Neptune Aquatics

48÷2(9+3) =

My guess : The confusion is due to the shorthand and implicit multiplication.
If in doubt, a good first step is to write it out fully:
48÷2(9+3) => 48 ÷ 2 x (9+3)
With the "x" in there, the parenthesis are nicely separated from the 2, so very obvious on order.
So clearly 288.

Now the only way to get the wrong answer of 2 is this:
48÷2(9+3) => 48 ÷ (2 x (9+3))
So in writing it out, you would go "hey wait, I just added another set of parenthesis - oops".
 
Two equations 48/2=24, 9+3=12, 24*12=288
Think it would be amazing not that people can't do math but how easy we get confused; I'm going through fourth grade again, my son's in fourth and sometimes fraction get complicated for me to explain my kido
 
I still think the answer is 2. I arrive at this because I used the internets ;-).

This next example displays an issue that almost never arises but, when it does, there seems to be no end to the arguing.

* Simplify 16 ÷ 2[8 – 3(4 – 2)] + 1.

16 ÷ 2[8 – 3(4 – 2)] + 1
= 16 ÷ 2[8 – 3(2)] + 1
= 16 ÷ 2[8 – 6] + 1
= 16 ÷ 2[2] + 1 (**)
= 16 ÷ 4 + 1
= 4 + 1
= 5

The confusing part in the above calculation is how "16 divided by 2[2] + 1" (in the line marked with the double-star) becomes "16 divided by 4 + 1", instead of "8 times by 2 + 1". That's because, even though multiplication and division are at the same level (so the left-to-right rule should apply), parentheses outrank division, so the first 2 goes with the [2], rather than with the "16 divided by". That is, multiplication that is indicated by placement against parentheses (or brackets, etc) is "stronger" than "regular" multiplication. Typesetting the entire problem in a graphing calculator verifies this hierarchy:

order12.gif


Note that different software will process this differently; even different models of Texas Instruments graphing calculators will process this differently. In cases of ambiguity, be very careful of your parentheses, and make your meaning clear. The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "×" sign) indicates that the juxtaposed values must be multiplied together before processing other operations. But not all software is programmed this way, and sometimes teachers view things differently. If in doubt, ask! (emphasis mine)

(And please do not send me an e-mail either asking for or else proffering a definitive verdict on this issue. As far as I know, there is no such final verdict. And telling me to do this your way will not solve the issue!)
 
I don't buy the "multiplication by juxtaposition" argument. Simply writing next to a parenthesis is simply a short hand form of multiplication, similar to writing a "dot". No other operation has short hand, so to say that it's "implied" to be first is just silly.
 
Interesting. I do remember that old argument now.
6/2(3) = 1 or 9 ??
For me : 9. But I took engineering classes. Never used any other convention.
:)

BTW: I think the reason it went out of style:
Using that convention for 1/2x = 8, x = 1/16.
 
So my mom the math teacher (middle school mind you) says 288.

16 ÷ 2[8 – 3(4 – 2)] + 1
= 16 ÷ 2[8 – 3(2)] + 1
= 16 ÷ 2[8 – 6] + 1
= 16 ÷ 2[2] + 1 (**)
= 16 ÷ 4 + 1
= 4 + 1
= 5
(16/2) * (8-6) +1
8*2 +1
17

She teachers her kids to complete what is in the parenthesis first, then go back and rewrite the equation. I agree with Mike about the juxtaposition thing...it's just shorthand to me although I tend to multiply them first anyways.
 
Funny - http://www.extremeskins.com/showthread.php?345936-48%F72%289-3%29/page30&s=349cbf2a362add29a0f94cc43694dadf
 
xcaret said:
So what does the winner get for solving the mystery? A brand new MP60?
Sure. Safe bet.
Since it depends on a sometimes used special convention, there will be no winner.

Simpler contest : Whomever posts the most in this thread gets the title "king of the nerds."
 
rygh said:
xcaret said:
So what does the winner get for solving the mystery? A brand new MP60?
Sure. Safe bet.
Since it depends on a sometimes used special convention, there will be no winner.

Simpler contest : Whomever posts the most in this thread gets the title "king of the nerds."

Since I have you all clamoring over the solution, wouldn't that make me the king and you my court jesters? :p
 
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