48÷2(9+3) = ???
Just a simple test of your math skills. What is the correct answer, and why?
2
because it's the right answer
(48/2)(9+3) = 144
48/(2(9+3)) = 2
Any other boring 3rd grade arithematic questions?
Oh yeah, 48/2=24 (duh), 24x12=288
UT wins!
288. The reason is
order of operations
The standard order of operations, or precedence, is expressed here:
terms inside brackets
exponents and roots
multiplication and division
addition and subtraction
288
(48/2)(9+3) = 144
48/(2(9+3)) = 2
Any other boring 3rd grade arithematic questions?
Oh yeah, 48/2=24 (duh), 24x12=288
UT wins!
No, terms inside brackets precede division.
288. The reason is order of operations
exactly. you did the division first. brackets first.
no i did the parens first and then, from left to right, division and then multiplication
brackets (parentheses to yanks) first: 9+3 = 12.
brackets are mutiplied by 2 = 24
.......
logically, how can 48 divided by anything be 288? I still say 2
the multiplication by 2 is part of the brackets phrase. Otherwise it would be written 48 / 2 * (9+3)
it is written that way.
brackets first 9+3 = 12
then division 48/2 = 24
then multiplication 24 * 12 = 288
I do not see any brackets.
logically, how can 48 divided by anything be 288? I still say 2
if you then multiply it by 12
no i did the parens first and then, from left to right, division and then multiplication
You don't do multiplication/division from left-to-right like it's prose. Multiplication comes first regardless of where it is. Assume that the parentheses are done first, so now we have:
48 ÷ 2 x 12
That is the same as
48 x (one-half) x 12
Your way puts the 12 as a denominator in the fraction, which it wouldn't be unless there were also parentheses around the (2 x 12).
The mnemonic they taught us in grade school was
My
Dear
Aunt
Sally: multiplication, division, addition, then subtraction.
Multiplication AND division are done first...
it is written that way.
brackets first 9+3 = 12
then division 48/2 = 24
then multiplication 24 * 12 = 288
(a) No, it isn't written that way
(b) you're relying on Wikipedia
Google and
Wolfram Alpha agree with me.
Multiplication AND division are done first...
there is no left to right in math. when there are both multiplication and division, multiplication goes first. that's why 2(whatever) means 2 * whatever. There is no division equivalent because it isn't needed because multiplication happens first
Google and Wolfram Alpha agree with me.
they're wrong.
Order of operations: PEMDAS
Parentheses, equations, multiplication, division, addition, subtraction.
However, multiplication/division and addition/subtraction are equal.
Therefore, the answer is 24 x 12 = 288
Slinking back into the shadows now.
Order of operations: multiplication, division,
However, multiplication/division and addition/subtraction are equal.
you are contradicting yourself. If they were equal, one wouldn't be before the other on the order of operations. Generally, there is no difference, but this is the illustration of why there is an order of ops that puts mult before div.
At what point do I point out my BSc (honours) in math? I don't care what wikipedia says that google fetches up and other shit..... The answer is 2.
Yes but you got that degree off the back of a cereal box and I claim victory.
PEMDAS is easier to say than PEDMSA but I guess you could do PEDMAS or BEDMAS (for brackets) and it wouldn't really matter. That's the way I was taught, back in the ice age.
Maybe I ought to ask my kids. I'm really not smarter than a 5th grader. :)
Or in my case, 7th grader and 9th grader . . . OMG, the 9th grader asked me for math homework help and I Could Not Do It. Algebra. Polynomials. :::scream:::
Yes but you got that degree off the back of a cereal box and I claim victory.
No, I didn't, and PEMDAS backs me up. Claim all the victory you like, you're still wrong.
Juniper, it does matter, that's why it's PEMDAS and nothing else. It just doesn't matter very often.
Math is not left to right -maybe that's why left-handers are good at it? :p:
288, just because I plugged it into my calculator as written.
Maybe my BSCS and three decades of computer programming will count for something?
Maybe my BSCS and three decades of computer programming will count for something?
you could outprogram me in a heartbeat (although my BSc was a joint honours with Computer Science) ...it just won't get you anywhere in math if the main hits on a google search are too simplistic. ;)
288, just because I plugged it into my calculator as written.
well done.
