48÷2(9+3) = ????

[UconnTim97]

My Google Fu is not strong this morning. Has anyone found or know the origin of this equation? I am just curious what started this internet sensation.

[Esel Mann]

The conf

[romad]

solve:

16 ÷ 2[8 – 3(4 – 2)] + 1


and the answers is NOT 17

[Esel Mann]

The confusion is coming from the order of operations and placing a precedence of multiplication over division and addition over subtraction.

firstly I believe it is generally accepted that when analyzing the equation for the operators present in the given equation, for each analysis step one moves from left to right.

secondly, many have mentioned or implied that there is a precedence between multiplication over division and addition over subtraction. I believe that the precedence is the following:

brackets/parenthesis
exponents
multiplication/division
addition subtraction

The key here is that when encountering either multiplication/division there is no precedence between the two other than analyzing from left to right. It is the same for addition/subtraction.

So for 48÷2(9+3) = ????

Firstly, moving left to right the first set of bracket or parenthesis encountered is the (9+3) term. Which results in 12. The equation is now at:

48÷2(12) = ????

Now we see that all that is left is multiplication and division. So moving from left to right:

48÷2 results in 24 so the equation then becomes:

24(12) = which is 288.


For the rules above though, don't take my word for it. Look it up. The above is all discussed in any C programming language reference manual. I suggest referencing Kernighan and Ritchies (they're the dudes who created C) "The C Programming Language".

[Esel Mann]

16 ÷ 2[8 – 3(4 – 2)] + 1

[] take precedence so first look at

[8 - 3(4-2)], where here the () take precedence so it is actually [8 - 3(2)]

here the multiplication takes precedence over the subtraction so [8 - 6] = [2]

so the equation is now at 16 ÷ 2[2] + 1

and here the multiplication and division take precedence over the addition

so moving left to right the division is performed first then the multiplication for

16 ÷ 2 = 8, so it is now 8[2]+1,

do the multiplication, 16+1 and lastly the addition for a result of 17

[masraum]

Originally Posted by Esel Mann

16 ÷ 2[8 – 3(4 – 2)] + 1

[] take precedence so first look at

[8 - 3(4-2)], where here the () take precedence so it is actually [8 - 3(2)]

here the multiplication takes precedence over the subtraction so [8 - 6] = [2]

so the equation is now at 16 ÷ 2[2] + 1

and here the multiplication and division take precedence over the addition

so moving left to right the division is performed first then the multiplication for

16 ÷ 2 = 8, so it is now 8[2]+1,

do the multiplication, 16+1 and lastly the addition for a result of 17

Yeah, that's right, but if you use his special rules, I'm thinking that he thinks the answer is...

5


.....which it's not

[romad]

Originally Posted by wdfifteen

People who work with numbers accept the convention that everything to the right of the division sign is the denominator. I never learned it as a "rule" it's just the way things are done in the technical world. If this equation was in a problem on an engineering exam and you got 288, you would fail the test. If you were designing an actuator for an airplane wing, the plane would crash.
I don't remember the third grade. Maybe if you were in the 3rd grade, you'd pass.

WHAT? "People who work with numbers accept the convention that everything to the right of the division sign is the denominator" the morons. "If you get 288 on an engineering exam you would fail, but the airplane crashes." Genius

Let see...the answers is 2 from a group of engineers with advance degrees and god knows how many patents in the fields of advance fluids and themodynamics, who could pass an engineering exam, but fail 3rd grade math....interesting take.

[romad]

Yes MY special rule

Here a better explaination.

The Order of Operations: More Examples

Oh and at the current rate 63% of the pelicans think so also......I'm guessing they are foolish engineers who work with number just accepting that silly convention.

[DARISC]

Originally Posted by romad

solve:

16 ÷ 2[8 – 3(4 – 2)] + 1


and the answers is NOT 17

No, it is NOT 17

Using MY special 'RULE OF 288':

16/(2 (8 - 3 (4 - 2))+ 1=288-283=5

the answer IS 5

and the answer to the OP's equation IS 288



Seriously, 16/(2 (8 - 3 (4 - 2))+ 1=5

Do you disagree?

[kach22i]

Originally Posted by Esel Mann

48÷2(12) = ????

Why the question mark?

Why not solve for "X"?

48÷2(12) = X

Doing the division first by canceling the 2 with the 48.

24÷1(12) = X

2 = X

Like I said, I'll go along with the 288 with the understanding that in school this would have been an extra credit question as the format is poor and would not be tolerated as an answer or sample problem by an author of text books.

[krystar]

you're still applying wrong order of operations on the left side of the equation.

the definition of "A/B*C" syntax is
A
-- * C
B



it is NOT:

A
-----
B*C

[Targa Me]

Originally Posted by kach22i

Why the question mark?

Why not solve for "X"?

48÷2(12) = X

Doing the division first by canceling the 2 with the 48.

24÷1(12) = X

2 = X

Like I said, I'll go along with the 288 with the understanding that in school this would have been an extra credit question as the format is poor and would not be tolerated as an answer or sample problem by an author of text books.

Why are you putting in another division sign after the 24? That division sign was cancelled after the first application. So it should be 24X12 =X

[Esel Mann]

For the two equations:

48÷2(9+3)

16 ÷ 2[8 – 3(4 – 2)] + 1

Why not try pumping them into excel and see what you get?

for excel one would pump in:

=48/2*(9+3)

=16/2*(8-3*(4-2)) + 1

my excel returns 288 and 17 respectively.


