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48÷2(9+3)=?????


Chiefinonhaze

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the exact conclusion I have come to, except i read intent and you do not. some see it as a lineal problem read from left to right, and others including me sees

48

2(9+3).

because that is how I read what was intended. When using parentheses, you indicate that the operations inside be conducted first, but in absence of other symbols you also imply the grouping of 2 and the action within the parentheses. If I wrote that I would either change it to one of the options you noted above, depending on the intent. I do not know of a single person who would write an equation 48÷2(12) when what they intended was 48÷2*12.

No one answer is wrong, the questions is wrong. Both the sets of kids with 2's and 288's on their answer page get a check mark, the teacher gets fired, tarred and feathed for creating such a public nuisance.

No, you don't. In the absence of other directions on how to evaluate, you fall back on the rules in the order of operations.

And you can't make up intent with no context. If all you're given is an equation, that's all you have. Otherwise you're just making stuff up.

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Except that no published order of operations I've ever seen make that distinction. Or mention this rule at all. Can you point us to a published set of rules that does?

I've never seen any published order of operations of any kind, it's just what I was taught at school but it has already been mentioned numerous times in this thread. From a quick google search:

http://mathforum.org/library/drmath/view/57021.html discusses the whole issue in some academic depth.

http://www.purplemath.com/modules/orderops2.htm has an example that illustrates the rule.

The rest of the google results seem to be from forum threads much like this one O_o

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Haven't read all the replies , but I haven't seen the division operator used since grade school, probably because of situations like this. The usual way to write the expression is like this

48

---------

2(9+3)

To which everyone would calculate to be 48/24 = 2. However, since we are using the division operator, and not the above notation, you do go left to write after the parenthesis, so 288 is the correct answer. Multiplication and division, like addition or subraction, are on the same level of precedence.... this does not however, mean the expression is ambiguious, because then you would evaluate left to write. and get (48/2)*12 = 288.

A great example of how confusing our natural language can be. We would all be much better of ir we learned RPN (also called Postfix) ...

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I would like to point out that you don't even have to do "parentheses first". you just treat all the items in them as a singular term. You an do all you want to an equation and not touch what's inside the parentheses and its fine. I do it all the time 'cause I'm a beast like that.

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the exact conclusion I have come to, except i read intent and you do not. some see it as a lineal problem read from left to right, and others including me sees

48

2(9+3).

because that is how I read what was intended.

Read what was intended?

Nonsense.

Now you have changed your argument from "the order of operations must be followed" to "I am solving this as the author intended" so in conclusion "everyone is wrong and we are all correct"

Here's the same equation that you tried to use a few pages ago. I just changed the "÷" to a multiplication of the inverse.

Solve for y and you get 2

48 ÷ y(9+3) = 288

(48) ÷ (y)(9+3) = 288

(48) (1/y)(9+3) = 288

(48)(1/y)(9+3) = 288

(48)(1/y)(12) = 288

(1/y)(576) = 288

(1/y) = 288/576

(1/y) = 1/2

y = 2

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i've shown this problem to some people....some came up with 2, some came up with 288.

For those saying it's poorly written, i think they're right. I still managed to come up with 288 the way it's written...but technically speaking, to get that answer, i think the problem SHOULD be written like this....

(48/2)(9+3) = 288

when you don't put the parenthesis around the 48/2....that's what leads people to do order of operations and get 2 as their answer.

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That might be true, but there are a lot people in this thread replying 2 as the answer. I don't know what they are thinking.

you dont know what they are thinking? or you disagree with it because you were taught a different way?

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you dont know what they are thinking? or you disagree with it because you were taught a different way?

I don't know what they are thinking. A ti-83 calculator will confirm the answer is 288. If these people thinking the answer is 2 wont believe a calculator, I really don't know what they are thinking.

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I don't know what they are thinking. A ti-83 calculator will confirm the answer is 288. If these people thinking the answer is 2 wont believe a calculator, I really don't know what they are thinking.

you can't trust computers when it comes to order of operations. they don't work like people. when inputting equations into a computer you have to make liberal use of parentheses because you don't know what kind of algorithm was used to break the equation down into individual instructions by the programmer.

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you can't trust computers when it comes to order of operations. they don't work like people. when inputting equations into a computer you have to make liberal use of parentheses because you don't know what kind of algorithm was used to break the equation down into individual instructions by the programmer.
Order of operations should be standardized, one way or the other. You'd think we would have standardized this type of equation syntax by now.
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I don't know what they are thinking. A ti-83 calculator will confirm the answer is 288. If these people thinking the answer is 2 wont believe a calculator, I really don't know what they are thinking.

chief, i think most people who think the answer should be 2 have explained how they got to that answer. it seems most of us were taught that you clear up the 2 (in this example) with the parentheses. and theres at least some backing for that. i posted links that explain that some people were, indeed, taught a different method, that there are people who are far more schooled in math than anybody i've seen on this board who go by a different method, that there is, at least, a lack of consensus on such a problem, and, possibly, the american mathematics association may agree that the answer should be 2 based on a priority of implied multiplication (if i could ever figure out how to actually get into the AMA site to i could see this for myself, it would be interesting).

PP already beat me as to why some calculators calculate the problem differently.

i'm just saying this so you know what the 2's are thinking, not to say youre wrong or anybody else is right. :thumbsup:

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Order of operations should be standardized, one way or the other. You'd think we would have standardized this type of equation syntax by now.

it is standardized in mathematics, but its not so easy when trying to make a computer recognize our order of operations because they don't think like we do.

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it is standardized in mathematics, but its not so easy when trying to make a computer recognize our order of operations because they don't think like we do.
In cases like that, it's our own fault.

Math should be done in a cold, calculating manner. Not that you can't have fun with math.

cyn_sample_1.GIF

hi2_matlab.jpg

But math itself should be as logical and immune to "interpretation" as this guy, IMO.

datas-head.jpg

And no, I'm no math wiz. The "Hi" graph stumps me.

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The answer is 2

Please Excuse My Dear Aunt Sally

The 2 in the question is in connection with Parenthesis not the 48. Left to right down not matter

Again....parentheses refers to expressions WITHIN parentheses, not numbers TOUCHING the OUTSIDE

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