Maybe my BSCS and three decades of computer programming will count for something?
Hopefully,
The answer would be two if the notation was written differently. ..but it's not
tired now.. will give my defense in the morning.
the answer is two
A.
http://blogs.edweek.org/teachers/coach_gs_teaching_tips/2011/01/math_teachers_please_excuse_dear_aunt_sally--forever.html
B.
http://www.angrymath.com/2009/03/pemdas-terminate-with-extreme-prejudice.html
C. I blame whoever wrote the equation, because it begs for misinterpretation. Extra parentheses for clarification are never wrong.
D. Why the hell did I open a math thread started by Flint? It's always trouble.
A. http://blogs.edweek.org/teachers/coach_gs_teaching_tips/2011/01/math_teachers_please_excuse_dear_aunt_sally--forever.html
B. http://www.angrymath.com/2009/03/pemdas-terminate-with-extreme-prejudice.html
C. I blame whoever wrote the equation, because it begs for misinterpretation. Extra parentheses for clarification are never wrong.
D. Why the hell did I open a math thread started by Flint? It's always trouble.
but you believe the answer is......
tired now.. will give my defense in the morning.
the answer is two
It needs more brackets to be two.
I stand by Occam's razor in this.
is a principle that generally recommends selecting the competing hypothesis that makes the fewest new assumptions, when the hypotheses are equal in other respects.[2] For instance, they must both sufficiently explain available data in the first place.
Excel says...
288
I tried it four times.
Maybe they do it different in the old country.
but you believe the answer is......
288.
In spite of MDAS, Multiplication and Division are equal in precedence. Evaluation proceeds from left to right. The use of the 2(..) notation for multiplication is tempting you to treat 2(9+3) as a single unit. 48 / 2 x (9+3), with the multiplication sign written out, seems less ambiguous (though I don't think it is).
Again, it's a screwy example.
I want to add something to my answer. I've been thinking about it (while cleaning my office - not like I'm obsessing or anything).
My "gut feeling" with this answer was to say it was 2, because of the way it's written. Sometimes I've found on tests you have to figure out what they want for an answer, which may not be what is technically correct. Which of course implies that math may not be as black-and-white as you'd think, that problems are open to interpretation, which is kind of weird, but anyway.
I think that if the intention were to get 288 as an answer, the question would have been written: (48÷2)(9+3) = ??? But because it lacked that one set of brackets, the author of the question wanted us to multiply 9+3 by 2 before dividing 48 by something. I've always felt that a number right next to a bracket implied a sense of urgency. But I still think the correct answer is 288.
And if you read this and rolled your eyes, you have a deeper understanding of why I am an English major. :thepain:
This is so why I'm not taking the GRE.
Let's Lynch Flint!
see? That'll fix everything.
Besides, Flint is crazy.
[YOUTUBE]N-Rer78WjbU&hl=en_US[/YOUTUBE]
What if you shuffle the cards on a treadmill while you solve the equation? Huh?
This is a good problem for an English major. It's analogous to a poorly written sentence; proper punctuation would clear up the meaning.
+1 above.
do math people call parentheses, "brackets" 'cause I still see no brackets in that equation.
thank goodness I slept through three years of algebra so I could stay awake during english
do math people call parentheses, "brackets" 'cause I still see no brackets in that equation.
No, English people do, apparently.
the ANSWER is cock
What is in that vagina, Alex?
beeep beeep beeep beeep
Yes, monkey?
What is "in the mouf" Alex.
No, English people do, apparently.
correct
so, the "brackets" in the order of operations refers to parentheses? what do English people call brackets?
and why would you want to multiply, when the equation clearly reads, "forty-eight divided by . . . "
very confusing! am frankly glad that I don't know the answer and don't need to know the answer!
I agree with the folks that have already said that this is an ambiguously written problem.
As a thread starter and fuel for conversation, it's pretty good.
As a example arithmetic question, it is poorly written, if the intent was to help the student learn about the order of operations.
In Flint's opening post, he says
**Title of thread** 48÷2(9+3) = ??? **end title**
Just a simple test of your math skills. What is the correct answer, and why?
