48÷2(9+3) = ?

[Hopalong X]

There is no left to right "thing". You typed in the wrong equation. Remove the outside parentheses. (48 =xx)

 

[fseal]

Heh the equation is ambiguous. It specifically exploits ambiguous math rules. Both answers are correct. What is /wrong/ is that the equation was improperly written for anything more than personal consumption. Any attempt to publish such a thing would have to have had the ambiguity removed.

Comp Sci is full of such things, and even though the rules are strictly defined, if you want a chance in heck that anyone is going to understand you, you explicitly disambiguate the equations.

(This is how space station parts mishaps happen, no good engineer would allow such an equation to escape his notebook)

 

[ignatzatsonic]

I did well at algebra and math, but cannot recall the exact order of operations as I learned them, but am not sure they are the problem here.

48÷2(9+3) = is ambiguous as written and the first consideration of communication is to not confuse the reader.

I don’t know the intent of the author, but I was taught 50 years ago to say “the quantity” in such situations. When using “the quantity”, the equation could mean:

1: The quantity (48 divided by 2) times the quantity (9 plus 3), which is clearly 288, but I would have written it this way to avoid ambiguity:

(48÷2)(9+3) = 288

Or it could mean:

2: The quantity 48 divided by the quantity two times (9 plus 3), which is clearly 2, but I would have written it this way to avoid ambiguity:

(48)÷(2(9+3)) = 2

So---as written, I’m not sure there is a correct answer and I would fault the equation writer for not being explicit and leaving unnecessary doubt. Who knows what the intent was?

Of course, maybe the correct notation has changed over the years and there is no ambiguity by current standards?

Or maybe I’m all wet, not for the first time.

 

[Hopalong X]

There is no ambiguity.
If the answer were 288 the equation would be (48÷2)(9+3) = 288
That is the only way the equation can be written that the 48 is divided by 2.

No wonder we have dropped to 25th in Math in the U.S.
U.S. Teens Lag as China Soars on International Test - Bloomberg

 

[fseal]

Clearly it is ambiguous, the mere existance of this "problem" is that this equation was formulated specifically to exploit an ambiguity in mathmatical conventions. If there was none, the problem would not exist.

But finally, even if it weren't ambiguous, as both Ignatz and I just pointed out, it's bad form to publish even /potentially/ ambiguous code or equations.

Things like "PEMDAS" are merely conventions for writing equations. Both parties have to agree on the convention. PEMDAS actually restricts true mathmatics since it places an operator precidence where none mathmatically exists. It merely lays out a ruleset for writing equations which, if both parties agree, leads to unambiguous communication. But unless both parties DO agree and know that they are adhering to the PEMDAS convention, then there is in fact ambiguity which could and should have been taken care of by more generally understood mechansims (more explicit use of parens)

 

[Everlong]

There is no left to right "thing". You typed in the wrong equation. Remove the outside parentheses. (48 =xx)

Yes there is a "left to right" thing. I stated before, and it's the order of operations.

Clearly it is ambiguous, the mere existance of this "problem" is that this equation was formulated specifically to exploit an ambiguity in mathmatical conventions. If there was none, the problem would not exist.

That's what it boils down to. The whole thing uses bad notation and without proper use of parenthesis will remain ambiguous.

PEMDAS (as well as BODMAS) has M and D at the same precedence, same as A and S are the same precedence. To force the multiplication before division, you'd have to write it has 48/(2((9+3)).

Creating a program to work it out, C, Python and MATLAB result in 288.

You can easily see how different calculators give different answers too. Open Windows calculator in standard view and do 2+2*2, then do the same sum in scientific view and you'll get a different answer.

 

[arkhi]

There is no left to right "thing". You typed in the wrong equation. Remove the outside parentheses. (48 =xx)

The outside parenthesis are merely programmatic to comply with MS Math's code; they are added and formatted automatically when a standard equation is added

i.e. solve(equation+sqrt(solve(equation)))

 

[Hopalong X]

The ambiguity if one exists is an algebraic equation has been written in basic math format.

The algebraic equation should be:

__48__ = x ......Which results in x= 2
2(9+3)

Sorry I do not have software to write algebra formulas. So I did the best I could.


_48_ (9+3) = x Which results in 288. Which would be (48÷2)(9+3)= x or 288
2

Complex algebra formulas are written as fractions not using ÷


__48__ = 48÷2(9+3)
2(9+3)

I changed to forward slash / for fraction or to denote division below.
a/b = c
a÷b= c when converted to algebraic expression is a/b= c


a=48
b= 2(9+3)
c= unknown

Division or the fraction in these equations is the primary action of the equation.

