Math Hurts: 48÷2(9+3)

[Stevisiov]

I see what you did there. I can do math but I can't figure out how to type it!

You can't do probability.

 

[BobK]

$ perl -e 'print 48/2*(9+3)'
288

$ php -r 'print 48/2*(9+3);'
288

$ python -c 'print 48 / 2 * (9 + 3)'
288

___48___
2 x (9+3)​

which is, of course, 2.

 

[JediRage]

Using order of operations, the answer is 288. Therefore 288 is obviously the correct answer. I'm not changing my view on this one, this is the math I'm good at, and excel at, so there's no chance in h:censored: that I'm wrong. 288! ITS 288!👍. Use BEDMAS, do the brackets, 9+3=12, then the division, 48 divided by 2=24, then multiply 24 by 12. 24x12=288.

The BEDMAS/BODMAS rule also implies that you perform all operations next to the brackets, to the answer from the brackets.

Really, this problem is just a different way of writing 48/(18+6).

 

[orimarc]

Let me see...

48 / 2 * (9+3) = 48 / 2 * 12 = 24 * 12 = 288

 

[Sharky.]

[perl, php and python]

In those examples you've used explicit multiplication, which is what leads to 288... because 2(9+3) won't compile/work correctly [language dependent] - as it's assumed to be a function call - you will always get 288 from a programming language. 48/2*(9+3) is not how the question is written, and in this case the addition of the multiply symbol affects the end result.

If there was a language that supported implicit parentheses multiplication in some way (probably through the idea that function names can't begin with a digit, so if the compiler finds <digit>(<expression>) it treats it as a mathematical expression), then you would get 2.

I'm in the camp where the division symbol is a fractional separator and everything to the right of it is the denominator (2(9+3) in this scenario), unless otherwise stated through explicit grouping of terms using parentheses.

 

[Dragonistic]

@ BobK
As above by Sharky and mentioned by myself and others, putting in the * sign actually changes the question unless you add brackets to compensate (and/or rearrange it to a fraction as Famine and others have). We're not being asked 48÷2*(9+3) but simply 48÷2(9+3), the two questions are not the same.

 

[BobK]

In those examples you've used explicit multiplication, which is what leads to 288... because 2(9+3) won't compile/work correctly [language dependent] - as it's assumed to be a function call - you will always get 288 from a programming language. 48/2*(9+3) is not how the question is written, and in this case the addition of the multiply symbol affects the end result.

If there was a language that supported implicit parentheses multiplication in some way (probably through the idea that function names can't begin with a digit, so if the compiler finds <digit>(<expression>) it treats it as a mathematical expression), then you would get 2.

I'm in the camp where the division symbol is a fractional separator and everything to the right of it is the denominator (2(9+3) in this scenario), unless otherwise stated through explicit grouping of terms using parentheses.

All very true, except no language supports the ÷ symbol, either, which is *not* identical to the / symbol (maybe ada does; that language includes everything but the including the kitchen sink).

 

[TB]

Its 288.

The exact same equation in my Casio returns... 2.

A multiplier is understood between the '2' and the '(' and as such gets taken care of before the divisor. Two it is.

 

[JediRage]

This shows that ... Texas Instruments suck.

Even the buttons are messed up.

 

[ASH32]

The windows calculator won't even accept 48/2(9+3), it ignores the 2 so it says the answer is 4 and if you do 48/2*(9+3) it says it's 288, both times the calculator is wrong.

 

[wfooshee]

So do you take 2/5x as written to mean 0.4x or 2/(5x)?

.4x

If you want 2/(5x), then write it with the parens.


I must respectfully disagree with Famine and say that the problem should be written:

48
&#8212; x (9+3)
2


As for "implied grouping" 2(9+3) is the same as 2 x (9+3)

Putting the 2 against the paren does not mean, or imply, "do this first before anything else in the problem." The number against the paren (or a variable) is just a multiplication operator. The multiplication is after the division in the problem, worked left to right. Therefore it's done afterwards.

Why does division group anything? It's just an operation. You do it as it's encountered, left to right. After parentheses and exponents, of course. A slash does not imply any grouping.

A multiplier is understood between the '2' and the '(' and as such gets taken care of before the divisor. Two it is.

Why??!?!?! It's AFTER the division when worked left to right!!! There's no other grouping symbol used to override the left-to-right order.

 

[Ibonibo]

288 just because.
The fact is:
There are considerable arguments for both answers, but the general consensus is that writing ambiguous fractions like &#8220;2/6x&#8221; makes solving such problems confusing, and it is considered bad form to write ambiguously written fractions in the first place

So it's bad written to begin with.