Others have given the (pretty easy) justification for why "2" is the answer; I've seen justifications for "288". Which is correct? Well, that depends on the author, doesn't it? Well, Flint? What is the correct answer, and why?
I could just as easily say the correct answer is "???" because it says so right there in the thread title. That's "correct", isn't it? I could say "the correct answer is what the teacher says is the correct answer" or "whatever gets me an A on this test". Those answers are equally valid given the level of ambiguity here. What if we're assuming this equation is written in base 10 but it's really base 12? Then the "correct" answer would be just as uncertain given the way it's written, but it wouldn't be 2 or 288. After all, (skyshide), since we should make the fewest assumptions, assuming base 12 is equally likely as base 10, and both sufficiently explain the data already given.
So, as a plain arithmetic problem, I say the answer is 2.
If it's not plain arithmetic, then that's an entirely different problem.
Oh Lordy, Miss O'Hara, Tara is all but deserted -the yankees have done taken all the darkies and trampled all the cotton. Looks like you're just going to have to do the work for yourself. Ain't no-one to pump your gas now or -Lord forbid you should blister your poor dainty fingers- type "brackets" into Wikipedia and see what comes up.
since feeling is first
who pays any attention
to the syntax of things
will never wholly kiss you;
wholly to be a fool
while Spring is in the world
my blood approves,
and kisses are a better fate
than wisdom
lady i swear by all flowers. Don't cry
- the best gesture of my brain is less than
your eyelids' flutter which says
we are for each other; then
laugh, leaning back in my arms
for life's not a paragraph
And death i think is no parenthesis
--e.e. cummings
what do English people call brackets?
Possum Pbweed.:p:
As a example arithmetic question, it is poorly written, if the intent was to help the student learn about the order of operations.
It may be intended to teach the left to right convention.
the ANSWER is cock
What is in that vagina, Alex?
beeep beeep beeep beeep
Yes, monkey?
What is "in the mouf" Alex.
I'd like "names for male animals" for $1,000.
(a) No, it isn't written that way
(b) you're relying on Wikipedia
not sure where the southern/yankee thing comes in?
Rather than relying on Wikipedia so you can turn around and belittle the poster for that, as above, I turned to Websters Dictionary, which defines brackets as:
"either of the pair of signs [ ], or sometimes < > used to enclose a word or words inserted as for explanation, quantities to be taken as a single quantity, etc."
parentheses are not mentioned.
[COLOR="Wheat"]oh for christ's fuck [/COLOR]
I'd like "names for male animals" for $1,000.
Alex: This hairy and regressive creature lives in the depths of cellars and regularly pounds his chest and salivates at the sight of boobies.
not sure where the southern/yankee thing comes in?
Rather than relying on Wikipedia so you can turn around and belittle the poster for that, as above, I turned to Websters Dictionary, which defines brackets as:
"either of the pair of signs [ ], or sometimes < > used to enclose a word or words inserted as for explanation, quantities to be taken as a single quantity, etc."
parentheses are not mentioned.
exactly cloud
and Big V. I assume that because, like the others who think 288 is the correct answer, based on the common assumption of bedmas, which HLJ points out, excel gives the answer of 288. Doesn't the financial/ business world trust excel to give the common( generally assumed answer) If the spreadsheet is going to go off half cocked and assume a notation other than what is written, I say, Cock too.
To get the answer of 2, a person would have to rewrite the notation using brackets. [ ]
Wow, I'm too dumb to be here.
:bolt:
288.
In spite of MDAS, Multiplication and Division are equal in precedence. Evaluation proceeds from left to right. The use of the 2(..) notation for multiplication is tempting you to treat 2(9+3) as a single unit. 48 / 2 x (9+3), with the multiplication sign written out, seems less ambiguous (though I don't think it is).
Again, it's a screwy example.
yes
Damn, it's like some knights of some round table all up in heah.
So, tell me, (no matter what you call the damn things) how does making them curvy or making them squared have anything to do with the conundrum of the problem?
