How old are you? 6 ÷ 2 X (2+1) = ?

[230RN]

I evaluated it as 1.

Apparently, the correct modern answer is 9.

I guess it depends on how old you are.

To me, the 2 X (2+1) should be evaluated first as a stand-alone quantity with known values.  Not so, by modern conventions on the order of mathematical operations.

I could see the "answer" of 9 if it were written (6 ÷ 2) X (2 + 1), but not otherwise.

https://www.youtube.com/watch?v=URcUvFIUIhQ

Terry

[Brad Johnson]

X = 6 ÷ 2 x (2 + 1)
X = 6 ÷ 2 x 3
X = 3 x 3
X = 9

Stand-alone exponents, then operations in parenthesis, then parenthetical exponents, then multiply/divide operations from left to right, then add/subtract operations left to right. Or at least that's how I learned it for when the equation doesn't clearly separate operations.

Brad

[makattak]

I came up with 9 immediately, too.

Parenthesis first, then division and multiplication are done in sequence. (As Brad illustrated, including the rest of the rules as I was taught.)

[just Warren]

PEMDAS!

And the answer I got is that math is an oppressive means for the privileged patriarchy to keep women and PoCs trapped in a whitemansplaining cycle where their voices are neither heard nor respected. 

[HeroHog]

9, unless the Rules of Order of Operations has been repealed/changed. If that is the case, there is a metric butt-ton of books that need rewriting and the old ones destroyed lest someone get confused and crash a spacecraft.

[Unisaw]

9 given the established (establishment  ) ordering rules.

[Cliffh]

If "you" get an answer of 9, "you're" young?

Cool!  Here I'd thought being >60yr I was at least bordering on old.

[MechAg94]

I think going to the parentheses first had me doing the second part right to left without thinking about it.  I am thinking left to right was the way I was taught but it has been a while.  My engineering side says it needs another set of parentheses. 

[Brad Johnson]

I think going to the parentheses first had me doing the second part right to left without thinking about it.  I am thinking left to right was the way I was taught but it has been a while.  My engineering side says it needs another set of parentheses.  

Your engineering side is correct. If the equation is so unclear it causes operation errors due to subjective interpretation, it needs to be re-written.

Brad

[Firethorn]

9 is what I got as well.  Well, after I realized that the "X" in this case meant "multiply" and not "unknown variable.  where I was getting "1/x"


Brad posted the rules. 

More iffy would be:

6 ÷ 2(2+1)

To me, the lack of a separate multiplication symbol ties the 2 to the parenthesis more.

[Hawkmoon]

I also thought it needed another level of parentheses, but I entered it into Excel just as written [ =6/2*(2+1) ] and hit ENTER expecting to get a result of ERR. To my surprise, I got ... 9.

[Sideways_8]

9 is what I got as well.  Well, after I realized that the "X" in this case meant "multiply" and not "unknown variable.  where I was getting "1/x"


Brad posted the rules. 

More iffy would be:

6 ÷ 2(2+1)

To me, the lack of a separate multiplication symbol ties the 2 to the parenthesis more.

The rules still remain the same.

[Phantom Warrior]

Your engineering side is correct. If the equation is so unclear it causes operation errors due to subjective interpretation, it needs to be re-written.

I have to disagree.  You posted the rules at the top of the thread.  Warren's link also sums it up nicely with examples.  It isn't immediately, intuitively obvious how this expression should be calculated.  Which is why these kind of articles are perpetual low hanging fruit for people that haven't done order of operations in a while.  But the rules are clear and there is no subjective interpretation.

-grouchy math major   

[Brad Johnson]

I have to disagree.  You posted the rules at the top of the thread.  Warren's link also sums it up nicely with examples. It isn't immediately, intuitively obvious how this expression should be calculated. Which is why these kind of articles are perpetual low hanging fruit for people that haven't done order of operations in a while.  But the rules are clear and there is no subjective interpretation.

-grouchy math major  

You've disagreed with your disagreement.  

Just because the equation can ultimately be solved properly doesn't make it any less sloppily written.

Brad

[Phantom Warrior]

Why do you consider it sloppily written?

[Brad Johnson]

Why do you consider it sloppily written?

See the bolded section of the quote above.

