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# Why you can't trust your calculator, or What is 48/2(9+3)?

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posted on Mar, 2 2014 @ 08:01 PM

bastion

Nope. I've got a degree in maths. You need to solve the brackets/parenthesis first. 2(9+3) simplifies to 2(12) not 2 x 12 - where no brackets/parenthesis are present, causing the mistake - so the denominator is 24, giving the answer 2.

Calculators can't do fuzzy logic.
If you have a math degree you're probably not holding steadfastly on to a rule that's taught in 5th grade, which like a lot of things we're taught in 5th grade, turn out to be simplified rules that are refined when we study subjects more deeply. I think this is why the author I cited in the OP expressed that some of these rules we teach to 5th graders are in some ways doing them a disservice. If you forget everything you learned since 5th grade, you might get 288 too?

The picture of the Casio calculator agrees the answer is 2 if the 2(9+3) is written in that implied format, but it gives the answer 288 if the denominator is written explicitly as 2x(9+3), so I'm not sure of the exact meaning of your fuzzy logic comment but I was surprised to see the calculator make that distinction, which seems to be programmed so implicit multiplication take precedence.

Pilgrum
What's been proven here without a doubt (as if it needed any proof) is that if we leave any room for misinterpretation in our expressions, they'll be misinterpreted by man & machine alike.
I hope everyone agrees with that. I do.

jonnywhite
Here's my opinion: 3(5) = 3 * 5.

...

And this is easier to write: 3(3+5)...

Versus: 3 * (3+5).

So the convenience of writing the formula wins.
It is more convenient, but if convenience leads to ambiguity that's bad. I'd like to point out if you wanted the answer to be 288, you could write the problem as 48(9+3)/2, and you don't need to add any extra parentheses, and I don't think it's ambiguous, is it? Or does someone get an answer other than 288 if it's written that way? People can avoid confusing themselves if they make the expression to the left of the slash the numerator and the expression to the right of the slash the denominator. This isn't taught universally but it can avoid some ambiguity.

What you said about 3(3+5) is not just a convenience if you publish in some physics journals (the APS journals), it's required, because you're not allowed to use the multiplication sign for multiplication; all multiplication must be written in the implied format as 2(9+3). The reason is that the multiplication symbols are reserved for vector products, to eliminate ambiguity and confusion which might result if the multiplication symbol was used for multiplication and for vector products. Apparently physicists have no problem using the implied format like 3(3+5) as they do it frequently.
edit on 2-3-2014 by Arbitrageur because: clarification

posted on Mar, 2 2014 @ 09:00 PM
If 48÷2(3+9) is used then there is no misinterpretation for sure, but no one ever uses it. lol

posted on Mar, 2 2014 @ 09:18 PM

There is still no ambiguity. Written as it was 48/2(9+3) is the exact same thing as what you wrote with the divided sign.

The only way it should be read the other way is if the entirety of 2(9+3) is written under 48 or it is written linearly as 48/(2(9+3)).

As it is written it is unambiguously 288. There is a reason for contingents and orders of operations. If you want it to read the other way, add the damn parentheses or write the 2(9+3) below the 48.

You must always (unless explicitly instructed otherwise) do parentheses, then brackets, then powers, then multiplication or division form left to right, then addition or subtraction from left to right. The left to right on the addition or subtraction doesn't matter but it should be followed that way anyhow to avoid confusion.
edit on 2-3-2014 by Masterjaden because: (no reason given)

posted on Mar, 2 2014 @ 09:19 PM

sean
If 48÷2(3+9) is used then there is no misinterpretation for sure, but no one ever uses it. lol

posted on Mar, 2 2014 @ 11:45 PM

you HAVE to do what's IN parentheses first, it is NOT a simplify equation. You HAVE to DO what is IN the parentheses FIRST!!!!!

posted on Mar, 2 2014 @ 11:55 PM

You CAN'T get to

48
-------
2(9+3)

Because that is NOT what is written...

The best way to look at this is to write out the equation in written language as presented.

forty eight divided by two times (nine plus three).

This is the way the equation is written.

It gives you 24 times (nine plus three) or 24 times 12 which equals 288.