It's like...oh you know what? That 9 has a curvy bottom, therefore it must be multiplied by the half-life of the foundation of the numerator. Now, if it were STRAIGHT, that there would be a whole different story. That right there would tell you that the product of the synapse near the juncture would be 23. [\thinktanktrifecta]
:lol2:
Wow, I'm too dumb to be here.
:bolt:
May I join you? ;)
:smack:
Please My Dear Aunt Sally = 288
Get out while the gettin's good, 'vana, it's a damn clusterfuck!
I, too, actually hate meth.
I mean math. I hate math.
So, tell me, (no matter what you call the damn things) how does making them curvy or making them squared have anything to do with the conundrum of the problem?
They're worlds apart. Like the difference between a dash and a hyphen. Like a capital I and a roman numeral I. Like tomato and tomato.
They're worlds apart. Like the difference between a dash and a hyphen. Like a capital I and a roman numeral I. Like tomato and tomato.
How, tell me how?
One means something other than the other one means? Please, tell me. I don't remember that from math class.
not sure where the southern/yankee thing comes in?
Rather than relying on Wikipedia so you can turn around and belittle the poster for that, as above, I turned to Websters Dictionary, which defines brackets as:
"either of the pair of signs [ ], or sometimes < > used to enclose a word or words inserted as for explanation, quantities to be taken as a single quantity, etc."
parentheses are not mentioned.
Well you said you stayed awake in English, so one would think you could manage a litle Gone With The Wind reference? Or should we call it American in your case. When trying to solve an international language difference, let's see, shall we use an American dictionary, or an international source readily available at the fingertips? Hmmmm. One which actually does contain the answers you seek. I would post them for you, but, Miss Cloud O'Hara, it's about damn time you learned to do some stuff for yourself. Or you could not think about it today, if you can't possibly bear it, after all, tomorrow is another day.
How, tell me how?
One means something other than the other one means? Please, tell me. I don't remember that from math class.
Yeah, I didn't think so. :rolleyes:
How, tell me how?
[COLOR="LemonChiffon"][SIZE="4"][CENTER][FONT="Comic Sans MS"]I don't know.[/FONT][/CENTER][/SIZE][/COLOR]
Well you said you stayed awake in English, so one would think you could manage a litle Gone With The Wind reference? Or should we call it American in your case. When trying to solve an international language difference, let's see, shall we use an American dictionary, or an international source readily available at the fingertips? Hmmmm. One which actually does contain the answers you seek. I would post them for you, but, Miss Cloud O'Hara, it's about damn time you learned to do some stuff for yourself. Or you could not think about it today, if you can't possibly bear it, after all, tomorrow is another day.
Wow, what an impressive gene pool you must have to come up with the most original trolling style I have ever seen.
I would not have thought a math problem would have so engaged the Cellar. I'm quite pleased. We need more.
[COLOR="LemonChiffon"][SIZE="4"][CENTER][FONT="Comic Sans MS"]I don't know.[/FONT][/CENTER][/SIZE][/COLOR]
:comfort:
That's all right, old buddy old pal.
No, terms inside brackets precede division.
I agree with UT. Order of operation.
terms inside brackets
exponents and roots
multiplication and division
addition and subtraction
so 48÷2(9+3) = ?should be written as
48/2(12) = (12x48)/2 = 576/2 = 288 (my keyboard doesn't seem to have a division sign)
I would not have thought a math problem would have so engaged the Cellar. I'm quite pleased. We need more.
It certainly awoke the Cellar brain trust. *snort*
For a minute there I was afraid we might implode!
Its fun watching someone turn into defensive bitch mode when they're proven wrong lol. Keep it up monster, this thread is going places.
Oh looky, a new one!
You guys keep going you'll have quite a little pussy, I mean posse. :lol:
You got a horse in this race, bullitt? Do you have an answer to either the math question or the semantics argument? 'Cause, I haven't seen ANYONE proven right or wrong. Just a bunch of wind a'blowin' if you ask me.
I'll ask you all again: NO MATTER WHAT YOU CALL THEM DOES IT MAKE A DIFFERENCE IN A MATHEMATICAL EQUATION IF (THOSE THINGS] ARE CURVY OR SQUARED?
