48÷2(9+3) = ?

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Originally Posted By: Reelizmpro
Bare with me...

Now without solving, the reciprocal of (5(2+3))/(8(1+2)) is (8(1+2))/(5(2+3)). Which is proven here...

http://www.algebra.com/algebra/homework/Inverses/FIND-reciprocal-of-a-FRACTION.solver

Yes because you've written the problem with parentheses in front of and behind the / symbol making it clearly a fraction. But originally you didn't write it that way.

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So the reciprocal of 2(9+3) is 1/(2(9+3))

Yes, because I interpret it that you want the whole thing reciprocated.

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In the end, when you multiply both fractions together you get 1. This is the essence of the reciprocal property.

So 48 * 1/(2(9+3)) = 2

I'm trying to prove it's incorrect to just take the 8 from 8(2+3), just as it's incorrect to just take the 2 from 2(9+3).


But if you take the original equation apart and reciprocate parts of it then put it back together, you are changing the equation. If you ask me, "what is the reciprocal of 2(9+3)?" I will say "1/(2(9+3))" but I'm not saying it would be proper to plug that into the original equation. Since 48 and 2 are the only numbers being divided, you can only ask and plug in the reciprocal of "48/2" which is 48*1/2, both equal 24 and always will. And if you asked me, "what is the reciprocal of 48/2(9+3)?" I will say 1/(48/2(9+3))" Which is 1/288 which is the reciprocal of 288.

Your argument seems compelling but it's based upon "/" being a fraction bar and not just a division sign, apparently because you believe the 2 is tied to the parentheses. And I'm saying due to the order of operations from left to right the 2 is tied to the 48 if anything.
 
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Since 48 and 2 are the only numbers being divided, you can only ask and plug in the reciprocal of "48/2" which is 48*1/2


I should rewrite that to say, "Since 48 and 2 are the only numbers being divided, you can only ask what is and plug in the reciprocal of "2" which becomes 48*1/2.

As you said the recipricol of a number multiplied equals 1, 48/2*2/48=1.
 
Originally Posted By: Quattro Pete
Originally Posted By: Reelizmpro

So 48 * 1/(2(9+3)) = 2


You do realize that this outer parenthesis wasn't there in the original problem, and that's why the answer was 288, right?

Just checking...



Exactly, so if we just plugged the reciprocal of 2(9+3) back in to the original formula it'd become 48/1/2(9+3) which still equals 288 lol.
 
Originally Posted By: mechanicx
Originally Posted By: Quattro Pete
Originally Posted By: Reelizmpro

So 48 * 1/(2(9+3)) = 2


You do realize that this outer parenthesis wasn't there in the original problem, and that's why the answer was 288, right?

Just checking...



Exactly, so if we just plugged the reciprocal of 2(9+3) back in to the original formula it'd become 48/1/2(9+3) which still equals 288 lol.


48*(1/2(9+3)) actually which is the point of taking the reciprocal in the first place but there's an argument there as well. Parentheses are added to show what "x" is. Remember, there are no parentheses around (48/2) or multiplication signs either so it goes both ways. When you take the reciprocal, you take the entire term...not just a single number and leave the parentheses behind because then the product of the original fraction and reciprocal will not be 1. But I guess your argument is it's not a fraction at all. There's a divide operation but it's not a fraction? All numbers are indeed fractions so I don't see why it's so hard to visualize it as such. Welp, I guess it comes down to if you believe "multiplication by juxtaposition" takes precedence. I was always taught that way and 8 out of 10 people I asked also believe this to be true.
 
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Anybody wants to take my generator example and reword it so that the problem

a) will show up as the OP's expression
b) and will actually have the answer of 288?

It seems rather difficult to put physical "things" behind the numbers "48", "2", "9", "3" and then arrange them using the division, parenthesis and plus sign (AND WITHOUT USING EXPLICIT multiplication sign).

- Vikas
 
48/(2(9+3))

This is exactly how I visualize the problem. Is it wrong to assume this? I don't know but it makes more sense than assuming (48/2)(9+3). Seems awfully clumsy to write it that way. Why not 48(9+3)/2 instead which is what the 288 people are doing? Let's just tear it away from the 2 and put it next to the 48 instead. Yeah, that's all better than seeing 2(9+3) as a denominator.
 
Originally Posted By: Reelizmpro
But I guess your argument is it's not a fraction at all. There's a divide operation but it's not a fraction? Welp, I guess it comes down to if you believe "multiplication by juxtaposition" takes precedence. I was always taught that way and 8 out of 10 people I asked also believe this to be true.



Yes, at least we are now on the same page. We just aren't in agreement that 'multiplication by juxtaposition' takes precedence. This is what I said long ago that the debate is really over whether implied multiplication or multiplication indicate by placement next to parentheses takes precedence.
 
Originally Posted By: Vikas
Anybody wants to take my generator example and reword it so that the problem

a) will show up as the OP's expression
b) and will actually have the answer of 288?

It seems rather difficult to put physical "things" behind the numbers "48", "2", "9", "3" and then arrange them using the division, parenthesis and plus sign (AND WITHOUT USING EXPLICIT multiplication sign).

