Simple Maths

Some of you might like the next link:http://www.purplemath.com/modules/orderops2.htm

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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!

 

(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!)

So, apparently the answer does indeed seem to be 2. Personally, I think the "juxtaposition"-rule is ugly as hell. If there are rules, like the pemdas, you'd expect them to be applied consistently. If the page is not lying, I'd say this is mathS at its most inconsistent.

actually fuck yes. I'm a retard.

in my defense I did actually get 2 the first time by agreeing with what goDel posted above - then I went and visited that stupid physics forum and changed my mind...

hm, never been taught that there are weaker and stronger notations for multiplication when dealing with simple arithmetic*.. that seems to needlesly complicate things-- as evidenced by chassis being unable to distinguish the meaning of "one-half times 6." in order to make the original problem clearly understood, an extra set of brackets ought to be used -- but that's just how i was taught.

i'm gonna go do my actual math homework now

*i was taught to add weight to juxtaposition when dealing with variables of course

I can't believe that people made 105 posts about this. This got to be some aprils fools joke or something.

  On 4/10/2011 at 7:19 PM, Adam Beker said:

I can't believe that people made 105 posts about this. This got to be some aprils fools joke or something.

Believe me, 105 posts is nothing.

Math (and mathS) is like a religion.

What, so now I was right?

But this 'issue' is taught when you're like 14 years old . So many people haven't finished school or what?

  On 4/10/2011 at 7:27 PM, Adam Beker said:

But this 'issue' is taught when you're like 14 years old . So many people haven't finished school or what?

What r u some kind of 12 year old genious or sometin ???

im pretty sure u rn't so shut ur smug face hole mr clarks

  On 4/10/2011 at 7:27 PM, Adam Beker said:

But this 'issue' is taught when you're like 14 years old . So many people haven't finished school or what?

People can be taught differently. As mentioned, even some teachers don't agree on the issue.

And yes gaarg, you were right all along!

There is an easy way to sort it if anyone is still unsure. My calculator seems to agree with 2, what are your calculators saying people?

Bloody technology. Times were much better when people could argue hazy concepts down the pub, without some bellend pulling out a processor.

edit: btw my calculator is kept in the gap underneath my monitor. Im not that much of a twat to go and find one =)

  On 4/10/2011 at 7:39 PM, goDel said:

 

 

People can be taught differently. As mentioned, even some teachers don't agree on the issue.

 

And yes gaarg, you were right all along!

How they can be taught differently. I don't even understand.

  On 4/10/2011 at 7:57 PM, Dirty Protest said:

My calculator seems to agree with 2, what are your calculators saying people?

 

288. You're doing it wrong.

i gave it up when i realized i couldnt even do 9+3 in less than half a minute

  On 4/10/2011 at 7:57 PM, Dirty Protest said:

There is an easy way to sort it if anyone is still unsure. My calculator seems to agree with 2, what are your calculators saying people?

  On 4/10/2011 at 8:01 PM, Adam Beker said:

  On 4/10/2011 at 7:57 PM, Dirty Protest said:

My calculator seems to agree with 2, what are your calculators saying people?

 

 

288. You're doing it wrong.

Thanks for keeping the vibe alive. Tomorrow this thread will be past 200 posts.

Well, he's really doing it wrong, It's obvious. Calculator

for the record, casio calculators will come up with 2 unless you specifically put in an "x" for multiplication

then it will be 288

it's incredibly ambiguous.

  On 4/10/2011 at 8:06 PM, luke viia said:

  On 4/10/2011 at 7:57 PM, Dirty Protest said:

There is an easy way to sort it if anyone is still unsure. My calculator seems to agree with 2, what are your calculators saying people?

 

No, thats wrong.

The original post says:

48÷2(9+3)

not:

48/2(9+3)

Both are not the same

the answer is 2

I hit the ÷ on my calculator and it shows up as /

btw, could you tell me what / means if it doesn't mean divide? im just wondering

  On 4/10/2011 at 8:13 PM, chassis said:

  On 4/10/2011 at 8:06 PM, luke viia said:

  On 4/10/2011 at 7:57 PM, Dirty Protest said:

There is an easy way to sort it if anyone is still unsure. My calculator seems to agree with 2, what are your calculators saying people?

 

 

No, thats wrong.

 

The original post says:

 

48÷2(9+3)

 

not:

48/2(9+3)

 

the answer is 2

 

Both are not the same

wat

48/2(9+3)

48÷2(9+3)

  On 4/10/2011 at 8:14 PM, luke viia said:

I hit the ÷ on my calculator and it shows up as /

 

btw, could you tell me what / means if it doesn't mean divide? im just wondering

/ implies that its already a number, just expressed as a fraction. At least thats what it means to me.

My Casio gives;

48÷2(9+3)=2

and;

48/2(9+3)=288

fuckin casio tryin to change the rules of the game!

  On 4/10/2011 at 8:18 PM, Adam Beker said:

  On 4/10/2011 at 8:13 PM, chassis said:

  On 4/10/2011 at 8:06 PM, luke viia said:

  On 4/10/2011 at 7:57 PM, Dirty Protest said:

There is an easy way to sort it if anyone is still unsure. My calculator seems to agree with 2, what are your calculators saying people?

 

 

No, thats wrong.

 

The original post says:

 

48÷2(9+3)

 

not:

48/2(9+3)

 

the answer is 2

 

Both are not the same

 

wat

 

 

48/2(9+3)

 

48÷2(9+3)

I didnt realise google was the b-all end all to maths.

Besides, that "*" implies that the search engine has interpreted wrong.

Surely this ambiguity means there is a glitch in the matrix and the remainder is causing the universe to exist.

(48 / 2) * (9 + 3) is not the same as 48/2(9+3). Shoving an operator in seems a bit much from google =)