Other than an answer for that, just try to look bright and say 2 or 288.
kthx
This is a good problem for an English major. It's analogous to a poorly written sentence; proper punctuation would clear up the meaning.
Precisely! It's the mathematical equivalent of "eats, shoots and leaves."
Please to explain to me how it makes the equation different.
kthx
I think you're all full of hot air and farts. :lol2:
Jebus Aitch!
To be more precise, and to appease the dullards in the audience, how is this
48÷2(9+3) =
different mathematically than this
48÷2[9+3] =
Even better, how does WHAT YOU CALL THEM change the mathematical equation?
This same type of discussion is happening all over the net.
My initial response was 2, and still is. I just need to solve 2(9+3) first. But I am more a right-brainer type gal, so there.
And death i think is no bracket
Fixed.
Oh looky, a new one!
You guys keep going you'll have quite a little pussy, I mean posse. :lol:
You got a horse in this race, bullitt? Do you have an answer to either the math question or the semantics argument? 'Cause, I haven't seen ANYONE proven right or wrong. Just a bunch of wind a'blowin' if you ask me.
I'll ask you all again: NO MATTER WHAT YOU CALL THEM DOES IT MAKE A DIFFERENCE IN A MATHEMATICAL EQUATION IF (THOSE THINGS] ARE CURVY OR SQUARED?
Other than an answer for that, just try to look bright and say 2 or 288.
kthx
tl;dr
288
NO MATTER WHAT YOU CALL THEM DOES IT MAKE A DIFFERENCE IN A MATHEMATICAL EQUATION IF (THOSE THINGS] ARE CURVY OR SQUARED
In an arithmetic context, () and [] are usually equivalent. Having different ones is handy if you have more than one set nested, to clarify which matches which. I believe it's fair to say that {} are many times equivalent and just serve as a third "layer" of grouping when needed.
However, there are many contexts in math when there's a difference, or at least a specific role. For example, ranges of numbers: [0,6] indicates a range including the endpoints, 0 and 6, while (0,6) indicates that the endpoints are not actually part of the range. When you get into matrices and other crap like that, there are definitely ways to change the meaning by changing the typography. Context and definition of terms are critical.
oh no
[YOUTUBE]wv19iAncrrQ[/YOUTUBE]
standing-O for Undertoad!
brilliant!
no i just find em, it turns out this is a rapidly developing meme.
[YOUTUBE]bwpWw-iVKHc[/YOUTUBE]
See?
Math=Angry
Literature=HappyGoLucky!
Holy fuck, you mean Flint didn't make this up? I figured it was up there with the card shuffling and the don't-use-zero.
Literature=HappyGoLucky!
That may have been true 40+ years ago (MAYBE), but not now. Don't get me started on fucking "theory."
I figured it was up there with the card shuffling and the don't-use-zero.
What? I love zero. My 4yo knows to start counting arrays at zero.
orly?
What is your 4yo's answer to the thread title?
What? I love zero. My 4yo knows to start counting arrays at zero.
My apologies. For some reason I was thinking you were the proponent of the Get Rid of Zero thread.
you may be thinking of HLJ
So, how 'bout them Red Sox?
Its fun watching someone turn into defensive bitch mode when they're proven wrong lol. Keep it up monster, this thread is going places.
Well I don't believe that I'm wrong, so that can't be me that you're talking about, but since I have no more proof/evidence that I'm right I have nothing more to say about that. I did however have something to say about learned helplessness. Not my fault some are to dumb to get it without it being spelled out and turning into a bitchfest.
Sky, dear, I would contest that trolling is nurture rather than nature. And also since you are the one whaling into an argument in which you are not directly involved and you are the one calling names, that would rather put you under the bridge rather than me, no? I know how desperately you want to play Rhet in this scenario -and I see Bullitt is vying for the part too, but we already have a call out to someone's agent and are expecting them to turn up any minute.
:)
No, I didn't, and PEMDAS backs me up. Claim all the victory you like, you're still wrong.
