a = 10, b = 2, 3a ÷ 3b = ?

5 or 20?

I'll fall for it......5

5 if you calculate the 3a and 3b separately and 20 if altogether?

I have no idea. I still think it's 20 and there people who think's its 5.

it's 20.

the formula not written out all confusing looks like this

((3*a)/3)*b
((3*10)/3)*2 = 20

in other words, to get 5 you would have to specify that the 3*b operation is carried out before the division, using a bracket. In this case it is not.

B racket
E xponent
D ivision
M ultiplication
A ddition
S ubtraction

yeah. if you calculate what's in the brackets first (3*10) =30 and then (3*2) =6; and finally 30 divided by 6, you'd get your 5. but if you do the whole equation through without brackets you'd get the 20. i dunno keke, i'm just bored.. :suspect:

Yeah, but like I said, doing the multiplication of 3b before the division is wrong. 5 is the wrong answer.

I am going to somewhat disagree. Division and multiplication are the same thing. In this case (writing it out; not in the special case where you are typing it in a calculator with necessary predefined rules to avoid ambiguity), there is not enough info. Is it 3xa/3xb or (3xa)/(3xb)? That is why God invented parenthesis.

20 for sure because multiply and divide are the same. They go in a straight order. : multiply 3 by 10, divide by 3, multiply by 2. There is no ( ) to block the equation into sequence.

BEDMAS is the standard notational convention. You can't say you don't want to follow it because they could have meant such and such. Division, then multiplication. That's how it works. If there was a bracket around the 3b term, it would superceed the division operation, but there isn't, so it doesn't. The answer is 20.

If whoever posed the question intended the answer to be five, they have to include bracketed terms. BEDMAS is around for a reason, to avoid ambiguities such as this.

well if u follow the rules of order of operations...

it goes like this..
Please Excuse My Dear Aunt Sally

Parenthesis Exponent Multiplication Division Addition Subtraction...

Multiplications get done first...

But with multiplication and division, you go left to right.

The standard is to remove all ambiguity. That way you dont have to have "rules" that make no fundemental sense. 3/b is the same as 3 x (1/b). If you want to say one thing dont write it to allow someone to think something else. (unless you are Faulkner or Melvile)

I see what's going on. It seems, just as america uses units different from the rest of the world, and needlessly complicated, they also have a different standard order of operation. PEDMAS.

What is the deal with you guys, why can't you just do what the rest of the world does!? it would make everyones life easier

you guys are silly. Silly Silly Silly

Multiplication and Division can be done in any order, because they are the same operation. So standard convention says just to do them from left to right.

Think about it for a second :)

^^^You mean 3xa/3xb? I would agree, if it was originally written that way. The way it was written suggests another interpretation.

i would also agree that I am Silly, silly but not silly, silly, silly. Sorry to disagree.

What is the deal with you guys, why can't you just do what the rest of the world does!? it would make everyones life easier Yeah, wtf is the deal with not switching to metric yet? We need to get with it. Inches make no farking sense.

whats the answer if you plug it into c++ or java or some programming language?

i think matlab does it in order from left to right...

I think it's 5, or at least, if you are forced to make an assumption. Otherwise, you need more information

Reasoning:
If you were to use / instead of ÷, you would see:

3a/3b

No one assumes that to be b * (3a/3) - because we can't type one over the other, we use visual grouping - 3b is under 3a. The same would apply to ÷, unless written like this:

3 * a ÷ 3 * b. Then just go left to right. (and it would be 20)

Mathematica says 3 a / 3 b (spaces are * in Mathematica) is = a b, which does not support the left to right arguement.

whats the answer if you plug it into c++ or java or some programming language?

i think matlab does it in order from left to right...

Programming languages do them left to right whatevers in order.

But the point is that it doesn't matter if you do multiplication or division first, there is no standard. To those who think otherwise: proof please?

There are some conceptual problems here.

Mathematica says 3 a / 3 b (spaces are * in Mathematica) is = a b, which does not support the left to right arguement.

That formula supports my argument. Any order, any direction.

b*(1/3)*a*3 = ab
3*(a/3)*b =ab
(b/3)*a*3 =ab
(a/3)*b*3 =ab

The simple way to do it is left to right. Edit: Because thats the direction we read in

Programming languages do them left to right whatevers in order.

But the point is that it doesn't matter if you do multiplication or division first, there is no standard. To those who think otherwise: proof please?

There are some conceptual problems here. The conceptual problem is that the original question was asked like this:

What does this question mean? "Where does the cat belong with you?"

