math problem

[oldjones]

The answer is both. The problem isn't in the math, but in the methodology used.

If you meant printing and typography methodology you're correct, that is where the problem lies. But both mathematical methods can be seen as correct, and they give two different answers. The typed numbers don't have enough internal clues to say which version was intended

The trouble is we type on these fancy computers as if we're banging away on old fashioned typewriters with red and black cotton ribbons. Together, they and we insist on putting everything into one single line. None of us learned our arithmetic, or any other maths that way, on one line, because Math notation is way more dimensional.

We used our pencils and pens to write denominators beneath numerators, and little teeny subscripts as exponents above the quantity being raised to that power. When all those differences disappear and everything is the same size on the same line who can be sure whether that (2+2) multiplier was meant to affect the entire fraction 8/2 or just its denominator 2?

And the arbitrary and inconsistency of the spacings just made it all worse. Is 8/2(2+2) the same quantity as 8/2 (2+2)? Is either, both or neither the same as the original: 8 / 2 (2+2)?

For no other reason than to compensate for their primitively typed notation, anyone who genuinely wanted their calculation done needed to at least add one more set of brackets: Either (8 / 2) (2+2)=? which would give 16 OR: 8 / (2 (2+2))=? which would give 1.

Of course the unknown person who thunk-up this puzzler was more interested in the question's entertaining ambiguity than the correctly calculated answer. Now just think of all the TeTERB-Typing that could have been saved if the Questioner had written: 8(2+2)/2 or 8/(2+2)2.

Pick either. For an extra Gold Star come back with Word Problems for one or both answers.
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For Mac Snobs who care, System Preferences>Language and Text>Input sources offers the option to put access to a KeyBoard and a Character Viewer in your MenuBar, which will gives you prettier vulgar fractions ¾, superscripts⁶, subscripts₆ aççénts and such. Windows™ however, is opaque to me.

 

[downbound123]

The answer is 5.
The answer is always 5.

No, the answer to life, the universe and everything (including the math problem) is 42.

 

[anon1]

No, the answer to life, the universe and everything (including the math problem) is 42.

Now that is just rediculous.

 

[K Douglas]

Saw this on CP24, this is going viral :


8 / 2 (2+2)=?

My answer is 1, others say answer is 16

rule of thumb-you do the brackets first is what I was taught.

You do what's inside the brackets first. 2+2=4. Then you do the 8/2 = 4. Then you do 4 x 4 = 16. Division and multiplication are in the same order of operations so you go left to right.

 

[Insidious Von]

16 is the correct answer . 8 divided by 2 = 4 . 4 times 2+2 = 16

Correct it's not 0.8 or 2/8.

 

[icespot]

You do what's inside the brackets first. 2+2=4. Then you do the 8/2 = 4. Then you do 4 x 4 = 16. Division and multiplication are in the same order of operations so you go left to right.

Hey, finally something we agree on, everyone forgets order of operations.

 

[basketcase]

...

8 / 2 (2+2)=?....

The original has the division symbol, not / which creates the ambiguity. I would thing that in the original, the 2(2+2) is a mathematical phrase and would be done before the division as if it was 8/[2(2+2)]

 

[benstt]

It is ambiguous. Math people in my experience would never write it like that, as the denominator for the / would be imprecise. If forced to use basic symbols like this they would add more brackets to make it absolutely clear. However, they would prefer to use real math typesetting, as they can understand at a glance what is trying to be conveyed.

 

[jeff5228]

https://www.educationquizzes.com/knowledge-bank/what-are-bodmas-bidmas-and-pemdas/

"Division and Multiplication rank equally so deal with these together from left to right"

Following this, the answer is 1

 

[oldjones]

https://www.educationquizzes.com/knowledge-bank/what-are-bodmas-bidmas-and-pemdas/

"Division and Multiplication rank equally so deal with these together from left to right"

Following this, the answer is 1

That's correct, but only if we ignore the space separating the 2 in the denominator from the the bracketed quantity (2+2), reading it as if it was written 2(2+2). But it certainly was not written like that.

Other people (and Google) read other spaces as intending the bracketed quantity (2+2) to be a multiplier of a vulgar fraction 8/2. But that calculates as equivalent to: 8(2+2)/2, and that version's well off what was actually typed.

There is more than one way to read the question as it has been typed. Each of the ways requires the reader to assume an intention the typist did not make clear when they put in all those spaces — and left out any multiplication sign. Looking at it another way: 2 4 is not the same as 24. Even if we put in some brackets, 2 (4) isn't the same as 2(4). But 2x4 is, even without any (). Gaaack!!

As the calculation was typed, each of us must pick and choose which spaces to ignore. Some, including you read: 8/2(2+2) assuming the typist was aiming at: ⁸⁄₂(₂+₂). Fair enough if you ignore all the other spaces.

However Google and others read 8/2 x (2+2), thinking the spaces were trying to represent:⁸⁄₂(2+2). Fair enough if you ignore all the other spaces.

Can't blame the readers. As in any communication, it's up to the author to be clear and unambiguous.

Meantime: A bad question can't have 'a right answer'. Give the student back their paper to try again.