PEMDAS
[FONT=Arial][SIZE=2][COLOR=#000000]A common technique for remembering the order of operations is the abbreviation "PEMDAS", which is turned into the phrase "Please Excuse My Dear Aunt Sally". It stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction". This tells you the ranks of the operations: Parentheses outrank exponents, which outrank multiplication and division (but multiplication and division are at the same rank), and these two outrank addition and subtraction (which are together on the bottom rank). When you have a bunch of operations of the same rank, you just operate from left to right. For instance, [/COLOR][/SIZE][/FONT][FONT=Times New Roman][SIZE=3][COLOR=#000000]15 ÷ 3 × 4[/COLOR][/SIZE][/FONT][FONT=Arial][SIZE=2][COLOR=#000000] is not [/COLOR][/SIZE][/FONT][FONT=Times New Roman][SIZE=3][COLOR=#000000]15 ÷ 12[/COLOR][/SIZE][/FONT][FONT=Arial][SIZE=2][COLOR=#000000], but is rather [/COLOR][/SIZE][/FONT][FONT=Times New Roman][SIZE=3][COLOR=#000000]5 × 4[/COLOR][/SIZE][/FONT][FONT=Arial][SIZE=2][COLOR=#000000], because, going from left to right, you get to the division first. If you're not sure of this, test it in your calculator, which has been programmed with the Order of Operations hierarchy. For instance, typesetting this into a graphing calculator, you will get:[/COLOR][/SIZE][/FONT]
[LIST]15/3*4=20
[/LIST][FONT=Arial][SIZE=2][COLOR=#000000]Using the above hierarchy, we see that, in the "[/COLOR][/SIZE][/FONT][FONT=Times New Roman][SIZE=3][COLOR=#000000]4 + 2×3[/COLOR][/SIZE][/FONT][FONT=Arial][SIZE=2][COLOR=#000000]" question at the beginning of this article, Choice 2 was the correct answer, because we have to do the multiplication before the addition.[/COLOR][/SIZE][/FONT]
[FONT=Arial][SIZE=2][COLOR=#000000](Note: Speakers of British English often instead use "BODMAS", which stands for "Brackets, Orders, Division and Multiplication, and Addition and Subtraction". Since "brackets" are the same as parentheses and "orders" are the same as exponents, the two acronyms mean the same thing.)[/COLOR][/SIZE][/FONT]
Of course, on page 2 of that article, it says the jury is still out on whether the shorthand of skipping a multiplication symbol changes its place in the order of operations.
(clears throat)
Everyone:
Shut Your Gob
and
Do Shut UP.
Thank Q.
PS
This is pretty much all Flint's fault.
He's crazy.
I don't see what the big deal is. Just do it the regular way.
you mean, like, in the butt?
I would say 288 myself, but in all honesty, I don't give a shit what the answer is.
Why not just write it as (48/2)(9+3) in the first place?
Why not just write it as (48/2)(9+3) in the first place?
Because then we wouldn't have to get into a fucking argument about the conventions of mathematical notation.
Because then we wouldn't have to get into a fucking argument about the conventions of mathematical notation.
lol Is that the reason? hehe
[SIZE="6"]42[/SIZE]
Why? Its the answer to life the universe and everything.
Thread won.
http://knowyourmeme.com/memes/48293
48÷2(9+3) = ? is a math problem that, depending on the order of operations used, leads to two different answers: 2 and 288. It can be a hot topic for debate, and is sometimes used to troll other users because of the argument that can result afterward.
Standard Order of Operations
If one strictly uses the standard order of operations to solve mathematical expressions, the answer to the problem would be 288, which is also the same solution provided by WolframAlpha and Google.
By convention, the order of precedence in a mathematical expression is as follows:
Terms inside of Brackets or Parentheses.
Exponents and Roots.
Multiplication and Division.
Addition and Subtraction.
If there are two or more operations with equal precedence (such as 10÷2÷5 or 7÷2*9), those operations should be done from left to right.
Therefore, the problem “48÷2(9+3) =” would be solved like this:
48 ÷ 2 * (9+3)=
48 ÷ 2 * (12)=
48 ÷ 2 * 12=
24 * 12=
288
However, the answer 2 could be justified by the principle of implied multiplication. For example, consider the problem "2/5x."
If one strictly follows the standard order of operations, the correct interpretation would be “(2/5)*(x).”