If it was written as 48 divided by (2 times (nine plus three)), THEN you would have two as the final answer.

The person who proclaimed themselves a math teacher is an idiot if that's what he's teaching his class. No wonder we have such stupid children.

I have an MBA and two bachelor's degrees in business and psychology and graduated with a 3.8 for my MBA. If I had used the methods some of you are describing in my accounting and statistics classes, I would've FAILED miserably.

posted on Mar, 2 2014 @ 11:57 PM

You keep stating that solving the problem left-to-right is incorrect, you reach this conclusion because you did not read your own source properly. The point of your source was that multiplication is commutative so that order of multiplication does not matter. Or, it tries to explain that:

48/2(9+3)

is exactly the same as:

(9+3)48/2

Which is also the same as:

48(9+3)/2

Division is not the same as multiplication in that regard, changing which way it is read does tend to change the answer unless you change division by c with a multiplication by (1/c). In other words:

2/(9+3)48 is not the same as 48(9+3)/2

But:

48(9+3)/2 is exactly the same as 48*(1/2)*(9+3).

This was explained very clearly in the article.
edit on 2/3/14 by C0bzz because: (no reason given)

posted on Mar, 3 2014 @ 12:38 AM
Interesting read from Berkley. Order of arithmetic operations I put the ÷ sign instead of / because I read somewhere someone said that if the / is used then multiplication should be used first before division. PEMDAS or PODMAS supposed to be read left to right after the brackets are calculated. As the clip from that link below states how does one interpret someone's equation if they simply put a-b+c? As far as interpretation goes, look at Chinese mathematics it looks completely alien.

Math as the universal language only holds true if both parties can agree on the same language or hash out each others interpretation of what math is. Same goes for 3rd dimension trying to figure out what the 4th dimension would look like. We can't because our math is locked into 3rd dimensional perspective & reasoning. We're missing the communication part of the equation to entangle the two. Ok this is to deep lol.

From correspondence with people on the the 48/2(9+3) problem, I have learned that in many schools today, students are taught a mnemonic "PEMDAS" for order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. If this is taken to mean, say, that addition should be done before subtraction, it will lead to the wrong answer for a−b+c. Presumably, teachers explain that it means "Parentheses — then Exponents — then Multiplication and Division — then Addition and Subtraction", with the proviso that in the "Addition and Subtraction" step, and likewise in the "Multiplication and Division" step, one calculates from left to right. This fits the standard convention for addition and subtraction, and would provide an unambiguous interpretation for a/bc, namely, (a/b)c. But so far as I know, it is a creation of some educator, who has taken conventions in real use, and extended them to cover cases where there is no accepted convention. So it misleads students; and moreover, if students are taught PEMDAS by rote without the proviso mentioned above, they will not even get the standard interpretation of a−b+c.

posted on Mar, 3 2014 @ 12:45 AM
I can't believe that this question even made it to the internet.

288

We really do live in that universe where the movie “Idiocracy” becomes a true story.

—Mathematical Physicist

posted on Mar, 3 2014 @ 12:58 AM

You CAN'T get to

48
-------
2(9+3)

Because that is NOT what is written...

In any math past remedial levels, if you see something like the debated problem is written, you instantly write it as a ratio. Can you remember a single math class you took having you do division with a division sign? They all were in rational form, no? If not, what class uses division symbols or slashes in place of them?

I guess it just depends on how you look at the problem. If you look at it as a linear set of instructions, then yes you wouldn't get to a rational number. But if you look as poorly written and needing reconfiguring before evaluating, putting it into a ratio is the first and proper step.

edit on 3-3-2014 by James1982 because: (no reason given)

posted on Mar, 3 2014 @ 01:05 AM

3mperorConstantinE
I can't believe that this question even made it to the internet.

288

We really do live in that universe where the movie “Idiocracy” becomes a true story.

—Mathematical Physicist

If

F(x) = 4(x^2) + 5x + 4
G(x) = 3x+4

What is (f o g)(x)?
What is (f o f)(x)?
What is (g o f)(3)?

