main question is 2. I got side tracked by the link i posted.
The mistake you are making is that you are assuming (if * is taken as multiplication)
48÷2(9+3) = 48÷2*(9+3)
This is not true. Here are the different answers:
48÷2(9+3) = 48÷(18+6) = 48÷(24) = 2
48÷2*(9+3) = 24*(9+3) = 24*(12) = 288
with 2(9+3), 2 is attached to the bracket, so 2(9+3) is treated as one value.
with 2*(9+3), 2 is not attached to the bracket, so 2*(9+3) is not treated as one value hence subjected to proceeding operators.
this is because, as I said, multiplication and division are the same god damn thing
There are some fucking idiots in this thread, the answer is 288 and if you disagree your a failure.
48÷2(9+3)
48÷2(12)
24(12)
24 x 12 = 288
This is not hard, I expect the retarded blonde bints on facebook to get this wrong, not people that should be earning money online and working out their own finances.
48÷2(9+3)
48÷2(12)
24(12)
24 x 12 = 288
This is not hard, I expect the retarded blonde bints on facebook to get this wrong, not people that should be earning money online and working out their own finances.
If 48 ÷ a(9+3) = 288, and you find a, you will get quite a wacky answer.
If 48 ÷ b(9+3) = 2, and you find b, you get 2 (which is what b should be).
I don't understand how the above algebra could ever be correctly rewritten as:
48 * (9+3) = 288
--
b
which is what the '288' guys seem to be doing.
So my answer is '2'.
If 48 ÷ b(9+3) = 2, and you find b, you get 2 (which is what b should be).
I don't understand how the above algebra could ever be correctly rewritten as:
48 * (9+3) = 288
--
b
which is what the '288' guys seem to be doing.
So my answer is '2'.
If it was all meant to be under the denominator it should be written that way:
48/[2(9+3)] = 2
48/2(9+3) = 288
> If it was all meant to be under the denominator it should be written that way
I agree that it could be more explicitly written, but even if it wasn't, I'd still do
the same thing.
Firstly because I would never rewrite 48/12a as:
48 * 12
--
a
but secondly here's another way to look at it:
With the expression 48/a(9+3) BIDMAS says brackets first.
But that a is part of the bracketed expression.
It means: (a*9 + a*3) which equals 12a
Likewise, 2(9+3) means (2*9 + 2*3) which equals 24
Even following BIDMAS to the letter, the answer is 48/24 = 2
I agree that it could be more explicitly written, but even if it wasn't, I'd still do
the same thing.
Firstly because I would never rewrite 48/12a as:
48 * 12
--
a
but secondly here's another way to look at it:
With the expression 48/a(9+3) BIDMAS says brackets first.
But that a is part of the bracketed expression.
It means: (a*9 + a*3) which equals 12a
Likewise, 2(9+3) means (2*9 + 2*3) which equals 24
Even following BIDMAS to the letter, the answer is 48/24 = 2