Okay Math Geniusues... What's 48÷2(9+3) ?

[Ellie May]

Ok sooo for the quadratic we can have a really long numerator that I don't want to retype over 2(a). In this case we are expected to multiply 2 by a. But then in this other problem we don't multiple 2 by 12 because the () just disappear? I can see how both ways could be right. It's just that by closeness to teh () I woule automatically multiply 2(12). There is no clear way to tell if the 12 is prat of the denominator or if it is not part of the division problem at all. Brackets or not, the 2 touching the () tells me to multiply by what is in the () and I have to clear () first.

[107barney]

Originally Posted by Ellie May

Ok sooo for the quadratic we can have a really long numerator that I don't want to retype over 2(a). In this case we are expected to multiply 2 by a. But then in this other problem we don't multiple 2 by 12 because the () just disappear? I can see how both ways could be right. It's just that by closeness to teh () I woule automatically multiply 2(12). There is no clear way to tell if the 12 is prat of the denominator or if it is not part of the division problem at all. Brackets or not, the 2 touching the () tells me to multiply by what is in the () and I have to clear () first.

I would agree, except for the order of operations that dictates we must go from L to R and treat multiplication and division the same after we deal with what is INSIDE the parenthesis. Once I'm done inside, it doesnt matter if 2 is married to another parenthesis, it's just another multiplication that has to be done from L to R. Therefore 48/2*12 = 288 for me.

ETA: if you had 48/(2*12) then I would agree that the answer is 2 but I dont see that in this problem.

[lisaly]

Originally Posted by 107barney

I would agree, except for the order of operations that dictates we must go from L to R and treat multiplication and division the same after we deal with what is INSIDE the parenthesis. Once I'm done inside, it doesnt matter if 2 is married to another parenthesis, it's just another multiplication that has to be done from L to R. Therefore 48/2*12 = 288 for me.

ETA: if you had 48/(2*12) then I would agree that the answer is 2 but I dont see that in this problem.

I agree with you. If you were to group (2 times 12) together, you would need parenthesis to come up with the answer 2. Without them, I came up with 288, which I believe is the answer.

[kjc]

Using the Distributive Property and the Order of Operations, I get:

48/2(9+3)= 48/2*9 + 2*3=48/18 + 6 = 48/24 = 2

These get done first bc they were in () to begin with, all I did was rewrite it... I still have to do the operations. Once all the operations that were in the () are done, then move on to 48/.

To get 288, (48/2)(9+3)


It is also true that any division problem can be written as a fraction, as was already posted. (which = 2)

[kjc]

Originally Posted by Ellie May

Ok sooo for the quadratic we can have a really long numerator that I don't want to retype over 2(a). In this case we are expected to multiply 2 by a. But then in this other problem we don't multiple 2 by 12 because the () just disappear? I can see how both ways could be right. It's just that by closeness to teh () I woule automatically multiply 2(12). There is no clear way to tell if the 12 is prat of the denominator or if it is not part of the division problem at all. Brackets or not, the 2 touching the () tells me to multiply by what is in the () and I have to clear () first.

[JesStang]

Originally Posted by linz06

I believe the answer is 288..

48÷2(9+3)

48 ÷ 2 x (9+3)

48 ÷ 2 x 12

24 x 12

=288

After the parentheses, there is only multiplication and division left to do, and they follow left to right.

x2, that's what I got. You have to do the parentheses work first, can't ignore them!

Glad I've still got it.

[shodanusmc]

Originally Posted by linz06

I believe the answer is 288..

48÷2(9+3)

48 ÷ 2 x (9+3)

48 ÷ 2 x 12

24 x 12

=288

After the parentheses, there is only multiplication and division left to do, and they follow left to right.

YES! I agree

[TatumsMom]

Interesting thread that I'm just now seeing.... I was a real Algebra geek in school (but hated geometry!). I got some weird satisfaction out of working out a problem and the more it filled up the page, the better! I have to admit though that high school for me was more than 20 years ago and I'm rusty. I originally got "2" as my answer but as soon as someone mentioned PEMDAS I reworked it and got 288. My girls are a Freshman and Junior in HS now and do not ask me for help with their work because from early on I would tell them how to do it and they would argue "that's not how the teacher did it" so I told them I wasn't trying to help anymore. They do very well without my help though. This was actually a very simple problem with just a hint of "controversy" but as long as you follow the PEMDAS rule, you got it. Thanks for waking my brain up!

