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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. |
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ETA: if you had 48/(2*12) then I would agree that the answer is 2 but I dont see that in this problem. |
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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) |
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Glad I've still got it. :cool: |
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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! :p 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! |
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. :D |
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. |
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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 |
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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. |
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I'm an accountant, so I guess I'm also a math nerd. :p |
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_48_ 2(12) Next _48_ 24 The underline stands for divide. So I'm with the two's. |
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288. 12(48/2) 12(24) =288 |
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To be clear....my answer is 2 |
Setting the problem = x still gives me 288 when I solve for x. 48÷2(9+3) = x x/48=1/2(9+3) x/48=1/2*12 x/48=6 x=6*48 x=288 |
Just thought of another way of saying it that might help.... My daughter is in 3rd grader and sometimes they have problems where they have to write math out in words. So, try saying it: Forty-eight divided by two times nine plus three. You have to find out what you are dividing 48 by. The key is finding out your denominator. 2 times 9+3 equals 24 Now your problem would read: 48 divided by 24. Don't know if that helps or not! :rolleyes: :) |
I think I'm still sticking with 2 as MY answer. To think, this may be my most popular thread ever on YT... ;p |
:DI actually teach this skill in 5th grade. YES, PEMDAS is used ANY time you have multiple operations however, what most people forget is even though multiplication and division are at the same level and the left to right rule applies, parentheses () outrank division. This problem is written with the 2 with the parentheses, therefore, the 2 must stay with them until it is complete. This indicates that the values must be multiplied before doing any other operation. 48÷2(9+3) is different than 48÷2X(9+3) this answer =2 this answer is =288 The 2 beside the () means you must X 2 by the answer inside to be finished. Now, thanks for making me work on my last day of spring break.:p |
Here is another example I found to look at if it helps... (4 / 2) + 4(5 - 2)^2 = (2) + 4(3)^2 = 2 + 4(9) = 2 + 36 = 38 ^2 is exponent ;) |
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48:aimeeyorks÷:aimeeyork:aimeeyork(9:aimeeyorks+:a imeeyork:aimeeyork:aimeeyork) = :animal-pa 288 s:aimeeyork when Teddy Bumpkins Solves for :animal-pa ETA: I can't get even get the # of yorkies right. Geez. |
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Another thing that might help.... Just now read some of the responses and I see that the () causes confusion. Someone said you can replace the () with * after you solve it. But, that is incorrect. The () were used to tell you to do that part first. 48/ 2(9+3) You have to solve the () first and then complete the denominator. The denominator includes the () which means you have to completely solve it before you move on. |
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Yes...that is exactly what I was trying to say! Thanks Teach! :) |
I love that a math problem has 6 pages (and counting) of responses to it! |
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