Could I even ask you that question if I was at an idiocracy level of education? It's incredibly easy math to me, but I can still see 2 as being correct depending on how you frame the initial problem.

posted on Mar, 3 2014 @ 01:09 AM
I think the issue with these "trick" math problems that are argued about on the internet is trying to write math problems on one line. If one was writing the problem on a piece of paper or a blackboard it would not be ambiguous at all. The answer I get is 2, because when I see 48/2(9+3) I interpret that to mean 48 is the numerator and 2(9+3) the denominator.

The distributive property, implied multiplication, and the order of operations are -I believe- red herrings. If one sees 48/2 as the fraction, then they would just distribute that to get 216+72=288. It's all about where one interprets the fraction bar to be, which would not be a problem if it were written on a blackboard rather than a computer screen.

Interestingly enough, I see the opposite when it's something like 1/2x. In that case, I would interpret that as "one half x" rather than "one over 2x".

posted on Mar, 3 2014 @ 01:47 AM

James1982

3mperorConstantinE
I can't believe that this question even made it to the internet.

288

We really do live in that universe where the movie “Idiocracy” becomes a true story.

—Mathematical Physicist

If

F(x) = 4(x^2) + 5x + 4
G(x) = 3x+4

What is (f o g)(x)?
What is (f o f)(x)?
What is (g o f)(3)?

Could I even ask you that question if I was at an idiocracy level of education? It's incredibly easy math to me, but I can still see 2 as being correct depending on how you frame the initial problem.

Am I now supposed to be impressed that you can ask me a question about … algebra?

(f • g) —> 4(3x+4)² + 5(3x + 4) + 4
(f • f) —> 4(4x²+5x+4)² + 5(4x²+5x+4) + 4
(g • f)(3) —> 169

a little knowledge is a dangerous thing, careful now Jamesey

posted on Mar, 3 2014 @ 01:56 AM

3mperorConstantinE

James1982

3mperorConstantinE
I can't believe that this question even made it to the internet.

288

We really do live in that universe where the movie “Idiocracy” becomes a true story.

—Mathematical Physicist

If

F(x) = 4(x^2) + 5x + 4
G(x) = 3x+4

What is (f o g)(x)?
What is (f o f)(x)?
What is (g o f)(3)?

Could I even ask you that question if I was at an idiocracy level of education? It's incredibly easy math to me, but I can still see 2 as being correct depending on how you frame the initial problem.

Am I now supposed to be impressed that you can ask me a question about … algebra?

Uh, no, your not. That's the point. Did you fail to read the part where I said that was extremely simple math?

You implied anyone that came up with 2 was some mouth breathing mongoloid from idiocracy. Would an idiot consider algebra to be simple math?

posted on Mar, 3 2014 @ 02:15 AM

James1982

mojo2012
what is 48/2(x+y)? i typically assume that 48 is being divided by 2(x+y). I guess it should be written like this 48/[2(x+y)].

Great way of looking at it.

That would be 48/2x+2y

x=9
y=3

Then you get 48/18+6 or 48/24 or TWO.

I can't believe some people still think it's anything other than two. Sad state of education for sure.

Oh the irony.
But seriously though, I'm just kidding ... you'll see your mistake in a second (we all make them)
So, this is the argument for the answer being 2.

We'll call it the "algebraic argument"
But this is wrong
x = 48
y = 2
z = 9
a = 3

the equation being:
x/y(z+a)

you're doing:
x/(yz+ya)

x(a+z)
————
y

do you see what's happening with the parentheses now?

edit on 3-3-2014 by 3mperorConstantinE because: (no reason given)

posted on Mar, 3 2014 @ 02:21 AM
Remember that parenthesis may be put in place as well...
48/2x+2y (x=9, y=3)

would give you 8 ⅔, not 2 => because:
(48/18)+6 ≠ 48/(18+6)

After you've "used up" the parentheses, then you must evaluate the expressions as per normal.
You can't arbitrarily put them back in the equation:

x(y+z) = xy+xz
x(y+z) ≄ (xy+xz)

Hope that clears it up
edit on 3-3-2014 by 3mperorConstantinE because: (no reason given)

posted on Mar, 3 2014 @ 04:20 AM
this. will. clear. things. up.

knowyourmeme.com...

posted on Mar, 3 2014 @ 04:31 AM

GogoVicMorrow

Its 288. Any college math class you go to will give you 288. You are applying incorrect attributes and/or changing the problem.
You do the addition first always as its in the parenthesis. Then you have 48/2·12.

