48÷2(9+3) = ?

[mechanicx]

Originally Posted By: Reelizmpro
Hmmm the distributive rule of algebra? The reason they remain is because it shows you need to add 9+3 before anything else...pretty important step. The problem is sloppy math. Take it step by step. Write the problem on paper and show each and every step. Get rid of the parentheses in the proper manner. The parentheses remain until the expression 2(9+3) = 24.

Please understand the difference...
2(12) shows multiplication through distribution. Gets priority.
2*12 shows simple multiplication only.
note: there are no multiplication signs in this problem so don't add any.



Now you are saying evalute inside the parenthesis first. Which is what I've been saying. 2(12)has no distribution and becomes simple multiplication. 2(12) means the same thing as 2*12. Even if I accepted that 2(12) is multiplication through distribution, that does not mean it takes precedence. So working left to right dividing 48/2 takes precedence over mulitiplication to the left. Now you are arguing implied multiplication 2(12) or "multiplication through distribution" takes precedence.

 

[d00df00d]

More confusion over terms. Some of you read "parentheses first" as "what's inside the parentheses." Others read it as "what's inside and immediately outside."

We have seen pages and pages of forum debates, "experts" who disagree, calculators that give different answers, and math websites that either contradict each other or acknowledge that the notation is ambiguous. When are we going to acknowledge that there is no consensus?


EDIT: Wasn't talking about you, mechanix.

 

[Reelizmpro]

Originally Posted By: mechanicx
Originally Posted By: Reelizmpro
Hmmm the distributive rule of algebra? The reason they remain is because it shows you need to add 9+3 before anything else...pretty important step. The problem is sloppy math. Take it step by step. Write the problem on paper and show each and every step. Get rid of the parentheses in the proper manner. The parentheses remain until the expression 2(9+3) = 24.

Please understand the difference...
2(12) shows multiplication through distribution. Gets priority.
2*12 shows simple multiplication only.
note: there are no multiplication signs in this problem so don't add any.



Now you are saying evalute inside the parenthesis first. Which is what I've been saying. 2(12)has no distribution and becomes simple multiplication. 2(12) means the same thing as 2*12. Even if I accepted that 2(12) is multiplication through distribution, that does not mean it takes precedence. So working left to right dividing 48/2 takes precedence over mulitiplication to the left. Now you are arguing implied multiplication 2(12) or "multiplication through distribution" takes precedence.


Do you still see parentheses in 2(12)? Multiply them...(24). Ok, single term (fully simplfied) so no need for parentheses 24. Now go ahead and divide into 48.

 

[mechanicx]

Originally Posted By: d00df00d
When are we going to acknowledge that there is no consensus?




I wonder just that if there is a trusted source that could make the standard order of operations clear in this situation. It's starting to look like there isn't, and perhaps a poorly constructed math equation leads to an answer with no consensus.

 

[mechanicx]

Originally Posted By: Reelizmpro

Do you still see parentheses in 2(12)? Multiply them...(24). Ok, single term so no need for parentheses 24. Now go ahead and divide into 48.


But you are ignoring the left to right order of division and multiplication, the 48/2 that precedes 2(12). Following order of operation 24(12)

.

 

[Reelizmpro]

Originally Posted By: mechanicx
Originally Posted By: Reelizmpro

Do you still see parentheses in 2(12)? Multiply them...(24). Ok, single term so no need for parentheses 24. Now go ahead and divide into 48.


But you are ignoring the left to right order of division and multiplication, the 48/2 that precedes 2(12). Following order of operation 24(12)

.


OK lol. 2(12) is not 2*12...don't think of it that way. Therefore left to right doesn't mean jack and is elementary at this point. Get rid of the parentheses first (PEMDAS.) How hard is it to understand?

 

[mechanicx]

It's not a matter of not understanding but of disagreeing. I've already stated my position that 2(12) means the same thing as 2*12, so why would I agree to multiply or get rid of the parenthesis first?

 

[Reelizmpro]

Originally Posted By: mechanicx
It's not a matter of not understanding but of disagreeing. I've already stated my position that 2(12) means the same thing as 2*12, so why would I agree to multiply or get rid of the parenthesis first?


OOOOHHH ok. Understand that the equation says 2(12) and not 2*12 right? the function may be the same but they are different. Therefore you do 2(12) first. Okay, I've done all I can do. Anymore would just be redundant.

 

[OttawaValley]

Good to see people still exercising their minds.

