48÷2(9+3) = ?

[Balefont]

Here's a thing. When I opened this thread (and got 288), I didn't care what the right answer was. But the emphaticness of the 2 brigade compels me to disagree out of principle. The only part of this equation that takes priority is that inside the brackets, I've seen nothing else to persuade me that the multiplication has to precede the division. And left-to-right makes as much sense as the alternative. Why not:

48

--- x(9+3)

2

?

Because the denominator is 2(9+3). You can't just take part of the denominator away and move it.

[Edda van Heefmstra Ruston]

Isn't the distributative property of the 2 being next to parenthesis also part of the P in PEMDAS?

No, because it's the distributive property of the M involving multiplication (if you're thinking just 2(9+3)). This left-to-right thing is such a pain in the hole - obviously, people need to be more explicit with their parentheses and/or quit trying to write fractions on a single line. :P

ETA: The denominator isn't 2(9+3), that's where all of us went wrong. The denominator is just 2.

[Balefont]

Well, again, spelling out the equation as 48 divided by 2(9+3), the equation could also be written as:

48

--------- (divided by)

2(9+3)

[Altherion]

Isn't the distributative property of the 2 being next to parenthesis also part of the P in PEMDAS?

No. The only part that gets evaluated as part of the parentheses is what is inside the parentheses. Old Zog gave a complete and exhaustive answer to this:

1. Parentheses (and other grouping symbols)

2. Exponents (and roots)

3. Multiplication and Division (from left to right)

4. Addition and Subtraction (from left to right)

In this problem, the division occurs before the multiplication (because it is to the left).

The key in this problem is that in the absence of parentheses, multiplication and division are evaluated from left to right.

[Mr. X]

ETA: However, whatever Mr. Zray says is the right answer, I'll believe.

I say the answer is beer.

Also, if whoever wrote the original question (not Waldo, the person who wrote what Waldo typed up) wanted the answer to be 2, he or she should have either written it as a fraction or included another set of brackets to show 48/[2(9+3)]. That way there's no ambiguity. As 48/2(9+3), anyone who was taught that a number next to parentheses is the same as multiplying those numbers could read it as 48 ÷ 2 × (9+3), which is 48 ÷ 2 × 12 or 288. Or they could rewrite division by 2 as multiplication by 1/2, which makes it 48 × 0.5 × (9+3) = 288.

Seeing as today is Friday, I stand by my original answer.

Beer.

Isn't the distributative property of the 2 being next to parenthesis also part of the P in PEMDAS?

If the denominator was [2(9+3)], yes you could distribute the 2 to get 18 + 6 = 24. Without the brackets, you distribute 1/2 instead to get 48 × 0.5 × (9+3) = 48 × (.5×9 + .5×3) = 48 × (4.5 + 1.5) = 48 × 6 = 288.

[sologdin]

coco, i'm telling ya: pi(nk) + str(et)/ch?

[Balefont]

The division sign means "divided by" though. So how can the denominator not be 2(9+3) as it all fall below the / ?

[Jon AS]

The only part of this equation that takes priority is that inside the brackets, I've seen nothing else to persuade me that the multiplication has to precede the division.

This is entirely correct, there is no priority in multiplication/division. I wasn't even aware some schools/countries taught nonsense like PEMDAS. We learned simple "Punkt vor Strich" ("dots before lines"), what the hell would you get if you applied something like PEMDAS to 7-4+2? 1?

[Balefont]

I say the answer is beer.

Also, if whoever wrote the original question (not Waldo, the person who wrote what Waldo typed up) wanted the answer to be 2, he or she should have either written it as a fraction or included another set of brackets to show 48/[2(9+3)]. That way there's no ambiguity. As 48/2(9+3), anyone who was taught that a number next to parentheses is the same as multiplying those numbers could read it as 48 ÷ 2 × (9+3), which is 48 ÷ 2 × 12 or 288. Or they could rewrite division by 2 as multiplication by 1/2, which makes it 48 × 0.5 × (9+3) = 288.

Seeing as today is Friday, I stand by my original answer. Beer.

You're right. Beer.

[Vestrit]

This is entirely correct, there is no priority in multiplication/division. I wasn't even aware some schools/countries taught nonsense like PEMDAS. We learned simple "Punkt vor Strich" ("dots before lines"), what the hell would you get if you applied something like PEMDAS to 7-4+2? 1?

