48÷2(9+3) = ???

[oidreez]

i would rather take "it's ambiguous" over "it's definately 288"

 

[oidreez]

i would rather take "it's ambiguous" over "it's definately 288"

 

[waystinthyme]

Originally Posted by sole vintage


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!)

please end it

again, this is personal opinion. post facts, with sources. this is someone's blog...telling their opinion (not fact) on the issue.

-waystinthyme

  

 

[waystinthyme]

Originally Posted by sole vintage


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!)

please end it

again, this is personal opinion. post facts, with sources. this is someone's blog...telling their opinion (not fact) on the issue.

-waystinthyme

  

 

[seasoned vet]

Originally Posted by kingcrux31

For team 288

Apparently not.

   

 
 
.......team 2!

Originally Posted by Stuntman Mike

almost 80 pages of heated, passionate discussion about math? 

 

 

 
 
- ive said it before ........this thread makes me proud of NT, 2 or 288.
 
*cheers*
 
 

 

[seasoned vet]

Originally Posted by kingcrux31

For team 288

Apparently not.

   

 
 
.......team 2!

Originally Posted by Stuntman Mike

almost 80 pages of heated, passionate discussion about math? 

 

 

 
 
- ive said it before ........this thread makes me proud of NT, 2 or 288.
 
*cheers*
 
 

 

[servechilled81]

a question for those saying 2
how would you answer these?

 

[servechilled81]

a question for those saying 2
how would you answer these?

 

[seasoned vet]

Originally Posted by ServeChilled81

a question for those saying 2
how would you answer these?

  

.....okay, i now change my answer to 288.
 
 

 

[seasoned vet]

Originally Posted by ServeChilled81

a question for those saying 2
how would you answer these?

  

.....okay, i now change my answer to 288.
 
 

 

[servechilled81]

Originally Posted by seasoned vet

Originally Posted by ServeChilled81

a question for those saying 2
how would you answer these?

  

.....okay, i now change my answer to 288.
 
 

i take it you did this
[h3][/h3]36÷4(5-2)+6
36÷4(3)+6
9(3)+6
27+6
33
[font=Arial, Helvetica, sans-serif]
[/font]

[font=Arial, Helvetica, sans-serif]and [/font]
4+6(8+2)-3
4+6(10)-3
4 + 60 - 3
64-3
61

 

[servechilled81]

Originally Posted by seasoned vet

Originally Posted by ServeChilled81

a question for those saying 2
how would you answer these?

  

.....okay, i now change my answer to 288.
 
 

i take it you did this
[h3][/h3]36÷4(5-2)+6
36÷4(3)+6
9(3)+6
27+6
33
[font=Arial, Helvetica, sans-serif]
[/font]

[font=Arial, Helvetica, sans-serif]and [/font]
4+6(8+2)-3
4+6(10)-3
4 + 60 - 3
64-3
61

 

[seasoned vet]

Originally Posted by ServeChilled81

Originally Posted by seasoned vet

Originally Posted by ServeChilled81

a question for those saying 2
how would you answer these?

  

.....okay, i now change my answer to 288.
 
 

i take it you did this
[h3][/h3]36÷4(5-2)+6
36÷4(3)+6
9(3)+6
27+6
33
[font=Arial, Helvetica, sans-serif]
[/font]

[font=Arial, Helvetica, sans-serif]and [/font]


4+6(8+2)-3
4+6(10)-3
4 + 60 - 3
64-3
61

   
 - i didnt do either.
 
 
- looking at those problems made me look at the equation in a different light:
 
48÷2(9+3)
48÷2(12)
 
....which also equals
 
48÷2X12
 
....written that way, in a classroom setting i would have then gone left to right......giving me 288. (and yes, i know this was pointed out earlier in the thread)
 
 
......but then it is math and i could still be wrong. its cool though, i like math.
 
 

 

[seasoned vet]

Originally Posted by ServeChilled81

Originally Posted by seasoned vet

Originally Posted by ServeChilled81

a question for those saying 2
how would you answer these?

  

.....okay, i now change my answer to 288.
 
 

i take it you did this
[h3][/h3]36÷4(5-2)+6
36÷4(3)+6
9(3)+6
27+6
33
[font=Arial, Helvetica, sans-serif]
[/font]

[font=Arial, Helvetica, sans-serif]and [/font]


4+6(8+2)-3
4+6(10)-3
4 + 60 - 3
64-3
61

   
 - i didnt do either.
 
 
- looking at those problems made me look at the equation in a different light:
 
48÷2(9+3)
48÷2(12)
 
....which also equals
 
48÷2X12
 
....written that way, in a classroom setting i would have then gone left to right......giving me 288. (and yes, i know this was pointed out earlier in the thread)
 
 
......but then it is math and i could still be wrong. its cool though, i like math.
 
 

 

[cadillacflow]

Originally Posted by seasoned vet

Originally Posted by ServeChilled81

a question for those saying 2
how would you answer these?

 
.....okay, i now change my answer to 288.
 

Yep, same here.

48÷2(9+3) = 288

48/2(9+3) = 2

 

[cadillacflow]

Originally Posted by seasoned vet

Originally Posted by ServeChilled81

a question for those saying 2
how would you answer these?

 
.....okay, i now change my answer to 288.
 

Yep, same here.

48÷2(9+3) = 288

48/2(9+3) = 2

 

[jokey iii]

my goodness

 

[jokey iii]

my goodness

 

[seasoned vet]

......let me also add:
 
 
48÷2(9+3) is the OG question from best i can find it. i say that because 48÷2(9+3) = 48/2(9+3) but 48/2(9+3) has the potential to be interpreted differently.
 
 
- for example: 48/2(9+3) could be interpreted 48         =
                                                                               2 (9+3)
 
 
...but its not. the OG equation doesnt even use / but somewhere it was added. if you stick with ÷, there's no other way to read it....no way you can mess it up. that / has the potential to throw off everything depending on how you interpret it.
 
 
......good fun. thanks guys.

 

[seasoned vet]

......let me also add:
 
 
48÷2(9+3) is the OG question from best i can find it. i say that because 48÷2(9+3) = 48/2(9+3) but 48/2(9+3) has the potential to be interpreted differently.
 
 
- for example: 48/2(9+3) could be interpreted 48         =
                                                                               2 (9+3)
 
 
...but its not. the OG equation doesnt even use / but somewhere it was added. if you stick with ÷, there's no other way to read it....no way you can mess it up. that / has the potential to throw off everything depending on how you interpret it.
 
 
......good fun. thanks guys.

 

[k2theablam]

Some people just don't get it.

* and ( ) aren't the same thing.

Just like the / and division sign aren't the same thing

 

[k2theablam]

Some people just don't get it.

* and ( ) aren't the same thing.

Just like the / and division sign aren't the same thing

 

[streetballer23]

87 pages...crazy.

I did okay at math, was not my best subject, I looked through the past couple of pages, but I still believe the answer is 2.

 

[streetballer23]

87 pages...crazy.

I did okay at math, was not my best subject, I looked through the past couple of pages, but I still believe the answer is 2.

 

[whyhellothere]

Originally Posted by jthagreat

so 2 or 288

i got $2.88 ridin on the right answer