because most people read 1/2x as "1 divided by 2x" and not as "x divided by 2"
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Solve this simple math problem: 48/2(9+3)
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because most people read 1/2x as "1 divided by 2x" and not as "x divided by 2"
I think it's helpful, in going by Order of Operations, to treat division as multiplication-by-inverse:
48/2(9 + 3)
48/2*12
48*1/2*12
24*12
288
48/2(9 + 3)
48/2*12
48*1/2*12
24*12
288
Hm.
Lol I don't understand how people can't get 2 as an answer. While following order of operations, you obviously do the parenthesis first, but that doesn't really matter since no matter which way you do it, you will do (9+3), first. So the real question is, do we divide 48 by 24, or do multiply 24 by 12? The Acronym PEMDAS suggest that we Multiply before we Divide, but that isn't the case, however. You do them in order from left to right, normally, so whichever comes first, you do that first, normally. I've read some post of people asking whether its a fraction sign or a regular division sign, but from what I understand, there is no difference between the two. If you simplify the fraction 48/24, is 48 not being divided by 24, ultimately giving you 2 as an answer? So after we solve the equation in the parenthesis, we end up with 48/2(12). That said, if we do simple Order of Operations, going left to right, we will end up with 288 as an answer. Going back to what I said about fractions and division being the same. When you look at fractions, and get something like 12(3x+5) OVER 6(3x+5), you would first solve the equation in the numerator, then the denominator, and then divide/simplify. That being said, if we have 48 OVER 24, the answer will ultimately be 2, which is why some people get 2 as an answer.
People have been taught correctly about Order of Operations, there is no fault in the way either of the Answer's Representatives are doing their math. It is all a matter of how you look at the problem, because both are correct, and with that being said, we know that is wrong. We cannot have math equations to be equal with more than one answer, unless you are using variables, < & > signs, or etc. However, both of the answers, 288 & 2, seem to be true. I can understand how each answer would be obtainable, but personally I believe 2 is the correct answer.
Lol I don't understand how people can't get 2 as an answer. While following order of operations, you obviously do the parenthesis first, but that doesn't really matter since no matter which way you do it, you will do (9+3), first. So the real question is, do we divide 48 by 24, or do multiply 24 by 12? The Acronym PEMDAS suggest that we Multiply before we Divide, but that isn't the case, however. You do them in order from left to right, normally, so whichever comes first, you do that first, normally. I've read some post of people asking whether its a fraction sign or a regular division sign, but from what I understand, there is no difference between the two. If you simplify the fraction 48/24, is 48 not being divided by 24, ultimately giving you 2 as an answer? So after we solve the equation in the parenthesis, we end up with 48/2(12). That said, if we do simple Order of Operations, going left to right, we will end up with 288 as an answer. Going back to what I said about fractions and division being the same. When you look at fractions, and get something like 12(3x+5) OVER 6(3x+5), you would first solve the equation in the numerator, then the denominator, and then divide/simplify. That being said, if we have 48 OVER 24, the answer will ultimately be 2, which is why some people get 2 as an answer.
People have been taught correctly about Order of Operations, there is no fault in the way either of the Answer's Representatives are doing their math. It is all a matter of how you look at the problem, because both are correct, and with that being said, we know that is wrong. We cannot have math equations to be equal with more than one answer, unless you are using variables, < & > signs, or etc. However, both of the answers, 288 & 2, seem to be true. I can understand how each answer would be obtainable, but personally I believe 2 is the correct answer.
Interesting.
I was looking at it as a fraction.
48
___ = 2
(2)(12)
which is
48
___ = 2
24
There isn't any definite answer. Since it is ambiguous one must use parenthesis.
But as it is written right now, I'd say it is 2. Since there is an implicit multiplication, I think it must be made before the division, even though the order of operations says otherwise. When you're used to calculus and higher algebra, x(y+z) usually ends up being treated as a single entity in your head (at least that's how I see it), since it can be developped and become (xy+xz).