Now you want to solve this math-style:
PEMDAS = 2 (used in the US)
BEDMAS = 288 (used in +- the rest of the world)

So BEDMAS would take the lead as majority of population learnt it that way.

But mathematicly speaking both are not true, because / and * are n the same level and + and - are on the same level. ANd if both are in an equation, the order is from left to right
BEDMAS AND PEMDAS differentiate between brackets and parantheses, which mathematicly is wrong to. Brackets come before parantheses and they can both exist in one equation.

It's the first time i ever heard of PEMDAS or BEDMAS, we never used it. All I know is XMAS (troll)

 

[webbyy]

its 288

 

[FullSpe3d98]

Its 288. Not hard, just remember BIDMAS (BODMAS, BEDMAS etc.) and you'll be ok I guess.
Could be wrong though, I'm only twelve

 

[Dragonistic]

I must respectfully disagree with Famine and say that the problem should be written:

48
— x (9+3)
2

All I know is for all advanced mathematics I've done it would have to be written as (48÷2)(9+3) or 48÷2*(9+3) or 48/2(9+3) in order to rewrite as the above, as I would be expected to then assume the 48÷2 is to be grouped. However as this is not the case I would be expected to group the 2(9+3) instead. Basically, from how I see it, the 'normal' 4 symbols of +-÷x are taken as 'seperating' terms unless there's brackets grouping them, once you swap out the symbol for a / or no space in the case of multiplication (NB. * is treated as x though as it's only generally used on computers) I'd get my marks if I grouped those as if brackets were there (implied).

My graphical (Sharp EL-9900) agrees 100%, infact the only way to arrive at 2 is if the question is put in EXACTLY as asked with no changes or interpretations of my own.

 

[zedextreme8177]

Fact is that the problem is badly written, thus allowing for two possible answers depending on how you read it

 

[Villain]

I can't even see what number that is

Oh noes!! That means you're colorblind like my brother.

It says "42" which is, of course, the answer to everything.

 

[tankuroded]

Actually. Yes I do. But I left it like that because I'm stubborn and had to choose one. I refuse to waffle!

http://www.mathgoodies.com/lessons/vol7/order_operations.html

FWIW, Google says 288.

On the green part: Yes. I did and so voted on that. 💡

 

[Owen.C93]

I'm going 288. Forget reading the whole question, I'm a man, I solve each bit as I go.

 

[Lucas]

I say 288.

48÷2(9+3) = 48÷2x(12) = 24x12 = 288.

Here we were thought that if there's no sign between a number and a parenthesis, there's a multiplication.

Never, ever heard of BEMDAS and PEMDAS before in my life, though. With time we knew what to do first. Also, we solve from left to right. Division and multiplication don't have any priority over the other.

 

[lbsf1]

These.

Written out correctly, the problem is:

___48___
2 x (9+3)​

Now tell me that is "288"...

Anybody? Anybody? Bueller?

Written like that I would agree with you however before It could look like.

48
___ X (9+3)
24

I also don't feel particulary pleased to be insulted by Omnis. I'm due to take my Maths GCSE in a month and got an A pretty easily in the mock test. So yes you could get much dumber.


Its a badly written as said, it depends on your point of view on how you interpret it. Also what proffesion you are in/ want to go in, since then you naturally interpret it differently.

 

[Famine]

Written like that I would agree with you however before It could look like:

Error aside, no it couldn't. Read it out loud.

Back in the day, we were taught BODMAS - Brackets, Of, Divide, Multiply, Addition, Subtraction. As you pointed out earlier, 2(9+3), which resolves to 2(12) doesn't make much sense on its own - and others are pointing out that you have to assume a multiplication function. This is where "of" comes into play - 2(9+3) is "two lots OF 9+3". You don't have to assume anything - and of course 2(12) means you haven't actually dealt with the brackets at all yet...

Brackets = (9+3) = 12
Of = 2 lots of 12 = 24
Divide = 48/24 = 2

Read it out loud. "Forty-eight divided by two lots of nine plus three". Write it down correctly. "48/2(9+3)". It's a fraction - 48 is the numerator, 2(9+3) is the denominator.

 

[lbsf1]

Error aside, no it couldn't. Read it out loud.

Back in the day, we were taught BODMAS - Brackets, Of, Divide, Multiply, Addition, Subtraction. As you pointed out earlier, 2(9+3), which resolves to 2(12) doesn't make much sense on its own - and others are pointing out that you have to assume a multiplication function. This is where "of" comes into play - 2(9+3) is "two lots OF 9+3". You don't have to assume anything - and of course 2(12) means you haven't actually dealt with the brackets at all yet...