Also, another way to look at the first equation:

48÷2(9+3) = 48÷2(9) + 48÷2(3) = 24(9) + 24(3) = 288

and another way to look at the second equation:

16 ÷ 2[8 – 3(4 – 2)] + 1 = (next line as expanded is longer)

16 ÷ 2[8] - 16 ÷ 2[3(4 – 2)] + 1 =

16 ÷ 2[8] - 16 ÷ 2[3(4)] + 16 ÷ 2[3(2)] + 1 =

8[8] - 8[3(4)] + 8[3(2)] + 1 = 17

The debate here is the notion that multiplying something in parenthesis gives the multiplier a higher precedence over simple left to right. The C reference I mentioned (and I could dig for other references which would agree if necessary), plus the results from excel suggest that the left to right rule applies.

If there is a reference or source out there which states that multiplying something in parenthesis takes a higher precedence over the simple left to right rule, please share with us!!!

[DARISC]

Originally Posted by kach22i

Why the question mark?

You'll have to ask z-man; he posted it that way.

Why not solve for "X"?

? * any n>0=X...ALWAYS!

48÷2(12) = X

Doing the division first by canceling the 2 with the 48.

24÷1(12) = X

2 = X

Nope. 288 = X.

Like I said, I'll go along with the 288...

Great! I'm sure Al Gebra will breathe a sigh of relief!

with the understanding that...

Uh, oh

in school this would have been an extra credit question as the format is poor...

48÷2(9+3) = X is neither 'poor' nor 'excellent' nor any other subjective adjective one may choose to use...it simply is what it is, i.e.,'valid', or any of its synonyms.

and would not be tolerated as an answer or sample problem by an author of text books.

Then that unqualified author should be banned from writing textbooks!
NO! He/she should be burned like a steak on a pile of any of his/her books that may have made it into circulation and then his/her ashes violently stomped into a mold to form a square pi!!

X=288

Seriously, just because 63% of those polled here stumble over their own math prowess and come up with the wrong answer isn't the fault of the equation.

..

[masraum]

Quote de kach22i

Why the question mark?



You'll have to ask z-man; he posted it that way.



Why not solve for "X"?



? * any n>0=X...ALWAYS!



48÷2(12) = X



Doing the division first by canceling the 2 with the 48.



24÷1(12) = X



2 = X



Nope. 288 = X.



Like I said, I'll go along with the 288...



Great! I'm sure Al Gebra will breathe a sigh of relief!



with the understanding that...



Uh, oh



in school this would have been an extra credit question as the format is poor...



48÷2(9+3) = X is neither 'poor' nor 'excellent' nor any other subjective adjective one may choose to use...it simply is what it is, i.e.,'valid', or any of its synonyms.



and would not be tolerated as an answer or sample problem by an author of text books.



Then that unqualified author should be banned from writing textbooks!

NO! He/she should be burned like a steak on a pile of any of his/her books that may have made it into circulation and then his/her ashes violently stomped into a mold to form a square pi!!



X=288



Seriously, just because 63% of those polled here stumble over their own math prowess and come up with the wrong answer isn't the fault of the equation.

..

How do you really feel?

[wdfifteen]

Originally Posted by krystar

you're still applying wrong order of operations on the left side of the equation.

Which side is the "left" side?

[masraum]

Quote de romad

solve:



16 ÷ 2[8 – 3(4 – 2)] + 1





and the answers is NOT 17

No, it is NOT 17



Using MY special 'RULE OF 288':



16/(2 (8 - 3 (4 - 2))+ 1=288-283=5



the answer IS 5



and the answer to the OP's equation IS 288







Seriously, 16/(2 (8 - 3 (4 - 2))+ 1=5



Do you disagree?

I don't see a difference between the two problems. One yields 288 and the other yields 17. The equation that you solved has an extra set of parentheses.

[DARISC]

Originally Posted by masraum

How do you really feel?

Fine, thank you! Hope I don't come across as nasty!

I'm just enjoying this thread.

???? = 288

[svandamme]

Order of operations - Wikipedia, the free encyclopedia

The standard order of operations, or precedence, is expressed in the following chart.
#1 terms inside brackets
#2 exponents and roots
#3 multiplication and division
#4 addition and subtraction

a


16 ÷ 2[8 – 3(4 – 2)] + 1
Apply #1

16 ÷ 2[8 – 3(2)] + 1


16 ÷ 2[8 – 3 x 2] + 1
#3 within the square brackets

16 ÷ 2[8 – 6] + 1
#1

16 ÷ 2[2] + 1

16 ÷ 2 x 2 + 1

Rule 2
8 x2+1
#3

16 +1
#4

17

So it is 17 after all.






48 ÷ 2(9+3)
Rule 1
48 ÷ 2(12)

48 ÷ 2x 12

Rule 3
24 x12

288

[DARISC]

Originally Posted by masraum

I don't see a difference between the two problems. One yields 288 and the other yields 17. The equation that you solved has an extra set of parentheses.

Oops...my typo.

16 ÷ 2[8 – 3(4 – 2)] + 1 = 5

One yields 288 and the other yields 5.