All secondary actions must be completed first.

 

[Everlong]

The ambiguity if one exists is an algebraic equation has been written in basic math format.

The algebraic equation should be:

__48__ = x ......Which results in x= 2
2(9+3)

Sorry I do not have software to write algebra formulas. So I did the best I could.


_48_ (9+3) = x Which results in 288.
2

Complex algebra formulas are written as fractions not using ÷

Doing the method you just did, you're giving division precedence over multiplication, which it doesn't have. You perform division and multiplication left to right.

It should be

__48__ = 48÷2(9+3)
2(9+3)

I changed to forward slash / for fraction or to denote division below.
a/b = c
a÷b= c when converted to algebraic expression is a/b= c


a=48
b= 2(9+3)
c= unknown

Division or the fraction in these equations is the primary action of the equation.

All secondary actions must be completed first.

Doing what you did, you're giving division precedence over multiplication which it doesn't have.

It should be

What you did would be written as 48/(2(9+3)).

 

[Win7User512]

2.

For the answer to be 288, the problem should have been (48÷2)(9+3)

+1.

Remember: PEMDAS.

 

[Hopalong X]

Sorry but the FRACTION is the primary function of this equation - not division or multiplication.

That is what I was attempting to explain.

This

converts to this in simple math/algebra (48÷2)(9+3)= x ...and that is not the way the origninal equation is written.

 

[arkhi]

Given the equation 48÷2Χ12 how would you solve it?

 

[Hopalong X]

Algebra equation it becomes 48/2x12. You have to account there is no division symbol - only fractions.

 

[Everlong]

Given the equation 48÷2Χ12 how would you solve it?

Just work simply from left to right.

Sorry but the FRACTION is the primary function of this equation - not division or multiplication.

That is what I was attempting to explain.

This

converts to this in simple math/algebra (48÷2)(9+3)= x ...and that is not the way the origninal equation is written.

And the notation you used isn't how the equation is written, because as I said, you're giving multiplication precedence over division, which results in the equation being written as 48/(2(9+3)). ÷ and / both simply mean divide, too. Doesn't change anything.

The expression is computed as




The main problem with it though is just how different people follow different standards. It is an ambiguous equation, because the way it's written should be avoided, and should be written as you said (48/2)(9+3) to make it crystal clear.

 

[arkhi]

Just work simply from left to right.

Well, that answers everything, right?

*Just a thought, would it make more sense if it were converted to have the same operator altogether?

e.g.
48Χ½Χ12 <-- 48Χ½=48÷2
(48)(½)(12)
(12)(48)(½) <-commutative property


Everything leads to 288

 

[Win7User512]

48 / 2 (9 + 3):

1. Parentheses: (9 + 3) = 12.
2. Exponents: none. (Actually there are: (48^1) / (2^1)((9^1) + (3^1)), but we can ignore them)
3. Multiplication: 2 * 12.
4. Division: 48 / 24 = 2.


Edit: Wow, only 63.89% of the respondents have answered this correctly?

 

[Everlong]

48 / 2 (9 + 3):

1. Parentheses: (9 + 3) = 12.
2. Exponents: none. (Actually there are: (48^1) / (2^1)((9^1) + (3^1)), but we can ignore them)
3. Multiplication: 2 * 12.
4. Division: 48 / 24 = 2.


Edit: Wow, only 63.89% of the respondents have answered this correctly?

Why are you giving multiplication precedence over division if they're the only two operands left after the parenthesis?

 

[Win7User512]

48 / 2 (9 + 3):

1. Parentheses: (9 + 3) = 12.
2. Exponents: none. (Actually there are: (48^1) / (2^1)((9^1) + (3^1)), but we can ignore them)
3. Multiplication: 2 * 12.
4. Division: 48 / 24 = 2.


Edit: Wow, only 63.89% of the respondents have answered this correctly?

Why are you giving multiplication precedence over division if they're the only two operands left after the parenthesis?

Ah, correct that when they are the remaining explicit operators, they are performed left to right.

I was thinking 48 / 2(12), while typing 48 / 2 * 12.

Consider this oddity, courtesy of purplemath.com:

 

[Joan Archer]

Whatever the answer the question started quite a debate and I got lost after the question so bye bye.

 

[alfred01]

Wow. Don't overthink it folks. Go back to simple math.

48÷2(9+3) Once you do the work in brakets this question becomes
48÷2x12 At this point you follow the math rule that you do complex problems in the order they appear, which gives you
24x12= 288