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48÷2(9+3) = ?

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Postby at1with0 » Tue Jun 12, 2012 6:30 am

Many people will get 2.


Subtraction is the same as adding the additive inverse (the opposite) and division is the same thing as multiplying by the multiplicative inverse (the reciprocal).

Therefore, 48/2(9+3) is 48*.5*(9+3) which is 24*12 = 288. (.5 is the reciprocal of 2)

When using the PEMDAS convention, M and D are done simultaneously left to right because multiplication is commutative and since D is really M by the reciprocal. When using the PEMDAS convention, A and S are done simultaneously left to right because addition is commutative and since S is really A of the opposite.

Every expression can be re-written to not use division and to not use subtraction. You'll have multiplication by the reciprocal and adding the opposite. When doing that, PEMDAS simplifies to PEMA.
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Postby Nesaie » Wed Jun 13, 2012 12:18 am

You math geek! :P

So maybe, as above so below? Or maybe we can exclude below or above? I'm sure you're one of the few people who could get these questions.
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Postby gumrosin » Thu Jun 14, 2012 6:28 pm

288
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Postby at1with0 » Fri Jun 15, 2012 1:12 pm

your signature is whack
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Postby SmokinJoe » Wed Jun 27, 2012 7:32 pm

at1with0 wrote:Many people will get 2.



Therefore, 48/2(9+3) is 48*.5*(9+3) which is 24*12 = 288. (.5 is the reciprocal of 2)

Every expression can be re-written to not use division and to not use subtraction


That is amazing. In school, you are taught to first work the right side of the problem (9+3). Then move left..so it looks like this:
(9+3) is 12...
2(12)
24
48/24
2

But he actually starts with 2 being the critical link between both equations.

48/2 (or 48*.5)
24
then he goes to the right side..

(9+3)
12

bringing it home...
24 x 12 = 288.

It is the exact same equation with 2 outcomes depending on one's interpretation of it. That is a great metaphor in life. Also, if you aren't open to other interpretations, you just won't see it.

AWESOME video, at1... :thumbup:
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Postby at1with0 » Wed Jun 27, 2012 7:47 pm

The result is 100% dependent on what convention you use.
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Postby SmokinJoe » Wed Jun 27, 2012 8:09 pm

at1with0 wrote:The result is 100% dependent on what convention you use.


LOL..yup!
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Postby at1with0 » Thu Jun 28, 2012 9:07 am

Apparently, this discussion (whether it "is" 2 or 288 or something else) rages on in the interwebs. A ring theorist studies generalizations of the integers (which form the prototypical example of a ring) all day long but that in itself doesn't make him an authority on integers because arithmetic is pretty far removed from what they do in day-to-day work. They think about pretty strange, abstract stuff far removed from actual numbers.
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Postby bionic » Thu Jul 05, 2012 12:02 am

I get 24..
there's another answer?
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Postby at1with0 » Thu Jul 05, 2012 5:49 am

"it is easy to grow crazy"
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