Simple Math?
 

Many have probably seen this in the past few weeks as it has been quite popular on the internet, but I have not seen a thread on this here and am curious what this board thinks.

48÷2(9+3) = ???

Seems pretty obvious to me.

My understanding is the 2 should not be done with the bracket as you solve what is in the bracket first. Once you add the 9 and 3 together the bracket can disappear and a multiplication sign now exists. Then following the order of operations you get 288.

Pie?

Yeah, that's what I would think. Just because there's no multiplication sign visible doesn't mean that you evaluate the 2*12 before you divide 48 by it.

Now I see the images, and I guess both Texas Instruments and Casio have some 'splaining to do.

That is what I'd think, but I've seen threads on other boards that are almost 3000 posts on such a seemingly obvious problem.

FOFC is behind the times. This has been breaking the internet for the last month. ; )

See, I would think that the parentheses remain, even after you add the 9+3, so you would multiply first, then divide by 48. My calculator's answer is 2 (which is the same as when I did it in my head).

*shurg*

I always took 2(9+3) to basically represent one number on that level of the problem, a number that needed to be addressed and placed before you work out anything else on the same level of the problem.

Although parentheses come first in order of operations, my understand is that's just for evaluating what's inside the parentheses. Once you have a 12 in the parentheses, it's just an element of the multiplication, and since division and multiplication are equal in the order, you just go from left to right.

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

Although from what folks are saying here, there's some faction on the internet and some calculators that disagree.

Dola

To get the number to be 2, I would think it'd have to be written as 48/(2(9+3)).

4th grade.
Please Excuse My Dear Aunt Sally
Parenthesis, Exponents, Multiply, Divide, Add, Subtract

48 /2(9+3)

Parenthesis, check
48/2(12)
Exponents, nope
Multiply, check
48/ 24
Divide, check
2
done.

Multiplication does not necessarily come before division, though. If you're evaluating something that has only multiplication and division in it, you just work left to right. Same with addition and subtraction.

5-4+3 == 4
5-4+3 != -2

+1

That's the issue with this. There is no standardized order of operations when it comes to "bracket multiplication". Some people say it makes it go ahead of normal division and multiplication in the order of operations (Otherwise it would be written as 48 ÷ 2 * (9+3) ), others say it's just short hand for normal multiplication. But there's no formal rule about it.

IT should be written like this instead.

The reason why some people are getting 288 is that they're forgetting that there's an invisible multiply sign in the expression.

No, I am absolutely aware that there's an invisible multiplication sign. In fact, that sign is precisely why I'm saying it's 288.

To sabotai's point, if there's no formal rule for the "bracket multiplication", then we'll never get everybody to come to agreement. The points both sides make are pretty obvious. It's just a matter of which you agree with. Given that this makes the discussion rather futile, I guess I'm done here.

That's a separate problem. Written that way, you'd do the multiplication first regardless of the debate over the way the multiplication is written since you always fully work out the numerator and denominator first before dividing.

48 ÷ 2(9+3) is not the same thing as that.

For instance: 40 * 2 / 10 * 10

If that division sign is shorthand for a fraction, then the answer is 0.8, since you do both multiplications first. If it's simply division, than the answer is 80, since you work left to right.

Math sucks.

Well shit. I have we even come to a time when we cant even agree on math answers.

I always assumed the order was like CU Tigers post but now the more I am reading up on this it appears around 50 percent of the nation use the same method as I believe Pumpy is using where

P
E
MD
AS

Yes, it's just like every other debate on the internet. :)

It's just what I read when it looked it up a week or two ago. There may be a formal ruling somewhere, but Google is keeping it secret from me.

There are actually two ways for it to be written. So I believe it is safer to stick with the order of operations rather than pick which way it should be written out on paper.



I'd argue if there is no formal rule one should go with a formal rule. Order of operations states you complete what is only inside the parentheses first. When the 2 appears next to them all it really is saying is multiply in shorthand as you stated. Which to me means it should be treated as such in the order of operations.

If we are going off of Google...

I believe the answer is 288

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

There's also the rule that a(b + c) = (ab + ac)

So that 48 ÷ 2(9 + 3) = 48 ÷ ((2 * 9) + (2 * 3)) = 48 ÷ (18 + 6) = 48 ÷ 24 = 2

48/2(9+3).............................? - Yahoo! Answers

I think this best sums it up.

You guys probably stand up to wipe your asses after you take a shit too, i bet. 288?gtfo---->

There's a very easy way to find out which is the correct answer, though. Replace one of the values with "x" and try to solve for both answers. I'll replace the 2 outside of the brackets with an x and which ever answer solves "x = 2" (to get us back to the original equation) is the correct answer.

