The Cellar - 48÷2(9+3) = ???

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- - 48÷2(9+3) = ??? (http://cellar.org/showthread.php?t=24914)

Quote:

Originally Posted by Undertoad (Post 724293)

Now, see, I would hold that Mathematics can't allow for anything "implied". It's either multiplication, or it isn't.

I don't think to extrapolate the problem was implied either.

I agree, when you solve it as it stands the answer is 288

Quote:

Originally Posted by Ibram (Post 724292)

Quote:

But many calculators and textbooks state that a higher value of precedence should be placed on implied multiplication than on explicit multiplication

Bullshit. Any cites of these calculators and textbooks? I've never heard this.

The root of all this is ambiguous use of the "/" in a single-line context, where properly-typeset multi-line usage would result in either

Code:

  2  

----

 5x

Code:

 2

--- x

 5

Any sensible reinterpretation of one of these into a single line would include appropriate parentheses or other clarification to make it clear how the calculation is carried out. As noted earlier, the entire point of the 48-whatever example is to start an argument.

In fact, I dare say that incorrect interpretation of the fraction bar by bogus separation of terms in numerators and denominators, for example

Code:

 x + 5     x     

------- = ---  +  5

   2       2

is a very common student error, and contributes to the misinterpretation of typographical disasters such as we're discussing.

Implied multiplication certainly looks like it should have higher precedence, but the idea that shorthand is actually a different operator is odd.

ok, so lets try this again ...

6÷2(1+2)=?

Quote:

Originally Posted by classicman (Post 728637)

ok, so lets try this again ...

6÷2(1+2)=?

It's a shark.
On. a. treadmill.

4y÷2y=?

I certainly see the logic behind putting implied multiplication above regular multiplication and division in order of operations.

Quote:

Originally Posted by Happy Monkey (Post 728818)

4y÷2y=?

I certainly see the logic behind putting implied multiplication above regular multiplication and division in order of operations.

That is one hell of an example. Goes to the root of the issue.

Even calculators can't be sure.

http://i.imgur.com/fcQHb.jpg

Quote:

Originally Posted by Pete Zicato (Post 729333)

Even calculators can't be sure.

http://i.imgur.com/fcQHb.jpg

pls post a larger image, I can't quite see it........

Quote:

Originally Posted by Happy Monkey (Post 728818)

4y÷2y=?

I certainly see the logic behind putting implied multiplication above regular multiplication and division in order of operations.

The question is not whether it's logical. The question is whether it corresponds to the generally accepted interpretation of ordering the operators.

Quote:

Originally Posted by Pete Zicato (Post 729333)

Even calculators can't be sure.

Quote:

Originally Posted by Texas Instruments web site

Type: Question and Answer Last Updated: 16-JAN-2011 23:45:41
Does implied multiplication and explicit multiplication have the same precedence on TI graphing calculators?

Implied multiplication has a higher priority than explicit multiplication to allow users to enter expressions, in the same manner as they would be written. For example, the TI-80, TI-81, TI-82, and TI-85 evaluate 1/2X as 1/(2*X), while other products may evaluate the same expression as 1/2*X from left to right. Without this feature, it would be necessary to group 2X in parentheses, something that is typically not done when writing the expression on paper.

This order of precedence was changed for the TI-83 family, TI-84 Plus family, TI-89 family, TI-92 Plus, Voyage™ 200 and the TI-Nspire™ Handheld in TI-84 Plus Mode. Implied and explicit multiplication is given the same priority.

Please see the graphing calculator guidebooks for additional information.

(source, if this horrible URL isn't one-time only)

Quote:

Originally Posted by morethanpretty (Post 723485)

42

Why? Its the answer to life the universe and everything.

Thread won.

Having been 42 for almost a year now, I have to say that 41 beats the shit outta 42.

Quote:

Originally Posted by Gravdigr (Post 729458)

Having been 42 for almost a year now, I have to say that 41 beats the shit outta 42.

Wait. You weren't with Baby when you were 41, were you?