 

[shakenbake]

The original has the division symbol, not / which creates the ambiguity. I would thing that in the original, the 2(2+2) is a mathematical phrase and would be done before the division as if it was 8/[2(2+2)]

Agreed. Of course, those who are more conversant with math will know what you have just written!

 

[oldjones]

Agreed. Of course, those who are more conversant with math will know what you have just written!

IF basket was referring to the original post, then of course he is incorrect, it used / not ÷. I believe he might have been trying to reference an earlier version that appeared somewhere else, from which he thinks the OP obtained his. Without citations who can say?

As to the topic: A clear and numerous consensus has emerged that the original expression is faulty, and must be corrected to make either answer a 'right' one. Or sixteen.

 

[TeeJay]

Saw this on CP24, this is going viral :


8 / 2 (2+2)=?

My answer is 1, others say answer is 16

rule of thumb-you do the brackets first is what I was taught.

The issue is the way it is written is not at all clear to many people (which is the intent)

8 / 2 (2 + 2)
8 / 2 (4)
Everyone agrees up to this point
But as written there is NO indication that the (4) is a denominator (to the contrary as written seems to imply it is a complete number, aka 4/1) BECAUSE they bracketed the number (if no brackets we could CONCLUSIVELY say that it was part of the denominator; aka 8 / 2 * 2 + 2 yields an entirely different answer, which is 10. 1 was NEVER a valid answer to this question if you understand math)
Brackets indicate a multiplication sign
8 / 2 (4)
4 (4)
= 16

But that is not the same equation. You can't just change it around.

The question is about the 2 beside the brackets. Yes that means you multiply but not in the way you have written it and in math, that counts.

If you doubt me type it into Google EXACTLY as written
=8/2(2 + 2)

That's correct, but only if we ignore the space separating the 2 in the denominator from the the bracketed quantity (2+2), reading it as if it was written 2(2+2). But it certainly was not written like that.

The space is MEANINGLESS (well besides making it more confusing for people which is exactly what the author intended)
You can enter either way the answer is still the same

 

[superstar_88]

With this detailed explanation it should be end of discussion and time for everyone to move on with their lives.

The equation as written was to trick people to do multiplication first from the right then division from the left. As we all know this is wrong. Left to right is correct. No ambiquity there. Left to right and right to left is like black or white. Not grey

 

[basketcase]

IF basket was referring to the original post, then of course he is incorrect, it used / not ÷. I believe he might have been trying to reference an earlier version that appeared somewhere else, from which he thinks the OP obtained his. Without citations who can say?
....

I'm talking about the twitter post that went viral with this question.

https://nypost.com/2019/08/01/viral-math-problem-baffles-mathematicians-physicists/

 

[oldjones]

I'm talking about the twitter post that went viral with this question.

https://nypost.com/2019/08/01/viral-math-problem-baffles-mathematicians-physicists/

Thanks. And the tweet brings up the NY Post who say they got it from Mashable, where there is no agreement. In self defence, I also note that the way people type the expression is also all over the map. Most egregiously, the Post types 8÷2(2+2) but shows heads their piece with a big graphic that shows 8 ÷ 2(2+2).The best post is the tweet from LUZZZ that shows a Texas Instruments calculator next to a Casio, each with a different answer.

Another poster, lauraM nails the issue writing on her tablet: The second line shows the two different, unequal expressions that can each be legitimately derived from the typed version, one giving 1, the other 16 i.e. 2x.

Any Real-Life Questioner would actually start there, trying to describe the real-life calculation facing them. But they would come up with just one of those two versions; with real things the order you divide or multiply is not optional. The trouble would begin when they tried to type it, and settled for the ambiguous version we're all discussing.

Gotta proofread. If someone can read it wrong, they will.

 

[TeeJay]

The best post is the tweet from LUZZZ that shows a Texas Instruments calculator next to a Casio, each with a different answer.

Its not as impressive as the poster makes it sound
The calculator has SETTINGS that can be changed
Anyone who ever attended school or read the manual knows this
Google it

 

[legmann]

8 / 2 (2+2)=?

If you treat the denominator [2(2+2)] as a single term, the answer is clearly 1. As written, I don't know why anyone else would consider otherwise.

 

[oldjones]

ç

Its not as impressive as the poster makes it sound
The calculator has SETTINGS that can be changed
Anyone who ever attended school or read the manual knows this
Google it

I made it sound impressive ? You're too kind. I thought all I did was point to someone clearly showing that even calculators can read the same written expression either way. And unlike many of the GI-humans neither of the AI-calculators introduced new ambiguities as they 'transcribed' the formula in their displays. Did you like some other post better then?

Whether their answers differed because one or both operators did, or didn't, mess with SETTINGS properly, or improperly, seems entirely beside the point: The original is written so ambiguously there is no single right answer.

If you imagine a real world situation where you needed to do that sort of calculation, you'd never write the numbers down as they were presented. You'd come up with one of the two versions on the tablet. Either the one that divides the 8, or the one that multiplies it. Never both.

But when you came to type it … Well, we'd hafta hope for at least another pair of brackets.

 

[Indiana]

Why is this a problem?