48÷2(9+3) = ??

48/2(9+3) = 48 / 2 * (9+3)

Order of operations:

First, do any operations in parenthesis = 48 / 2 * (12)

Nest, exponents (none).

Then, division and multiplication from left to right =

24 * 12 =

288

Then, addition and subtraction.

Travis_K wrote: I would have said 2 doing it in my head, but on my TI89 (which allows you to enter it in the exact same format as the question posed) says 288. iPhone says 288 also.

that is exactly why you got the wrong answer... you can't possibly plug things in from left to right. You have to solve them in priority order, otherwise the entire language of math is irrelevant.

You have to use the TI89 correctly in order to get the correct answer.

Plug this one in on your TI89 and tell me what you get:

Pi = 256/14 + x

Your TI89 will read that as:

3.14... = (256/14) + x

which would then equal:

3.14 = 18.2857 + x

and give you the answer of x = -15.1442. And it would be incorrect.

the proper way to solve that equation is to think of it like this:

3.14 = 256/(14+x)

It MUST be that way because the parenthesis do not exist surrounding the 256/14. In math language, if it is not implied, it can't be assumed. Therefore my equation has no option but to be read:

Pi equals two hundred fifty six, divided by fourteen plus x.

NOT

Pi equals two hundred fifty six divided by fourteen, plus x

Notice the change in the comma. This also means (in math language) that the only way for the OP's formula to be read is:

forty eight, divided by two parentheses nine plus three.

NOT

forty eight divided by two, parenthesis nine plus three.

Sorry, but this is pretty cut and dried. 288 is an incorrect answer, and no amount of arguing would win you partial points on a test.

what about PEMDAS and the multiplication and division cancelling each other out if next to each other, also with adding and subtraction??? I'm not going against anyone here but I guess my math teacher was wrong then........and again there is both answers here, but it all depends on how it is written

2.

Jay wrote: the equation in question is 100% completely, unarguably, identical to writing "48 ÷ 2x = ?, where x=9+3."

I believe this makes it so.

Salanis wrote: 48/2(9+3) = 48 / 2 * (9+3)

Okay, this is the problem. You CAN'T make that equivalency. It looks right but it isn't.

What you can actually write is 48/2(9+3) = 48/(2 × (9+3)), which equals 2.

The problem is that a number adjacent to a bracket (so-called implicit multiplication) is multiplied, but it isn't treated as a × sign for "BEDMAS" purposes. Think of it as a way of implying that there are brackets around the whole term.

Look at it this way. "2x" is not a short form of "2 × x". It's a short form of "(2 × x)". This is a very important distinction! A 2(x+y) term in an equation is the same thing as having (2 × (x+y)).

You can also think of it as a function:

Let f(x)=(9+3)x

So f(2)=(9+3)·2=24

Then you have

48 ÷ 2(9+3) = 48 ÷ f(2)

which is a perfectly valid way of expressing the same thing. I haven't changed anything, contextually, implicitly, or otherwise. And the only way to evaluate that is

48 ÷ f(2) = 48 ÷ (2(9+3)) = 2.

BEDMAS is not the be-all and end-all of equation parsing. In higher level math (calculus, algebra, etc), BEDMAS generally goes out the window. You have to learn to "read" equations contextually.

Okay, I'm going to quit before I waste my whole morning on this, like I did last night. I've got solderin' to do.

Damnit, I'm algebra right now and I STILL got this wrong.

By the way, HalfTrac: you bastard! Last night I DREAMT I was arguing with people over this stupid problem. Thanks for that.

Jay wrote: By the way, HalfTrac: you bastard! Last night I DREAMT I was arguing with people over this stupid problem. Thanks for that.

My girlfriend was foaming at the mouth over this. (She agrees with you by the way, and considering she probably just took this stuff in high school like... 2 years ago or whatever...)

mtn wrote:

92CelicaHalfTrac wrote:

imirk wrote: I say it is 288 becarze: you cannot distribute the 2(9+3) without first dealing with the division sign so you get 48/2(9+3)=24(9+3)=216+72=288

Not to nitpick, but you messed that up. 48/2(9+3) = 24/(9+3) = 24/12 = 2

Huh? Where did you get the 24? Answer: you did 48/2. The "/" is gone. You have 24*(9+3)

No... i factored 2 out.