TL;DR: use LaTeX and produce .png files. No more problems. I started learning it today, so I was struggling with the document headers and such, but otherwise I would have used this to illustrate my point of view.
Totally agree.
But as it is written right now, I'd say it is 2. Since there is an implicit multiplication, I think it must be made before the division, even though the order of operations says otherwise. When you're used to calculus and higher algebra, x(y+z) usually ends up being treated as a single entity in your head (at least that's how I see it), since it can be developped and become (xy+xz).
TL;DR: use LaTeX and produce .png files. No more problems. I started learning it today, so I was struggling with the document headers and such, but otherwise I would have used this to illustrate my point of view.
Totally agree.
Fair enough, missed where you said that. Just seems more elegant with them in, but it's easy to rephrase to remove X. (Just like the equation above could be written 48/2(9+3)=X)
What about simple 'sqrt4'? Or 'arcsin(1)'? More than one answer to those.
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I still maintain my original opinion using a '/' is forgivable on a forum like this, but when hand writing or using decent software use '_' instead like actual maths-y people do. If you have to use '/' have the courtesy to use lots of brackets!
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Not if you follow the order of operations.
Parentheses
Exponents
Multiplication/Division
Addition/Subtraction
48/2(9+3)=48/2(12)
48/2(12)=24(12)
24(12)=288
To get 2, it should read: 48/(2(9+3))
The "/" mark is exclusively division. It can only operate as a fraction bar when both the numerator and denominator are either single values or bound by parentheses.
To you what is a division? To me it is the same exact thing as a fraction, except that the result of a division is usually expressed as a real number while a fraction stays in fractional form because it's simpler to work with.
Well... Yet another math thread.
You do (9+3) first, so you get 48/2(12). Then you divide 48 by 2 to get 24 making the equation 24(12). When you multiply, you get 288. How are people getting 2? I read their posts and I still don't understand.
You do (9+3) first, so you get 48/2(12). Then you divide 48 by 2 to get 24 making the equation 24(12). When you multiply, you get 288. How are people getting 2? I read their posts and I still don't understand.
Because it's all in the way you look at the problem. For those who normally do calculus level math their minds may tend to see it as
48
_____
2*(9+3)
not as 48÷2*(9+3)
Both are correct ways of looking at the problem. It's just a matter of mathematical semantics.
I'm referring strictly in the operational sense. The "/" mandates an operation, even if it is being used to denote an unsimplified fraction. Because of the way the problem in the OP is written, the fraction is properly viewed as: 48/2*12 because the 2 and (9+3) are not bound by additional parentheses, making 48 the numerator and 2 the entire denominator.
Same thing.
Most people don't use ÷ after 5th grade though because algebra encourages us to view things in fraction and decimal form.
They reduce 48/2(12) to 48/24 by saying that the implied multiplication takes precedence over the division.
i.e. 48/(2*(12)) vs (48/2)*12.
B
And now we have resulting confusion because of math semantics. So it's easy to see how you can get both answers, depending on how you approach the problem.
Not for me. I read it the way it should be written, which is fairly obvious if you know the OOO
False. If it was written correctly for you to do order of operations (basic math level) than it should have been written:
48÷2*(9+3)
not 48/2(9+3) which is:
48
_____
2(9+3)
In calculus you don't write equations like 48/x+6(9+45) or anything like that, you write it as
48
_____
x+6(9+45)
I've already pointed out that it is very easy to interpret this either way, and it's just semantics. But the problem was written as I've shown in the second and third example, not the first. What's obvious to you is unfortunately incorrect.
Huh, in all my programming I've never seen a time when I am supposed to use ÷ to represent divide. It's always / instead. I guess my math background (4 semesters of calculus) is making me confused
I guess I must be missing something obvious
My official position on this is the answer is that it is, strictly speaking, 288. However it is perfectly understandable for people to see it as 2 given how poorly written the problem is.
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