[TatumsMom]

LOL..... a coworker of mine who considers herself a "math person" and just graduated college a couple years ago disagrees with the 288 answer. She says it's "2". She's gone back to her desk to research it now.

[AMD]

The two is a factor so you cannot take it apart from the parenthesis. That's why it helps to put brackets around the denominator to see it.

Distributive Property: it makes no difference whether you add two or more terms together first, and then multiply the results by a factor, or whether you multiply each term alone by the factor first, and then add up the results.

Adding up the term first; then multiplying by the factor = multiplying each term by the factor first, then adding up the resulting terms

Factor(Term1 + Term2 + ... + TermN) = Factor(Term1) + Factor(Term2) + ..... + Factor(TermN)

2(9+3) = 2(12) = 24
2(9+3) = 2(9) + 2(3) = 24

Answer: 48/24 = 2

If I gave you 1/(12x+24), you could factor it into 1/12(x+2). 12(x+2) is a factored form of 12x+24. You CANNOT split it up and divide by the 12 and then multiply by the x+2, or you'll get a completely wrong answer.

To be allowed to divide before distributing there have to be parentesis stating such: (48/2)*(9+3). Otherwise it's all one term that cannot be separated before performing another operation.

[linz06]

Originally Posted by AMD

The two is a factor so you cannot take it apart from the parenthesis. That's why it helps to put brackets around the denominator to see it.

Distributive Property: it makes no difference whether you add two or more terms together first, and then multiply the results by a factor, or whether you multiply each term alone by the factor first, and then add up the results.

Adding up the term first; then multiplying by the factor = multiplying each term by the factor first, then adding up the resulting terms

Factor(Term1 + Term2 + ... + TermN) = Factor(Term1) + Factor(Term2) + ..... + Factor(TermN)

2(9+3) = 2(12) = 24
2(9+3) = 2(9) + 2(3) = 24

Answer: 48/24 = 2

If I gave you 1/(12x+24), you could factor it into 1/12(x+2). 12(x+2) is a factored form of 12x+24. You CANNOT split it up and divide by the 12 and then multiply by the x+2, or you'll get a completely wrong answer.

To be allowed to divide before distributing there have to be parentesis stating such: (48/2)*(9+3). Otherwise it's all one term that cannot be separated before performing another operation.

You could only factor it into 1/[12(x+2)] if you are writing it in a line form. In fraction form, that would be

1
_______
12(x+2)

and to write that in a line, you would have to show [ ] around the bottom to show it is all a denominator. Without those brackets, 1/12(x+2) would just be:

1
__ (x+2)
12

[linz06]

Originally Posted by JeanieK

My degree is in accounting, but I didn't want to play that card. thanks for verifying.

haha, engineering here... I'm kind of a math nerd too

[OwnedByJezebel]

The difference in answers here is due to when some believe the "parentheses goes away."

I don't happen to believe that just because you add the 9 and the 3, the parentheses has gone away. After you add the 9 and the three, the equation becomes:

48 / 2(12)

Adding two numbers in a parentheses does not eliminate the parentheses. Taking what is in the parentheses and multiplying it to the number just to the left (or unknown, such as "x", "y", etc.) does eliminate the parentheses.

[Wylie's Mom]

Originally Posted by TatumsMom

LOL..... a coworker of mine who considers herself a "math person" and just graduated college a couple years ago disagrees with the 288 answer. She says it's "2". She's gone back to her desk to research it now.

LOL. Who knew math would create such a popular thread ?

[BonBon]

Originally Posted by OwnedByJezebel

The difference in answers here is due to when some believe the "parentheses goes away."

I don't happen to believe that just because you add the 9 and the 3, the parentheses has gone away. After you add the 9 and the three, the equation becomes:

48 / 2(12)

Adding two numbers in a parentheses does not eliminate the parentheses. Taking what is in the parentheses and multiplying it to the number just to the left (or unknown, such as "x", "y", etc.) does eliminate the parentheses.

I agree. That's the way I was taught in both my high school and college courses.

I'm an accountant, so I guess I'm also a math nerd.