Math of the Demon Duck

[ArtDrake]

If you have a math problem you need help with, I'll give help.

Rules:

• I won't help you with more than one of the same type of math problem; this is to avoid doing your homework for you.
• I will discuss a problem I've explained, but will not reattempt to demonstrate the same method on another problem.
• I expect you to be able to do the math I explain, once I do so.
• Don't give me trivial math problems designed to waste my time. If you do so, I shall ask a moderator to delete the post. With luck and cooperation, this shouldn't happen too much
• I can't help with anything as complicated or more so than integral calculus.

Guidelines:

• If you have a question, post it in a separate post from the one where you discussed the previous problem, if you did. It's not a double post, since the subject matters are completely different, and the post is at a later time.
• If you'd like to discuss a problem, post only once after each problem. If you have something more to say, modify it in. After a few days, if the conversation is over or nearly over, I'll put the conversation in a spoiler, where one can go back and read it. Once I've done that, I'll ask people who participated in the conversation to delete their posts. That way, I maintain a clean question-answer format.

[Ertxiem]

I just wanted to say that I think that, sometimes, the doubts raised in the discussion may be interesting for others to understand the result...
(If you want, I can delete this post.)

By the way, can we ask you to give us things like an exact formula for the perimeter of an ellipse?

[MikeW781]

This is one I've seen floating around facebook recently, and I thought it had the potential of being open to interpretation. It depends on how you interpret the older division symbol, and what priority you consider the multiplication by parentheses to have. I know what I think is the correct answer. I just want to see your response.

6÷2(1+2)=?

[Duskling]

This is one I've seen floating around facebook recently, and I thought it had the potential of being open to interpretation. It depends on how you interpret the older division symbol, and what priority you consider the multiplication by parentheses to have. I know what I think is the correct answer. I just want to see your response.

6÷2(1+2)=?

It equals 9, because, in the order of operations, parenthesis come first, so, 2+1=3, now it's 6/2x3, so, now you go left to right, 6/2=3, 3x3=9. Sorry for stealing the show, DD.

[Idozen Cair]

I came upon the same answer.

[MikeW781]

This is one I've seen floating around facebook recently, and I thought it had the potential of being open to interpretation. It depends on how you interpret the older division symbol, and what priority you consider the multiplication by parentheses to have. I know what I think is the correct answer. I just want to see your response.

6÷2(1+2)=?

It equals 9, because, in the order of operations, parenthesis come first, so, 2+1=3, now it's 6/2x3, so, now you go left to right, 6/2=3, 3x3=9. Sorry for stealing the show, DD.

The thing is, that some people put forth the argument that multiplication by parentheses took priority, so one would multiply the 2 by the (3) before dividing, resulting in a final answer of six.

Also, others interpreted the division symbol as applying to both the 2 and the (1+2), so it would look like:

__6__
2(1+2)


While I agree that the answer is 9 based of what I've been taught, I was curious to see the point of view of somebody else who had been taught either of the above methods for solving this.

[Duskling]

This is one I've seen floating around facebook recently, and I thought it had the potential of being open to interpretation. It depends on how you interpret the older division symbol, and what priority you consider the multiplication by parentheses to have. I know what I think is the correct answer. I just want to see your response.

6÷2(1+2)=?

It equals 9, because, in the order of operations, parenthesis come first, so, 2+1=3, now it's 6/2x3, so, now you go left to right, 6/2=3, 3x3=9. Sorry for stealing the show, DD.

The thing is, that some people put forth the argument that multiplication by parentheses took priority, so one would multiply the 2 by the (3) before dividing, resulting in a final answer of six.

Also, others interpreted the division symbol as applying to both the 2 and the (1+2), so it would look like:

__6__
2(1+2)


While I agree that the answer is 9 based of what I've been taught, I was curious to see the point of view of somebody else who had been taught either of the above methods for solving this.

This is what I thought at first, until one of my friends explained it to me.

[ArtDrake]

I would disagree.

6/2(1 + 2) = x	Given
a/b(1+2) = x	Let a = 6 Let b = 2
a/b(3) = x	Addition
a/bc = x	Let c = 3
(a) / (bc) = x	Terms cannot be separated by order of operations. a/bc is not equal to ab-1c, but rather to ab-1c-1
(6) / (2*3) = x	Substitution of symbols
6 / 6 = x	Multiplication and removal of parentheses
x = 1	Division

I think that where you got lost was where you made the mistake of equating bc and b*c. b*c can be separated if the group of symbols is divided. Then, only the b is inverted. However, bc is a separate term, and cannot be separated using the hierarchy of left-to-right.

[bugfartboy]

Uh, I don't think I'm gonna be here much if that's the form answers are going to be in.

[Ertxiem]

I don't really think that you covered all the details of the subject, Demon Duck.

The main problem here is that writing ab/cd isn't following the standard for math notation (at least, as far as I know).



So, when we write ab/cd do we mean:
(a.b)/(c.d), where "." means the multiplication period, i.e.,

a.b
-----	?
c.d

Or does ab/cd means:
a.(b/c).d, i.e.,

b
a.-----.d	?
c

=a.b.d/c



If we're programming, when we write a*b/c*d (with "*" meaning multiplication), this is equal to a*b*d/c. If I want to have the first case, I'll have to write a*b/(c*d) or a*b/c/d.
By the way, usually the computation of a*b/(c*d) is slightly faster and uses a bit more memory than a*b/c/d.

[MikeW781]

I would disagree.

a/bc = x

(a) / (bc) = x

This is incorrect. a/bc = a/b*c= a/b THEN *c
Basically, you added parentheses when you were not supposed to.

[The Holy namelesskitty]

I can't stop laughing, this would be shown in a textbook to be 9 end of story. I find this interesting but more than anything funny!

[MikeW781]

I can't stop laughing, this would be shown in a textbook to be 9 end of story. I find this interesting but more than anything funny!

Well, yeah, it is sad. On the facebook poll millions of people picked 1

[Duskling]

I can't stop laughing, this would be shown in a textbook to be 9 end of story. I find this interesting but more than anything funny!

Well, yeah, it is sad. On the facebook poll millions of people picked 1

Not sad, I'd just say they have a different view on it, is all, I think picking 1, while incorrect, is perfectly rational.

[The Holy namelesskitty]

Yeah, I'm not sure where the one came from, but in any case it's interesting to see different viewpoints.