I've come to realize that there's people who will consider 2(9+3) as a number in this context, and there's people who will consider it as a problem that must be solved.

It's back to Jay's example of 2x. Seems Jay and I for example see "2x" as a value, not as a problem, and that value happens to be twice the value of "x."

This is just interesting to me at this point. It's damn near a 50/50 split from every sample i can see across the internet. We've got college professors taking both sides, engineers taking both sides, high school kids, college grads, etc etc etc...

NickF40 wrote: The way I was told, by my math teacher, was switched from what you said.

My math teacher told me never to arbitrarily insert function signs in equations to suit my purposes.

It was interesting coming back and reading this... but it's plain that it's going to remain deadlocked. Half of us were taught differently from the other half, and either side can easily find someone or something somewhere to back up their claim.

Didn't want an argument, and it's been pretty good so far, i was just curious to see what GRM would say since i value your input over most. (Even you mtn, even if i don't necessarily agree )

Travis_K wrote: I would have said 2 doing it in my head, but on my TI89 (which allows you to enter it in the exact same format as the question posed) says 288. iPhone says 288 also.

Funny thing is... if you enter it into both a TI85 and a TI86, they'll give you two different answers.

If you just "enter it in" to a calculator or whatever, it's going to make a mistake for the same reason that typing Russian into an online translator gives you garbage when you convert it to English: computers can't read. You have to formulate it in such a way that the calculator/computer can parse it, and that involves reading the equation yourself first in order to pick out its meaning. If the calculator comes up with an answer anyway it's the programmer's best guess as to what you meant, and it can just as easily be wrong.

Matlab, for example, won't let you enter the equation as it's written in the OP. It doesn't accept 2(x+y) type elements and will MAKE you clarify that into ((2×x)+(2×y)) or (2×(x+y)) or whatever. This is done on purpose, it would be trivial to allow it to accept 2(x+y) but it would lead to ambiguities or lazy programming by the users so they didn't do it.

(Actual Matlab syntax uses a * instead of ×, as mentioned before, but if you use the asterix more than once in a post this board software makes it into wonky italic codes, so I'm not.)

If you said "I got 2 in my head but the calculator says 288", then hey! You did it right! Don't reject your own intelligence and trust a dumb machine instead.

Wow, I went home, hung out with the wife and kids, watched TV, slept for eight hours, went running, came to work, and... this is still going strong.

At least we aren't arguing about politics.

nderwater wrote: paste 48 / 2(9+3) into Google and it says: (48 / 2) * (9 + 3) = 288 Is there anything it can't do?

Math apparently.

92CelicaHalfTrac wrote:

Jay wrote: By the way, HalfTrac: you bastard! Last night I DREAMT I was arguing with people over this stupid problem. Thanks for that.

My girlfriend was foaming at the mouth over this. (She agrees with you by the way, and considering she probably just took this stuff in high school like... 2 years ago or whatever...)

pictures or I don't believe you

I agree also, it is interesting.

but still, like you said, on 2x with it being 2 TIMES x, don't you still have to do division first? I just think it's funny how I put it in WITHOUT the multiplication sign before the parenthesis, which isn't how it's written......and then got 2It's all in the 2(9+3) although it's like what a lot said, learned from basic math, 2 x 12, but it's apparent that both sides are right on this and yeah, at least it's not politics.

NickF40 wrote:

92CelicaHalfTrac wrote:

Jay wrote: By the way, HalfTrac: you bastard! Last night I DREAMT I was arguing with people over this stupid problem. Thanks for that.

My girlfriend was foaming at the mouth over this. (She agrees with you by the way, and considering she probably just took this stuff in high school like... 2 years ago or whatever...)

pictures or I don't believe you I agree also, it is interesting. but still, like you said, on 2x with it being 2 TIMES x, don't you still have to do division first? I just think it's funny how I put it in WITHOUT the multiplication before the parenthesis, which isn't how it's written......and then got 2But it's apparent that both sides are right on this and yeah, at least it's not politics.

Yep you still have to do the division first in this case.

You're dividing 48 by 2x. You're not dividing 48 by 2, and them multiplying that result by x, since x is not standing alone in this case.