48 ÷ x(9+3) = 288
48 ÷ (9x + 3x) = 288
48 ÷ 12x = 288
48 ÷ 12x * 12x = 288 * 12x (The two 12x on the left cancel each other out)
48 = 288 * 12x (divide both sides by 288)
48 ÷ 288 = 288 * 12x ÷ 288 (the two 288s on the right cancel out)
48 ÷ 288 = 12x (now divide both sides by 12)
48 ÷ 288 ÷ 12 = 12x ÷ 12
48 ÷ 288 ÷ 12 = x
0.013888888888888888888888888888889 = x

Well that didn't work out. Let's try 2

48 ÷ x(9 + 3) = 2
48 ÷ (9x + 3x) = 2
48 ÷ 12x = 2
48 ÷ 12x * 12x = 2 * 12x (The two 12x on the left cancel each other out)
48 = 2 * 12x (divide both sides by 2)
48 ÷ 2 = 2 * 12x ÷ 2 (the two 2s on the right cancel out)
48 ÷ 2 = 12x (now divide both sides by 12)
48 ÷ 2 ÷ 12 = 12x ÷ 12
48 ÷ 2 ÷ 12 = x
2 = x


The answer is 2.

:D

I guess I'm not done here. I can't resist.

You're taking a hell of a leap here on the bolded parts. The distributive property doesn't tell you to put those pieces in parentheses. a(b + c) = ab + ac, necessarily. a(b + c) does not imply (ab + ac) when put into an equation as above.

Yes, yes, I know the debate is if you can do that or not. I'm just being difficult. And bored. And wide awake at 2 am.

I'm just happy I got Serious Pumpy to make a special appearance on FOFC. :D

2/3

Well, I'm not even sure if people who are asserting one or the other even think about it that way. Your post just seemed so definitive that I was trying to squelch others' cheers of "SEE, IT'S CLEARLY 2!!! THERE'S THE PROOF!!!" because I'm being difficult, too.

I'll acknowledge that a case could be made either way, so I'll concede this as somewhat ambiguous. With that said, I still can't parse the logic that shows the answer as 2, but that could be my fault.

And I'm only serious because I used up all my fun at bowling a few hours ago. So you did catch me at the right time.

I haven't heard of this till just now, but using what I was taught in high school, I got 288.

...I'm just confusing myself.

48÷2(9+3) = ???

That part screws me up ÷


48/2(9+3)=288

Either learned or assumed the fact that the 2 was linked to the parentheses made me think I needed to multiply that part first.
In order for this equation to equal 2 it should look like 48/(2(9+3))

Id like to change my vote:)

The answer I get is too gross to share.

That is the method I was taught so I got 288.

And if we're going off of Wolfram.

Anyone that says 2 is wrong. There is no ambiguity. If you want to use the distributive property, then 24 (not 2) must be distributed over the additive clause so it becomes (9*24) + (3*24).

obviously the correct answer is simply 42

It's been a while since I've contemplated this type of ruleset with any conscious effort.

Going on what I recall being taught (which may not be the correct recollection)...my answer would have been 2. After checking with Excel, I see I am incorrect (btw...excel forces the * between the 2 and the (9+3) ). :)

But thinking about it further...I see I would be wrong on many occasions.

5+3/1+3 = 11

11 doesn't feel natural to me as I would tend to solve the sides of the fraction (in my mind) and come up with 2.

Hmm...not much of a point to my post other than to point out how evil & tricky the number 2 can be.

I saw this problem on another site. I teach Math and have a Math degree and it is funny to me that all of the mathematicians agree that the answer is 288. :)

Well, it's a good bit of comeuppance for anyone who's ever said, "why do we need to learn this stuff? Let the calculator do it."

This is the most incomprehensible part of this whole thread.

288 looks right to me. Evaluate the parenthesis first, then work left to right since division and multiplication are both the same level of "importance".

This is why when I write code, I put all the parentheses in to make sure the compiler evaluates it in the order I intended. I'd hate for the PS3 compiler to evaluate it one way and the 360 compiler to evaluate it another.

I agree, the original formula is a stupid way of writing out what you want, just like 4 * 2 / 10 * 3 is stupid. Put the parentheses in to be clear.

That said, I'm on the side of "you solve math problems via simplification". So when you write 48 / 2 ( 9 + 3 ) you get:

48 / 2 (12) = 48 / 2 * 12 = 24 * 12 = 288

Anyone else is just getting tricky with the formula. They're not WRONG per se, they're just going about math the hard way...