- Vikas


Are you asking how one would divide 48 by whole numbers that aren't less than 1 and get 288? Good question. They aren't dividing 48 by the (9+3) but actually multiplying 48 (or 24) by (9+3). They just aren't seeing it as 48 divided by 2(9+3) just 48 divided by 2. There are often problems with 2 results but one doesn't quite fit while the other does. hmmmmm
 
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I can't believe we are still arguing about a poorly worded problem. Although I have my opinion (not repeating it). I have never seen one formatted in this form in any text. And I'm an ME heavy on the math end.


The person who came up with this problem is a psychopath

But that's the purpose of the internet.
smile.gif
 
Originally Posted By: Volvo_ST1
Originally Posted By: Reelizmpro
Bare with me...


I prefer doing math while wearing clothes.


+1

With sharp pencils and all...
 
Originally Posted By: Reelizmpro

Are you asking how one would divide 48 by whole numbers that aren't less than 1 and get 288? Good question. They aren't dividing 48 by the (9+3) but actually multiplying 48 (or 24) by (9+3). They just aren't seeing it as 48 divided by 2(9+3) just 48 divided by 2. There are often problems with 2 results but one doesn't quite fit while the other does. hmmmmm


No. Even if I change my example in to a twisted one such as:-
I have 48 generators each taking 1/2 gal per hour and I run them 3 (daytime) hours and 9 hours (nighttime) and the question is how many gallons of fuel is needed per day, the equation will NOT be as entered by OP.

It will be written as (by any sane person :-)
48 * 1/2 * (9 + 3 )

I could change the wording and say each generator runs 2 hours on one gallon of fuel but then I would write the equation as
48 * (9 + 3) / 2

Or I could say I am stranded on the island for 48 days and how many total gallons would I need etc but the equation would still be not as entered by OP.

I just don't see a real physical situation in which a reasonable person will come with a equation as entered by OP with 288 as the answer.

It fails the "reasonable person" test :-)

- Vikas
 
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But you're working under the assumption that the equation as written must make sense and fit easily into a word problem. My view is that the equation is (intentionally)poorly written, so doesn't necessarily make a lot of sense and doesn't fit easily into a word problem.

The standard isn't how can one solve an equation so it makes the most sense and fits easiest into a word problem. The standard is how does one solve a an equation as written per the order of operations. The problem is there's no consensus on order of operations for this equation lol.

What your saying goes to how an equation should be written, not how an equation should be solved . The point is it's a poorly written equation.

Besides that, you've created a word problem with an almost forgone conclusion. If we say, Y=48/2 and X=2(9+3), Y*X=288 someone could come up with a word problem but it wouldn't necessarily fit the generator model you chose.
 
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Originally Posted By: Reelizmpro
I was curious...how do you 288 guys reciprocate 5(2+3)/8(1+2)?


Assuming "reciprocate" here means "What's your guys' answer to this".

If you abide by the mathematical order of operations, then it becomes:

5x5/8x3 =

Then multiply and divide from left to right since there are no parentheses in the boiled down equation.

Answer = 9.375

Most people might see the equation as 5x5/8x3 = 25/24 = 1.042 ... but only if the equation was written as (5x5)/(8x3).

Use the "order of operations" and you'll always get the correct answer.

Type the equation in and see how the answer is achieved through the order of operations in the link below.

http://www.mathsisfun.com/algebra/operations-order-calculator.html
 
30 pages! Good grief!

The answer is 288. Close the thread!
smile.gif
 
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Originally Posted By: tpitcher
35.gif
Oh God, no wonder there's so many mistakes.
35.gif


What does the equation represent? Nothing. Its solution is moot and a near pointless exercise. If I wrote the equation, I would know the order of operation and would have written it in an unabiguous fashion not in a mixed algebra / elementary math form. All my colleagues queried solved the equation and get ans=2. The operation outside the parenthetical addition is performed BEFORE the linear division. Quibbling about such near-nonsense is a waste of valuable time - and the stuff of professional students not professionals, imagineers and visionaries. We are the people who make things work and created some of the greatest invention in the past century, e.g: Laser, Maser, the transistor, stereo analogue microgroove recording, talking pictures, microwave xmtrs, SATCOM, digitalMUX, CCD, 1 chip DSP, micro-machine like gyros and accelerometers, tempest communications and computing equipment. Now, what have YOU done for ME lately?
 
Originally Posted By: ARCOgraphite
What does the equation represent? Nothing. Its solution is moot and a near pointless exercise. If I wrote the equation, I would know the order of operation and would have written it in an unabiguous fashion not in a mixed algebra / elementary math form. All my colleagues queried solved the equation and get ans=2. The operation outside the parenthetical addition is performed BEFORE the linear division. Quibbling about such near-nonsense is a waste of valuable time - and the stuff of professional students not professionals, imagineers and visionaries. We are the people who make things work and created some of the greatest invention in the past century, e.g: Laser, Maser, the transistor, stereo analogue microgroove recording, talking pictures, microwave xmtrs, SATCOM, digitalMUX, CCD, 1 chip DSP, micro-machine like gyros and accelerometers, tempest communications and computing equipment. Now, what have YOU done for ME lately?

01.gif
 
It's poorly written equations like this that get space probes crashed on Mars. I know, it wasn't exactly like that, but it was a similar flavor of bone-headed-ness.
 
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