It's still just the difference between 48÷2x vs. 48÷2*x. They yield two different answers.

There are no () around the 2(9+3), you can't just assume that there are. If it was written as 48/(2(9+3)), then yes the answer would be 2. But the way it is written by order of operations it must 288.

well yeah exactly haha this goes with a few other problems that we learned in math, that literally have more than one answer. and 93excivic, yes exactly.

I just think it's funny of all the people that are hot and heavy into this lol I asked a math teacher who also teaches trig, calculus, math, and algebra and my sister which was really good at all of those since she took it and you got myself...and after asking them I understand how everyone is getting 2 but with both of them, I stand by my 288....that's all i'm sayingI'm not asking for everyone to agree, if you don't fine, call me wrong, I really don't care

Got a 2 factored out of (9+3). Might make more sense as 48÷(18+6)=?

Jay wrote:

Salanis wrote: 48/2(9+3) = 48 / 2 * (9+3)

Okay, this is the problem. You CAN'T make that equivalency. It looks right but it isn't. What you can actually write is 48/2(9+3) = 48/(2 × (9+3)), which equals 2. The problem is that a number adjacent to a bracket (so-called implicit multiplication) is multiplied, but it isn't treated as a × sign for "BEDMAS" purposes. Think of it as a way of implying that there are brackets around the whole term. Look at it this way. "2x" is not a short form of "2 × x". It's a short form of "(2 × x)". This is a very important distinction! A 2(x+y) term in an equation is the same thing as having (2 × (x+y)). You can also think of it as a function: Let f(x)=(9+3)x So f(2)=(9+3)·2=24 Then you have 48 ÷ 2(9+3) = 48 ÷ f(2) which is a perfectly valid way of expressing the same thing. I haven't changed anything, contextually, implicitly, or otherwise. And the only way to evaluate that is 48 ÷ f(2) = 48 ÷ (2(9+3)) = 2. Okay, this is the problem. You CAN'T make that equivalency. It looks right but it isn't. What you can actually write is 48/2(9+3) = 48/(2 × (9+3)), which equals 2. The problem is that a number adjacent to a bracket (so-called implicit multiplication) is multiplied, but it isn't treated as a × sign for "BEDMAS" purposes. Think of it as a way of implying that there are brackets around the whole term.

Except that you're wrong. Sorry. I took higher level math in college too. Brackets only apply to what's INSIDE them.

2 is not some sort of function call.

that is the one that confuses me as these 2 up there had said, putting brackets in....there are no brackets so yeah

the way I was taught was 2xX and 2X are the same which even that it still, through pemdas have to do division first, there are no brackets because you should know already that it's 2x(9+3), and with that, you can't just put brackets in the equation because that changes the whole outcome......obviously

Standing alone.... 2*(9+3) = 2(9+3), sure...

But in the larger context, you're all fabricating brackets to make (48÷2)(9+3). There's no parentheses separating 2 from (9+3) like that in the original equation.

scardeal wrote: Except that you're wrong. Sorry. I took higher level math in college too. Brackets only apply to what's INSIDE them. 2 is not some sort of function call.

I'm not wrong! I'm not saying anything about the operation in the brackets or that brackets somehow "apply to what's outside themselves"??? I'm not really sure what you meant by that.

If you have an expression, such as 2x or 2(y+b) or 2(e^iθ - 1), or anything like that, there is a so-called implied multiplication where the 2 meets the bracket. This is not the same as just writing an × sign! What it is is a shorthand for doing the whole expression in brackets, so 2(y+b) is actually (2 × (y+b)). Mathematical notation is full of "shorthands" and implicit syntax like that.

Stop trying to throw BEDMAS at a term which it's not applicable to!

Here's another way of thinking about it if that's not clear. 2(expression) means (double the value of this expression), and not 2 × (expression). A lot of the time they evaluate to the same thing, but not always! This is one of those cases.

I'm not relying on my "credentials" to bamboozle y'all into agreeing with me, this is how mathematical syntax works and has for hundreds of years. You can't argue that.

exactly, while you do that in your head, that's not how it's written, so that's where the LAW of equations comes in..........I don't understand the brackets being added, you add parenthesis and brackets it changes things around! 2 TIMES (9+3).....parenthesis first