So you are trying to sell us that 48/2·12 = 2? You are incorrect.

48/2 (9+3)
48/2·12
24·12
= 288

You and a few other is this thread are trying to manipulate the problem. Why? I dont know, its a very simple problem.

You always know there is a multiplication sign between a number and a parenthesis. You always solve a problem with division and multiplication in order (if there is no parenthesis).

So after you solve the addition in the parenthesis you have a simple division and multiplication job.

Anyone getting something other than 288 has forgotten basic math.. maybe because they've done too much math, I dont jnow, but regardless as to the reason, 2 is wrong. 288 is correct.
edit on 2-3-2014 by GogoVicMorrow because: (no reason given)

Totally agree..

I wonder why people here are saying that 2 is the correct answer and 288 is just how machines do it.
If you've written programs that parse expressions, like compiler stuff, it pretty much follows PEMDAS rule, it uses expression stacks to make the calculations efficient. Division and multiplication is done in order of occurence - left to right. Same thing applies to addition and subtraction. It's PE(MD)(AS), or PE(DM)(SA). The TI-85 or other calculators that gave 2 probably had minor bugs in their algorithms that it didn't account for this kind of expression.

And what's taught in gradeschool about PEMDAS is a simplified sometimes ambiguous version of the nature of real numbers. It will take time to discuss abstract algebra concepts to gradeschool.. that's why they use PEMDAS approach.

And the algebra analogy is incorrect, too. 48/2x is not equivalent to 48/2(9+3) where x = (9+3). Algebra treats 2x as a single algebraic term whereas 2(9+3) are two separate elements. When this is parsed in an expression calculator and separated into terms with the operators in between, 2x is considered one term, while 2(9+3) are considered 2 separate terms.

posted on Mar, 3 2014 @ 05:10 AM

GogoVicMorrow

And the algebra analogy is incorrect, too. 48/2x is not equivalent to 48/2(9+3) where x = (9+3). Algebra treats 2x as a single algebraic term whereas 2(9+3) are two separate elements. When this is parsed in an expression calculator and separated into terms with the operators in between, 2x is considered one term, while 2(9+3) are considered 2 separate terms.

--------------------------------------------------For 2 people, yay
Assume
48
--- = 2
z

expanding z as y(x)
48
--- = 2
y(x)

48 = 2*y(x)

48
---- = y(x)
2

24 = y(x)

if y = 2 then x should be 12 or 9 + 3, wins!

--------------------------------------------------288 people who dont like algebra
Assume
48
--- = 288
z

expanding z as y(x)
48
--- = 288
y(x)

48 = 288*y(x)

48/288 = y(x)

0.1666 = y(x)

if y = 2 then x should be 0.083, whoops
Equation is correct, but numbers is not.

--------------------------------------------------288 people who use weird algebra
Assume
48y
--- = 288
x

expanding y as (2), this is where it weird
96
--- = 288
x

x = 288/96

x = 3 , failure ? x supposed to be (9 + 3) or 12, whoops!

As far as memory serve, if equation like this

48y
--- = 288
x

should be written something like this
48y/x = 288

which is way off from 48/2(9+3)
I think algebra always right or am I missing something ?

edit on 3-3-2014 by NullVoid because: This text formatting sux eh ?

posted on Mar, 3 2014 @ 05:26 AM

You are 100% correct; the words of your 3rd paragraphic are the perfect captions to the equations in my last two posts.

The people here and elsewhere on the web, thinking that *2* could be seen as correct, were (edit: are) making what I'd refer to as an "appeal to algebra" argument… while unfortunately at the same time misunderstanding the actual mechanics of the algebra to which they were attempting to appeal.

Essentially the SOLE reason that this 42/2(9*3) equation has persisted as a "meme", is because of a perceived ambiguity; where really, in the world of mathematics (of which computer-science is a branch)
— there's nothing remotely unambiguous about it.

~E
edit on 3-3-2014 by 3mperorConstantinE because: (no reason given)

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