 

[UncleS2]

OK, I've let this run long enough without posting.(FWIW, I hold a B.S. in Mathematics. We'll discuss the initials([censored]) of Bachelor of Science- and how well or poorly chosen they may be, as well censoring them- another time.

)

As always, most folks go straight for the answer. Those who do fall back to the rules- as they should- may well disagree. Why is that? It's the same set of rules.

Let me ask you a question.

Did you ever have a good English or Language Arts teacher who explained to you that while certain things or usages were not exactly *wrong*, they might very well be Awkward, or Ambiguous, or Clumsy, or plain old Unclear, when used in print or in speech? Yes? Excellent! Keep that in mind.

Our original equation in this thread could be said to be a mathematical equivalant of one of those awkward/unclear usages of language. As someone who holds a both a Math degree, and Secondary Ed(grades 7-12) Teaching Certification in Math, I would say that the original equation, *as written*, is simply asking for trouble. If I gave an Order of Operations question like that on a test, it would be only to show how important it is to be clear on your intention. No foolin'.

Here's a similar expression and the problems that ensue at PurpleMath dot com. It's the last one at the bottom of the page, " Simplify 16 ÷ 2[8 – 3(4 – 2)] + 1". Link: http://www.purplemath.com/modules/orderops2.htm

Read to the bottom. See what they have to say? And to think- when I chose Math as my major, one of my considerations was that when I was right no one could tell me I was wrong!

If I wanted clarity, I would re-write that as48/2)(9+3)= ; or 48/[2(9+3)]= . If you want confusion, leave it exactly as is. And yes, the single set of parentheses is the sticking point.


(Let's not bring calculators or computers into this either. They can only do what they were programmed to do. As shown previously, the same entries, input into a TI 85 calc vs a TI 86 calc, give different answers. QED.)

 

[mechanicx]

So in other words according to that link, those that are saying its 288 and I are wrong.
Quote:
That's because, even though multiplication and division are at the same level (so the left-to-right rule should apply), parentheses outrank division... That is, multiplication that is indicated by placement against parentheses (or brackets, etc) is "stronger" than "regular" multiplication.


A link to PurpleMath dot com was posted earlier in this thread pointing out the same claim but was dismissed by several posters as well as by several scientific caclulators. Should that site's statement be considered definitive? Is multiplication that is indicated by placement against parentheses "stronger" than "regular" multiplication a hard and fast rule in order of operation? If so, I have no problem admitting I'm wrong.

Quote:
(Let's not bring calculators or computers into this either. They can only do what they were programmed to do. As shown previously, the same entries, input into a TI 85 calc vs a TI 86 calc, give different answers.


But that still begs the question if it is really a hard and fast rule then why would the calculator designers not use it?

 

[d00df00d]

Originally Posted By: Stuart Hughes
Let me ask you a question.

Did you ever have a good English or Language Arts teacher who explained to you that while certain things or usages were not exactly *wrong*, they might very well be Awkward, or Ambiguous, or Clumsy, or plain old Unclear, when used in print or in speech? Yes? Excellent! Keep that in mind.

Our original equation in this thread could be said to be a mathematical equivalant of one of those awkward/unclear usages of language.

 

[UncleS2]

I said that this equation is confusing for many & that using it or one like it is asking for trouble. I stand by that.

However, note that I did *Not* say that one answer is as good as another. There *is* a correct way, whether a calculator is programmed to do it or not.

The confusion on this eq is caused by whether or not the "2" is "tied" to the parentheses. Agreed?

It's a commonly held *convention* that the 2 *is* tied to the parentheses. That convention(notice I did not use the word "rule") is (right or wrong? Your choice determines your answer).

48÷2(9+3) = 48÷2(12); agreed?

Here comes the algebra- Let X = (12).

48÷2(12) = 48÷2X

Insert a multiplication sign, if you like, for clarity, we get:
48÷2*X

Still the same thing. Yes, it is. (I heard that in the back row!)

Working from left to right, we get:
48÷2=24*X;

Re-inserting (12) for X, we get:
24*(12) = 288

The parentheses are a grouping symbol, *BUT*: once we've simpified the contents to a single term, they serve no real purpose. 2(12) = 2*12. Parentheses are not a "Magic Magnet" that ties any "immediate outside" multiplying term to them. That's no different than inserting that outside multiplier *inside* the parentheses after the fact.

To illustrate: Consider 2X^2(that's two X Squared). PEMDAS: Parentheses come before exponents, yes? So if X = (3), and "2" is magically tied to the parentheses, it effectively goes *INSIDE* the parentheses, which gives us 6^2 = 6*6 = 36, which is wrong, Wrong, WRONG!

It's 2*3^2; exponents before multiplication, = 2*(3*3)= 2*9= 18.

Remember, 3 = (3); X = (X); thing = (thing).

The convention of tying the outside multiplier to the contents of parentheses may be useful as a reminder most of the time, but it does *NOT* nullify the Order of Operations.

Not even on a stinker of an equation like the above!

Tomorrow we will discuss the Door Number Three problem. Class Dismissed!

 

[KrisZ]

Quote:
I would say that the original equation, *as written*, is simply asking for trouble.


Thank you sir for confirming what few people, including me, have already brought up, which was totally ignored by people caught up with the final answer.

 

[Volvo_ST1]

This thread exemplifies that basic math skills have become a lot more basic over the past 20 years. As I have mentioned in another thread a few weeks ago, 5th grade math is now being taught at uni. I am no longer surprised at that!

People seem to not know basic math rules. If they knew the rules, there wouldn't be great confusion and bickering.

48:2(9+3) = ?

There are two groups: 48:2 and (9+3). The 2 does not belong to (9+3), as denoted by the lack of an operator. Therefore we must calculate (48:2):12 = 2.

If the calculation is written as 48:2*(9+3), we must calculate (48:2)*12 = 288

I have an inexpensive Tozai scientific calculator. If I type the calculations as indicated above, I get the respective and proper results, as expected.

I'm not amused by this thread, but rather saddened.

 

[Vikas]

What is "lack of operator"? If you really believe that, then this has no solution i.e. we have a "syntax error".

How would you solve the following problems?

48÷1(9+3) = ?
48÷1*(9+3) = ?
48÷(9+3) = ?

For example, following makes perfect sense and the calculator is doing "DO WHAT I MEAN"

 

[OVERKILL]

Originally Posted By: hate2work

Somehow I missed this thread until this morning. Since my math skills are rather lacking, I asked someone I know that has multiple degrees in math and computer science, my brother Jeff. Below is his answer, and I'm willing to bet he's correct. His response is below. My comments are preceded with an >


And your brother agrees with my sister, who is about to get her PhD in math.

 

[Quattro Pete]

Originally Posted By: Reelizmpro
Originally Posted By: hate2work


So, 48/2(9+3) = 48/2(12) = 24(12) = 288.


48/2(12) = 48/24 = 2
LOL...Parentheses first. Ask him to check his work with pen/paper...no calculators.

The rule of parentheses doesn't refer to getting rid of them first. It refers to performing operations in the parenthesis first before proceeding with all other regular business (which is left to right division/multiplication in this case).

 

[mechanicx]

I found your post interesting and it seems you and Iare agreeing with mostly (except for the 2 being tied to the parentheses) but I'm left a little confused what your final verdict is lol. First you posted the PurpleMath link that said the convention was multiplication next to parentheses first, ie the 2 is tied to the parentheses. Further you say,

Quote:
However, note that I did *Not* say that one answer is as good as another. There *is* a correct way, whether a calculator is programmed to do it or not. It's a commonly held *convention* that the 2 *is* tied to the parentheses. That convention(notice I did not use the word "rule") is (right or wrong? Your choice determines your answer).


So if that is the convention then apparently the correct answer for this math problem is "2".

But then you go on to solve the problem algebraically with the answer being 288:

Quote:
48÷2(9+3) = 48÷2(12); agreed?

Here comes the algebra- Let X = (12).
48÷2(12) = 48÷2X

Insert a multiplication sign, if you like, for clarity, we get:
48÷2*X

Still the same thing. Yes, it is. (I heard that in the back row!)

Working from left to right, we get:
48÷2=24*X;

Re-inserting (12) for X, we get:
24*(12) = 288



Further you go on and seem to contrasdict the convention that 2 is tied to the parentheses. Which was my position as well:

Quote:
The parentheses are a grouping symbol, *BUT*: once we've simpified the contents to a single term, they serve no real purpose. 2(12) = 2*12. Parentheses are not a "Magic Magnet" that ties any "immediate outside" multiplying term to them. That's no different than inserting that outside multiplier *inside* the parentheses after the fact.


Am I wrong to be confused lol?

 

[wavinwayne]

My calculator's results, FWIW: