48÷2(9+3)=?

scottdye wrote:

Another look at this tells me, the problem is with the ÷ v. a /. If the problem was written with the /, I would agree the answer is 288.

They are different ways of representing the same operation.

So somehow multiplying by the inverse is different than dividing by the number because they are two different ways of representing an operation?

x / a = x * a^(-1) = x ÷ a

THEY ALL MEAN THE SAME THING

You implying that the rules change because of using ÷ instead of / is simply ludicrous. Wow.

Hard to believe that folks are arguing over what is a simple mathematical fact. Many posters here understand math and have given the correct answer (about 97 times), along with various and sundry explanations. Many others simply don't understand math.

For those who understand math, do you really think that you can educate the ignorant among the LRC crowd? If not, what exactly are you trying to accomplish?

This is truly a weird thread. But maybe not so unusual. In a way, it has the same flavor as all those global warming threads.

Math Guy #288 wrote:

I feel sorry for any engineering firm that hires you or allows you to do any meaningful work. The question is not written: 2*(9+3). It is is written: 2(9+3). You must multiply out the 2 before moving on to the left to right convention. Jezzuz. Calculators do not understand this, you must enter the extra set of brackets when inputting this into a calculator. Please start a new thread when you graduate telling us which projects you have worked on so we can avoid them.

I'm guessing you're a troll based on your name and the sheer idiocy of your arguments. Congrats, you got us.

If not, I'm blown away that someone thinks 2(9+3) is a different operation than 2*(9+3). They're the same - you're just omitting the operator for convenience. Some programs won't recognize that as a correct operation without the *.

Finally, calculators and math programs do indeed understand this. They'd be pretty irritating to use if the programmers hadn't built order of operations into them.

scottdye wrote:

YES

Sweet Jesus. Remind me never to use Stoughton CPA.

48÷2(9+3) is essentially 48÷2*(9+3), which is 288.

48/2(9+3), in which 48 is above 2(9+3), is a different equation than the former because the figures above and below the slash are generally grouped separately in parenthesis. So it would be 48÷(2(9+3)), and the answer would be 2.

The answer to the OP's equation falls under the first example, so the answer, then, is 288.

I will just put my opinion that the answer is 2 according to convention. There are conventions (that I have learned) that do generally see 2(9+3) as different than 2*(9+3).

Regardless, it really is mathematically irrelevant to argue about what the "correct" order of operations as they really are conventions that are agreed upon or assumptions that are defined. Mathematics is more interested in how we use the rules of logic to take assumptions and draw conclusions based on those assumptions. The argument in this strangely long thread is sort like arguing what side of the road you are supposed drive on without stating what country you are on.

Seriously guys wrote:48/2(9+3), in which 48 is above 2(9+3), is a different equation than the former because the figures above and below the slash are generally grouped separately in parenthesis. So it would be 48÷(2(9+3)), and the answer would be 2.

That is wrong.

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

Here is what you were looking for:

48÷(2(9+3)) = 48 / 2 / (9+3)

You don't assume parentheses in any cases. Either they are there or they are not. If they are not, you do exactly what the operation states.. in the OP's case you multiply AFTER you divide.

This is correct. I think it has been conclusively proven that it equals 288.

Point 1: Parentheses (as in 2(12)) are JUST ANOTHER WAY OF WRITING multiplied by when used this way(same EXACT thing as 2*12, or 2x12). It doesn't create magical mythical brackets around the term, and it doesn't mean you have to do it first. I probably learned this when I was 7.

Point 2: Stop arguing that you have to multiply the 2 through the parentheses because of the distributive property. The distributive property would only apply here if the 2(9+3) was a separate term, meaning it came after a + or - (as in 48+2(9+3)). Because it's division before that, and because multiplication and division go left to right according the the order of operations (I think we've established this in 8 pages), the 2 is not "distributed" through. The 48 gets divided by it first.

Point 3: 48/2(9+3) would still =288, unless it was written as 48/[2(9+3)], or if it was written on separate lines (i.e. the 48 above the rest of that). Because it's hard to write this on separate lines on letsrun, I'll give the poster of this one the benefit of the doubt.

I don't often get that worked up over stuff on letsrun, but for some reason, this is killing me. For the record, I grew up with a math professor for a mother, got A's in every math course I ever took, and scored perfect on the quantitative section of my GRE's. Seriously, people.

Flagpole wrote:

the letter why wrote:

First of all, no. It's PE(MD)(AS). And yes, if the acronym doesn't even work then it's hardly useful.

As someone earlier said, it's an interpretation problem and open to debate.

My interpretation is that it is clearly equivalent to 48÷2(12) and that this is NOT equivalent to 48÷2x12.

More generally, I think that causing a controversy because someone can't write a math problem clearly is the real issue here.

Well, like I said, I'm not a math guy. I think what others have said is true...that to be clear, more parenthesis should have been used.

There is a PLURAL to "parenthesis". It is "parentheses".

Whoops! wrote:

There is a PLURAL to "parenthesis". It is "parentheses".

In the United States, we put punctuation inside of the quotation marks.

Hmm, over 150 posts for a question that has one and only one objective answer.

Please state you background and answer.

I have a Math degree and say the answer is 288.

When studying math you can only get so far without understanding the order of operations. As formulas get more and more complex you can get way off course if you miss one step up in the order of operations as we can see by this rather simple example.

toro wrote:

Hmm, over 150 posts for a question that has one and only one objective answer.

Please state you background and answer.

I have a Math degree and say the answer is 288.

When studying math you can only get so far without understanding the order of operations. As formulas get more and more complex you can get way off course if you miss one step up in the order of operations as we can see by this rather simple example.

And I am a professor of mathematics and I say the answer is 2 and that you are wrong. In regards to your math degree, you should ask for a refund.

lllll wrote:Finally, calculators and math programs do indeed understand this. They'd be pretty irritating to use if the programmers hadn't built order of operations into them.

If you own a scientific calculator, go read the instructions. It will explain this to you as you don't believe me.

no way are you a professor and think the answer is 2.

Seriously guys wrote:

48÷2(9+3) is essentially 48÷2*(9+3), which is 288.

48/2(9+3), in which 48 is above 2(9+3), is a different equation than the former because the figures above and below the slash are generally grouped separately in parenthesis. So it would be 48÷(2(9+3)), and the answer would be 2.

The answer to the OP's equation falls under the first example, so the answer, then, is 288.

Essentially is not the same as is, you are also wrong.

You are wrong and your mother would be ashamed. Give her a call and ask her, you'll find out that are you wrong.

Chris Wasnetsky wrote:That is wrong.

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

Here is what you were looking for:

48÷(2(9+3)) = 48 / 2 / (9+3)

You don't assume parentheses in any cases. Either they are there or they are not. If they are not, you do exactly what the operation states.. in the OP's case you multiply AFTER you divide.

Sorry Chris, you are wrong as well.

MathGuy wrote:

This is correct. I think it has been conclusively proven that it equals 288.

Nope.