48÷2(9+3) =
- Thread starter Gomer
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LordHelmet
Supporting Member
i got 3.14.
G
GreshamH
Guest
melly mel said:
Basil said:
[youtube]s6EaoPMANQM[/youtube]
:lol:
rygh
Guest
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".
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".
sid700
Supporting Member
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:
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!)
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:
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!)
sfsuphysics
Supporting Member
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.
phishphood
Guest
So my mom the math teacher (middle school mind you) says 288.
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.
(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.