See, in a New Zealand accent, you basically just said 'Pink Stretch'.

Meaning that Coco and Solo are right

So is Mr X. Beer is never the wrong answer

[Mr. X]

See, in a New Zealand accent, you basically just said 'Pink Stretch'.

:lol: I was about to make a similar comment.

[Altherion]

The division sign means "divided by" though. So how can the denominator not be 2(9+3) as it all fall below the / ?

Not everything that is after a division sign falls "under" the division sign. What would you say the answer to 4 / 2 + 2 is?

[IheartTesla]

behooves you to specify the base

that's the correct reply. is it decimal, octals, hexadecimal, rads, golden ratio, i--WTF? THE QUESTION IS NOT ANSARIBBLE!!

Exactly. Interesting that the question regards the multiplication operator (*) as implicitly there, when you could easily assume the question to be 48/2(9+3)=48/212=0.226=0 (I assume we are working in the integer field, another assumption, but if you sow the hurricane you reap the whirlwind in math questions). The answer is 0, a philosophical comment on the value of mathematical problems with poorly defined parameters.

[Balefont]

Not everything that is after a division sign falls "under" the division sign. What would you say the answer to 4 / 2 + 2 is?

( 4 / 2 ) + 2 because the addition sign is farther down the order of opperations. The + essentially breaks up the equation where as 2(x) is stuck together.

[Seli]

This is entirely correct, there is no priority in multiplication/division. I wasn't even aware some schools/countries taught nonsense like PEMDAS. We learned simple "Punkt vor Strich" ("dots before lines"), what the hell would you get if you applied something like PEMDAS to 7-4+2? 1?

you just need to rewrite it properly to 7 + -4 + 2

[Jon AS]

See, in a New Zealand accent, you basically just said 'Pink Stretch'.

:rofl:

Of course I'll be happy to be a witness at Waldo's eventual trial.

you just need to rewrite it properly to 7 + -4 + 2

I know that, but someone blindly applying the acronym probably wouldn't.

[Ser Scot A Ellison]

I thought the answer was 288 as well.

[Altherion]

( 4 / 2 ) + 2 because the addition sign is farther down the order of opperations. The + essentially breaks up the equation where as 2(x) is stuck together.

"2(2)" is not stuck together -- it should be interpreted in exactly the same way as "2 * 2". I think I understand your point of view, but it goes against the rules. You can verify this by looking in a math textbook or using any calculator capable of taking such an expression is input (Microsoft Excel can do it).

[Seli]

Yes, but it's taught as PEMDAS, which is why so many of us came up with the wrong answer. There is no PEMDAS or PEDMAS (or PEMDSA or PEDMSA, for that matter).

It is, in fact, as the others later corrected:

Parentheses

Exponentials

Multiplication OR Division, moving from left to right across the expression.

Addition OR Subtraction, moving from left to right across the expression.

However, the real answer is that it's an empty door (or a goat).

Well, I was taught PEDMAS (or actually Meneer Van Dalen Wacht Op Antwoord, which lower the priority of taking roots to below multiplication and division), which has since been superseded by the rules you mention. But no-one told me that and I had to find it out myself.

Still it is no excuse to lazy writing resulting in a question that can be interpreted in different ways depending the system you learned, especially if there is a proper 2D way of writing things down that can make everything clear immediately.

I blame the rise of calculators and computers for this new set of rules. Those were too stupid to interpret a calculation properly before starting, it is the same idiot way that gave us the SMILES system for chemical structures while proper 2D systems were already long time in existence.

[Mudguard]

( 4 / 2 ) + 2 because the addition sign is farther down the order of opperations. The + essentially breaks up the equation where as 2(x) is stuck together.

I'll admit I came up with "2" at first (doh!), but I'm convinced that the answer is 288.

48/2*12=288 correct? You simply go left to right. Or do you see 2*12 being grouped as well?

I don't think replacing 2*12 with 2(12) makes a difference in the order you do the computation. 2(12) is not stuck together, but in contrast, [2(12)] would be. The problem would be a lot clearer written in fraction form.

Man, who would have thought that such a simple math problem, on its face, would cause this much debate.