Brackets = (9+3) = 12
Of = 2 lots of 12 = 24
Divide = 48/24 = 2

Read it out loud. "Forty-eight divided by two lots of nine plus three". Write it down correctly. "48/2(9+3)". It's a fraction - 48 is the numerator, 2(9+3) is the denominator.

Yeah I get how you explain it now.

However since it written so badly you have to assume the times, which is pretty shocking for a maths question. Maths only has one answer (as proven in this thread) so assuming isn't good.

 

[DriverD00d]

To re-word the problem:
48÷2x(9+3)=
9+3=12
48 Divided by 2=24
24x12= 288

 

[Famine]

You don't need to assume it at all. 2(9+3) means "2 lots of nineplusthree".

It is deliberately written badly - perhaps to expose a culture gap in teaching caused by PEMDAS and BEDMAS conflict (the reality being that division and multiplication have equal weighting - so there is no conflict), the loss of "of" in teaching and by teaching left-to-right problem solving (which has no basis in mathematics).

That scientific calculators get it right doesn't surprise me.

To re-word the problem:
48÷2x(9+3)=
12
24 x 12 = 288

It doesn't need rewording - and if you do, you run the risk of rewording it wrongly. As, in fact, you have.

 

[DriverD00d]

No
Ive learned VERY recently that numbers placed in front of perenthesis means to multiply.
The steps I learned way back was PEMDAS
Perenthesis
Exponents
Multiplication
Division
Addition
Subtraction

You start off with Perenthesis- 48/2(9+3)
After solving is complete (12), you move on to the next step. We can cross out Exponents as there are none in the problem.
After that, we move on to multipliying. However, in problems like these, we have the option of skipping to Division as we have not yet solved 48/2. 48/2= 24.
Now, we can move on to Multiplying. We multiply 24 times 12, and get 288. I honestly dont see how people are getting 2.

 

[Famine]

No
Ive learned VERY recently that numbers placed in front of perenthesis means to multiply.
The steps I learned way back was PEMDAS
Perenthesis
Exponents
Multiplication
Division
Addition
Subtraction

You start off with Perenthesis- 48/2(9+3)
After solving is complete (12), you move on to the next step.

Note that you still have parentheses after you claim to have solved that step. (12) is still a number in parentheses. You haven't solved it, but have moved onto the next step...

After that, we move on to multipliying. However, in problems like these, we have the option of skipping to Division as we have not yet solved 48/2. 48/2= 24

Interesting. You get to skip a rule if you want to? Sounds a bit fudged to me...

I honestly dont see how people are getting 2.

Brackets = (9+3) = 12
Of = 2 lots of 12 = 24
Divide = 48/24 = 2

Read it out loud. "Forty-eight divided by two lots of nine plus three". Write it down correctly. "48/2(9+3)". It's a fraction - 48 is the numerator, 2(9+3) is the denominator.

 

[DriverD00d]

Note that you still have parentheses after you claim to have solved that step. (12) is still a number in parentheses. You haven't solved it, but have moved onto the next step...



Interesting. You get to skip a rule if you want to? Sounds a bit fudged to me...

I was just pointing out that we have solved and got 12. At the time 12 does not have perenthesis until it has been solved completely.
Yes, we learned that if you cannot do a step, you can skip it and return to it. However its only done with Multiplying and Dividing. It goes like this:
P
E
M-[Always before D unless the problem is unsolvable without first dividing]
D -[Always after M unless the problem cannot be solved without using M]
A
S

Im starting to think that this problem can officially be solved 2 different ways. Using PEMDAS, which states brackets and perenthesis immediatly following a number are to be multiplied, or dividing. Ive learned that it means to multiply and im sticking with that, OR to divide the number before the brackets or perenthesis.

 

[lbsf1]

To everyone who is confused, as famines has just taught me. The brackets stage is turning the 9+3 into 12 and then timesing it out. That is all one stage.

Thats what suddenly made it click to me.

 

[Famine]

I was just pointing out that we have solved and got 12. At the time 12 does not have perenthesis until it has been solved completely.

If the parentheses have not been eliminated, they have not been solved.

Yes, we learned that if you cannot do a step, you can skip it and return to it. However its only done with Multiplying and Dividing. It goes like this:
P
E
M-[Always before D unless the problem is unsolvable without first dividing]
D -[Always after M unless the problem cannot be solved without using M]
A
S

In your "reworded" notation, you can do that step - you skipped it incorrectly:

48÷2x(9+3)

Solve the (9+3) and you get 12. Your reworded version now says "48÷2x12". Look, there's the multiplication step you can do (even though you had to insert a multiplication symbol originally)! Now your reworded version says "48÷24"...