But many calculators and textbooks state that a higher value of precedence should be placed on implied multiplication than on explicit multiplication:
Because “5x” is implied to be "5*x," it gets higher priority than "2/5." In this case, "2/5x" would be interpreted as "(2)/(5*x)."
Returning to the original problem, if one utilizes the principles of implied multiplication, then “2(9+3)” gets higher precedence than the explicit “48/2,” and would be solved like this:
48 ÷ 2(9+3)=
48 ÷ 2(12)=
48 ÷ 24=
2
However, there is a lack of consensus on the value of implied multiplication.
But many calculators and textbooks state that a higher value of precedence should be placed on implied multiplication than on explicit multiplication
Now, see, I would hold that Mathematics can't allow for anything "implied". It's either multiplication, or it isn't.
Thats a great response Ibram! I feel vindicated...thank you,:p:
Now, see, I would hold that Mathematics can't allow for anything "implied". It's either multiplication, or it isn't.
I agree with this, and also think the answer is 288. But there's at least some debate even among mathematicians about the legitimacy of implied multiplication.
Now, see, I would hold that Mathematics can't allow for anything "implied". It's either multiplication, or it isn't.
I don't think to extrapolate the problem was implied either.
I agree, when you solve it as it stands the answer is 288
But many calculators and textbooks state that a higher value of precedence should be placed on implied multiplication than on explicit multiplication
Bullshit. Any cites of these calculators and textbooks? I've never heard this.
The root of all this is ambiguous use of the "/" in a single-line context, where properly-typeset multi-line usage would result in either
[code]
2
----
5x
[/code]
or
[code]
2
--- x
5
[/code]
Any sensible reinterpretation of one of these into a single line would include appropriate parentheses or other clarification to make it clear how the calculation is carried out. As noted earlier, the entire point of the 48-whatever example is to start an argument.
In fact, I dare say that incorrect interpretation of the fraction bar by bogus separation of terms in numerators and denominators, for example
[code]
x + 5 x
------- = --- + 5
2 2[/code]
is a very common student error, and contributes to the misinterpretation of typographical disasters such as we're discussing.
Implied multiplication certainly looks like it should have higher precedence, but the idea that shorthand is actually a different operator is odd.
ok, so lets try this again ...
6÷2(1+2)=?
ok, so lets try this again ...
6÷2(1+2)=?
It's a shark.
On. a. treadmill.
4y÷2y=?
I certainly see the logic behind putting implied multiplication above regular multiplication and division in order of operations.
4y÷2y=?
I certainly see the logic behind putting implied multiplication above regular multiplication and division in order of operations.
That is one hell of an example. Goes to the root of the issue.
Even calculators can't be sure.
Even calculators can't be sure.
pls post a larger image, I can't quite see it........
4y÷2y=?
I certainly see the logic behind putting implied multiplication above regular multiplication and division in order of operations.
The question is not whether it's logical. The question is whether it corresponds to the generally accepted interpretation of ordering the operators.
Even calculators can't be sure.
Type: Question and Answer Last Updated: 16-JAN-2011 23:45:41
Does implied multiplication and explicit multiplication have the same precedence on TI graphing calculators?
Implied multiplication has a higher priority than explicit multiplication to allow users to enter expressions, in the same manner as they would be written. For example, the TI-80, TI-81, TI-82, and TI-85 evaluate 1/2X as 1/(2*X), while other products may evaluate the same expression as 1/2*X from left to right. Without this feature, it would be necessary to group 2X in parentheses, something that is typically not done when writing the expression on paper.
This order of precedence was changed for the TI-83 family, TI-84 Plus family, TI-89 family, TI-92 Plus, Voyage™ 200 and the TI-Nspire™ Handheld in TI-84 Plus Mode. Implied and explicit multiplication is given the same priority.
Please see the graphing calculator guidebooks for additional information.
(source, if this horrible URL isn't one-time only)[SIZE="6"]42[/SIZE]
Why? Its the answer to life the universe and everything.
Thread won.
Having been 42 for almost a year now, I have to say that 41 beats the shit outta 42.
Having been 42 for almost a year now, I have to say that 41 beats the shit outta 42.
Wait. You weren't with Baby when you were 41, were you?