Brad

[freakazoid]

See the bolded section of the quote above.

Brad

How is it not immediately, intuitively obvious? PEMDAS.

[Doggy Daddy]

How is it not immediately, intuitively obvious? PEMDAS.

Agreed, but I would leave out the word "intuitively".  Intuition is inappropriate when there is established procedure: PEMDAS.

Leftys use intuition.  "Well, it seems to me that if we... (BS feeling to follow)"  Smart people use procedure, logic, and process.

[just Warren]

PEMDAS BOOT: The story of a German U-boat saved from certain doom because of the crew using the proper order of operations to plot a solution when trapped by enemies off the coast of Algebrazil. 

[MechAg94]

Why do you consider it sloppily written?

If I were to write it as a chemical plant operating procedure, you generally set it up to remove all doubt of how the numbers are to be calculated.  Remove the risk of using the incorrect order of operations by adding extra parenthesis.  This is a bit beyond just doing a math problem.

[Doggy Daddy]

Fully agree. ^^^^

There are times when you need to dumb it down for safety.

[230RN]

I think going to the parentheses first had me doing the second part right to left without thinking about it.  I am thinking left to right was the way I was taught but it has been a while.  My engineering side says it needs another set of parentheses.  

Pretty much ditto.  That's the same way I saw it.  It's just a different logical (yay, huzzah) way of looking at it.  Apparently the problem (and I'm sure, other examples) was sufficiently broad at one point in time (and perhaps even now) that somebody had to standardize the PEMBRAS acronym as the least likely "logic" in terms of mathematical heirarchy to cause errors.

In fact, the author of my posted link  (OP) mentions that a great many pro/con comments have been made on social media, and somewhere in that link he refers to the "old" methods, which is why I set it up as a "how old are you" premise.

In other words, what seems "logical" to one set of people (PEMBRAS folks) is not so logical to others, who have insultingly been called leftist-intuitive folks.

Anyhow, you can't have too many parentheses to establish heirarchy, in this old guy's old opinion.  I mean, you know, they don't cost all that much.

But yeah, OK, 9 it is.

(Terry) (230) (R) (N) ( :) )

[just Warren]

1. 9 +2 x 5 -11

2. (3+4) x (4-3)

3. 14 x (15-7+4)

4. 12 ÷ 2 +9 x 6

5. 18 ÷(3 x6 -9) x 3

6. 3+4 x 4-3

7. 16 ÷ 8 + 2x5 -21 ÷7

8. (18 ÷3 +28 ÷4 +2 x 4)÷3

9.  2+15 ÷3 -2 x 3+ 10

10.  3x (24 ÷2 -3 x 4 +2x6)


Answer Key (use mouse to highlight it to see it)

1. 8   2. 7   3. 168   4. 60   5. 6   6. 16   7. 9   8. 7   9. 11   10. 36   

[230RN]

I donated these to APS for free:

(((((( ((((((((( (((((((((((((( (((((((((((
))))))))))) ))))))))))) )))))))))))) ))))))

I see Warren's already used three pair.

Whenyou run out, let me know.

[230RN]

Fully agree. ^^^^

There are times when you need to dumb it down for safety.

Incidentally, I just realized how come I'm kinda fixated on parentheses.

Years ago in the mid-1980s I got a pair of programmable Sharp calculators (see below) to do routine very complex calculations where I worked.  Those things were "dumb" in that sense and  I had to really work out the sequence of operations with a lot of parentheses.

I remember the Pres of the company on one of his routine checks around the plant wondering what I was doing with those calculators as I punched in numbers.
 
He wanted the chief scientist to laboriously check my answers "by hand," meaning on one of the clunky Friden mechanical calculators because he didn't trust the idea that a "programmable" 'lectronic hand calculator could handle those complex equations.  His results agreed 100% with mine and the Pres let me continue with my Sharp calculators.

Hence my reliance on parentheses and why I started that initial calculation in the OP from the parentheses.

I still have both of them, but they're retired in a desk drawer.

FYI, these were Sharp EL-5100 and EL-5101 Scientific Calculators and were the cat's meow for the time.

Or maybe the cat's pajamas, I forget after nearly forty years.

Terry, 230RN

ETA Here ya go: