48÷2(9+3) = ?

[HTSS_TR]

Originally Posted By: Vikas
... when you write similar construct, you write it so that there should be no question about misinterpretation.


Originally Posted By: Hokiefyd

Obviously, the best lesson from this is to be as explicit as possible. If more brackets were used, there would be no room for question here.


I agree with both. When I write a fraction less than 1, I always include a zero. Rather then write .7, I write 0.7 so that if the printer/copier did not show the dot/point clearly everybody would recognize 07 as 0.7 as oppose to 7 if the dot is missing in the ".7".

 

[bigmike]

Another expression:

48/2(9+3)=x
48/2=x/(9+3)
48/2=x/12
2x=576
x=288

 

[Hokiefyd]

48/2(x+3)=2
48=2(2(x+3))
48=2(2x+6)
48=4x+12
36=4x
9=x

Doing this this way, keeping implied multiplication as a priority over linear division or multiplication, I get x=9, which supports 2 as a result of the original equation.

 

[Drew99GT]

I think this is the missing piece of the puzzle. I was always taught that 48/2(9+3) is the same expression as (48/2)(9+3). Anyone agree? The only way you can get 2 is if the equation is written 48/(2(9+3)).

 

[Al]

Originally Posted By: cp3

But if more brackets were used....48÷(2(9+3))....it would be a different question and the answer would be 2!

Exactly and what people are failing to see is to get '2' it would have to be written:

48÷2÷(9+3) =2

48÷2(9+3) seems to hide the 48÷2 * (9+3)=288

Originally Posted By: Drew99GT

There's a consensus among the people who are right.

There, I just added some psychology to the debate.


Hahahahah

 

[Hokiefyd]

Originally Posted By: Drew99GT
I think this is the missing piece of the puzzle. I was always taught that 48/2(9+3) is the same expression as (48/2)(9+3). Anyone agree? The only way you can get 2 is if the equation is written 48/(2(9+3)).


I agree with both of the above. I was taught that if you have 2(9+3), you do that implied multiplication first, before you evaluate anything else.

In other words, 48/2(9+3) really IS different than 48/2*(9+3)

By looking at various math websites, calculation softwares, and other folks on the internet today, it appears that there's a 50/50 split on which method is the correct method.

 

[cp3]

Originally Posted By: Drew99GT
I think this is the missing piece of the puzzle. I was always taught that 48/2(9+3) is the same expression as (48/2)(9+3). Anyone agree? The only way you can get 2 is if the equation is written 48/(2(9+3)).


I do. But then I've never heard of implied multiplication.

 

[Hokiefyd]

Originally Posted By: cp3
But then I've never heard of implied multiplication.


You have and just don't know it.

2x is implied multiplication. There's no * between the 2 and the x, but you know you multiply them together. It's implied.

http://www.lifeisastoryproblem.org/vocab/en/i/impliedmultiplication.html

 

[Hokiefyd]

Further:

http://library.thinkquest.org/20991/gather/main/messages/15460.html

Quote:
5. By CONVENTION (not by "law") the associativity of multiplication, division, addition and subtraction is left to right. Therefore, in the absence of parentheses, BY CONVENTION, these operations are simply evaluated sequentially from left to right. There is no "mathematical law" that requires this; it is simply a convention that is (nearly?) universally accepted. Without this convention, expressions like 105 / 3 * 5 would simply be ambiguous. There would be no way for people to agree as to how to evaluate such expressions in the absence of parentheses.
6. There is NO SUCH CONVENTION concerning "implied multiplication". SOME PEOPLE choose to say ab => (a*b). Most people would say ab => a*b.

 

[bigmike]

 

[Drew99GT]

Here is the correct answer. The original equation is written incorrectly. It's either one depending on how you interpret it. Using correct algebra expressions, it can be either one. I hope this doesn't interrupt the space time continuum...

 

[Hokiefyd]

Originally Posted By: Drew99GT
Here is the correct answer. The original equation is written incorrectly. It's either one depending on how you interpret it.


Bingo.

 

[cp3]

bigmike,

Hokiefyd, Thanx, I see what you are saying I guess I just wasn't taught that expression. Or that it applied once the equation inside the brackets was complete.

 

[Drew99GT]

Actually, following please excuse my dear aunt sally, I'm going with 2.

Hopefully my dog will eat my homework and we can stop this madness.

 

[Hokiefyd]

Originally Posted By: Drew99GT
For sure 288. You have to multiply the number outside the parenthesis with the 2 numbers inside them, then add them.


Woah, a reversal, and into the 2 camp! How dramatic!

This has been a great discussion. Nobody seems to agree, and yet nobody got mad at anyone else. This is how ALL discussions on BITOG should go.

 

[Hokiefyd]

Originally Posted By: cp3
Hokiefyd, Thanx, I see what you are saying I guess I just wasn't taught that expression. Or that it applied once the equation inside the brackets was complete.


Well, though I gave my personal answer as 2, I'm not saying I'm right, either. It's just how I evaluated that expression.

 

[cp3]

Who? Not me!!....lol Not saying I'm right either, far from a mathematician!!

I do agree that this should be a model for discusions here though!

 

[Al]

Originally Posted By: Drew99GT
Here is the correct answer. The original equation is written incorrectly. It's either one depending on how you interpret it. Using correct algebra expressions, it can be either one. I hope this doesn't interrupt the space time continuum...

You seem to have flip-flopped. The original question is written correctly (answer =288) and is the second expression.

I can cite any number of examples where you don't use a '*' or 'x' between two parenthetic expressions or between a parenthetic expression and an integer. Then again, that's probably not the issue.

try "Calculus and Analytic Geometry" by Thomas...pretty much the standard for the last 40 years.

I see where you are coming from though.

 

[rpn453]

I went with 2 because, since I would never use a division sign in a calculation because of its inefficiency in conveying information, I simply saw it as a big forward slash, putting the rest of the numbers below it.

To really know the answer, you'd have to ask the writer about the intent and meaning of his poorly written mathematical expression.

 

[javacontour]

The problem is that an equation without any context is not very useful.

Sure, one can argue one syntax or another if one is learning the mechanics of math.

I look at it this way, what is the underlying problem one is trying to solve. Once you have that context, you can understand if the original equation is best represented as:

48/(2(9+3)

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

Just because something is written a certain way does not mean that expression accurately represents the problem one is trying to solve.

For example, if you had the following word problem:

"There are 48 widgets in the warehouse. If we have two sites and each site is organized in two groups, one group of nine and another group of three. We want to distribute the widgets evenly between the two sites, how many widgets does each group get?"

If that's the underlying problem, the answer is 2 widgets per group. This would be the 48/(2(9+3)) expression.

Thinking about a word problem that produces the expression:

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

"OK, a person can produce 48 widgets in two shifts of work. If we have nine employees working one day shift and three on the night shift, how many total widgets will both groups produce after each group completes their respective shift? Assume uniform productivity for each worker, regardless of the shift they work."

So one can argue which order, but the real power of mathematics is not in following rules to mechanically solve equations, but to use math as a tool to solve problems, answer questions, etc.

So what is the actual problem we are trying to solve and that determines the correct expression and how we should organize the operations.