You need some punctuation.

yah.. its left to right.. i just tried in my ti-83....

i believe all programming languages also go left to right...

That formula supports my argument. Any order, any direction.

b*(1/3)*a*3 = ab
3*(a/3)*b =ab
(b/3)*a*3 =ab
(a/3)*b*3 =ab

The simple way to do it is left to right. Edit: Because thats the direction we read in Ah, but you made your argument clear by using parenthesis!!! UNFAIR!!! How dare you be clear about what you speak!

Also, computers need rules to default to when you give them garbage. You should always approach math rules as if you were writing the equatinos on paper. An equation that works on paper will always work on a computer (or the program is crap)

I see what's going on. It seems, just as america uses units different from the rest of the world, and needlessly complicated, they also have a different standard order of operation. PEDMAS.

What is the deal with you guys, why can't you just do what the rest of the world does!? it would make everyones life easier

No No No!:nono: I have been taught all my math life (hurray) that it is PEMDAS. We Americans normally make things too complicated, but in this case it is identical as you Canadians. aY?

Please Excuse My Dear Aunt Sally.
Parenthesis Exponents Mult Divide Add Subtract
((((((( ))))))) ^^^^^ XXXXXX ////// ++++ --------



I think I see the confusion of the problem. People are reading the problem and seeing it logically and grouping things even when they should not.

3a ÷ 3b

That looks like the 3a is one group and 3b is another group. It is kind of like reading "thnik" and seeing "think". As you progress through the fun levels of math you stop using big 'X's for multiplication. You also stop using periods in the middle of a line to show multiply. We now just put the variable and its coeffecient together.

It is always the elementary problems that kill people. This kind of elementary problem requires the elementary process to solve. PEMDAS

This is how I entered it into my calculator:

3(10)/3(2)

If you use that order of operations you will come to the right answer of 20.
:Eyecrazy:

Using programming languages is bogus. Programming languages *have their own strict specification of order of operations*. They are normally made to more or less model normal abstract mathematical order of operations, but that is no guarantee. Asking what C or java say is like being unsure about what the word "attend" means in English and trying to resolve it by asking what it means in French (it means "wait").

20 is the right answer. Multiplication and division bind tighter than addition and subtraction, but neither binds tighter than the other, so all mults and divs have to be done left-to-right. It is NOT true that they are "the same" and therefore can be done in either order; multiplication is commutative and associative, division is NOT. The very fact that this example yields a different solution depending on the order in which you do the operations proves that they are NOT the same, you can NOT do them any old way. a*(b*c) = (a*b)*c, but
a/(b/c) != (a/b)/c. Again, if the only operators are * and /, you have to do them left to right. ab / ac = (((a*b)/a)*c).

Note: I'm using / for simple division because I don't know how to make my keyboard produce the --:-- kind of division symbol. You get a different answer, of course, if you assume that / means long-line division like this:

ab
____
cd

because that IS implicitly (a*b) / (c*d).

Using programming languages is bogus. Amen.

The rest of your arguement is not completely sound. (You should still use the damn parenthesis! ab/cd, written like this on a computer for the purpose of educating a forum, could be interpreted as (ab)/(cd) because we dont know if you are really writing

ab
___
cd

Just write d(ab/c). and be done with it.)

The reason people are getting this problem wrong is not because of a Multiplication and Division error, its because people's minds insert parenthesis where there are none, which shows they are subconsciously using the order of operations.

Sigh, kids in grade school in US and Canada are BOTH taught that its:

Parenthesis, Exponents, Multiplication AND Division, Addition AND Subtraction.

or

Brackets, Exponents, Division AND Multiplication, Addition AND Subtraction.

Both Division and Multiplication or Addition and Subtraction can be done in any order, any direction. Again: the only convention is left to right because we read from left to right.

Jeez, you guys don't even remember the quirks of the acroynm correctly.

It is NOT true that they are "the same" and therefore can be done in either order; multiplication is commutative and associative, division is NOT. The very fact that this example yields a different solution depending on the order in which you do the operations proves that they are NOT the same, you can NOT do them any old way. a*(b*c) = (a*b)*c, but
a/(b/c) != (a/b)/c.

You are partially right, and partially wrong.

You have conceptual problems, I suggest a math course at your local college.

You are partially right, and partially wrong.

You have conceptual problems, I suggest a math course at your local college.ooooo, Spanked :spank: You cant be partially right and partially wrong. TF=F. You need to take a logic course (am joking here) Yeah, x and / are the same thing.

We did BODMAS/BOMDAS here in Australia. Brackets, Of, Division, Multiplication, Addition, Subtraction. Some maths professor is going to come in here and say I'm correct.

Go to hell you blokes!! :mdrmed: :mdrmed: :mdrmed:

ooooo, Spanked :spank: You cant be partially right and partially wrong. TF=F. You need to take a logic course (am joking here) Yeah, x and / are the same thing.

<Sigh> I know, any false is totally false. But he was correct in multiplication being more associative than division.

But it is totally and completely fundamentally wrong to think that multiplication and division are not totally and completely compatible with each other.

His example showed that the processes of division and multiplication are different (duh), but they gave no example to the order of operations, other than to say that stuff in parenthesis comes first.

0/3 is zero
3/0 Does not Exist

Show me a Does not Exist in Multiplication please?

Multiplication and Division are indeed different, but the Order of Operations deals with how the operations should relate to each other, and Multiplication and Division are totally and completely related. The same with Addition and Subtraction.

Hi Mrs Gomez here,

You are correct that 3.10/3.2=20 because that is using basic order of operations that you all know and love under different acronyms.
HOWEVER the stated problem was 3a/3b=?
Note: variables a and b have been used. They are functions (ie can be graphed) and hence must be solved prior to applying order of operations. This means once you put in values for a=10 and b=2, you have the problem 30/6 which you all agree is 5.

Hubby got lucky this time, normally he is never right. :wiggle: :wiggle:

Shit....will wonders never cease....

no

Hi Mrs Gomez here,

You are correct that 3.10/3.2=20 because that is using basic order of operations that you all know and love under different acronyms.
HOWEVER the stated problem was 3a/3b=?
Note: variables a and b have been used. They are functions (ie can be graphed) and hence must be solved prior to applying order of operations. This means once you put in values for a=10 and b=2, you have the problem 30/6 which you all agree is 5.

Hubby got lucky this time, normally he is never right. :wiggle: :wiggle:

<Sigh>

Wrong.

sigh, sigh, sigh....


okay, solved for function: 3*10/3*2

Now what? back to square one. You skipped a complete step by just putting up 30/6. And that was precisely the step some were arguing over.

do i need to spell it out????
there are 2 functions. f(a)=3a and f(b)=3b
solve functions you get 30/6=5

that's easy order of operations and substitution the 3a isn't substituted as 3(10) not 3*10, two totally differant expressions..

3(10) / 3(2)

30/6

5

no other answer..

do i need to spell it out????
there are 2 functions. f(a)=3a and f(b)=3b
solve functions you get 30/6=5

For a second I actually believed you...

If you want functions, we can function all right.

Here is the problem in function form:

3*f(a) / 3*f(b)

Given function of f(a)=a
Given function of f(b)=b

a=10
b=2

What you are doing is essentially changing the problem into creating two new variables:

f(a)/f(b)

My world just exploded because of this ambiguity.

Hiya staticlag, Mrs Gomez again,

I maintain f(a)=3a and f(b)=3b

Remember we are doing maths. When we write an equation with a variable it is to represent or model a real life situation.

eg pay is $3/hour. variable a= no.hours worked, f(a)=pay received
and family of 3. variable b=no. meals , f(b)=total no. meals for family
The given equation could model amount money available to be spent per meal.

I haven't changed the problem, it has always been f(a)/f(b).

I believe what you propose is meaningless, so nobody would solve as you suggest.

Though I look forward to reading your examples.

Cheers for now.

It's a trick question, people. The correct answer is 42.

By giving the problem a context you have implied the parenthesis, changing the nature of the problem. As a pure mathematics exercise, the answer is 20. As a real-world scenerio the answer is 5. This is why so many people have trouble with "word problems".

Just like English, the context changes the outcome.

It's 20. I thought it was 5 at first, but since there aren't any parentheses, each operation has to be done in order left to right. Arguing it right now is pointless until Bankotsu clarifies the equation.

i'm gonna agree with mrs. gomez. if it was written 3*a/3*b id agree its 20. But the 3a implies 30 and 3b does imply 6 so the answer has to be 5. Its poorly described.

Nope, sorry. 3a implies 3*a, it's just shorthand.

I had a similar dispute with my 6th grade math teacher, but that was purely syntactical.

"It was Andy's 10th birthday. His uncle offered him a choice between two gifts:

1) 25 dollars for 5 birthdays including this one.
2) Twice his age plus 2 dollars a year for 5 birthdays including this one.

Andy naturally wants the most money from his uncle, so which choice should he make?"

Naturally, being the pretentious asshole I was in 6th grade, I chose number 2. Since my bitch of a math teacher made no indication that his age was a fixed variable. So, I calculated his gift for the next 5 years:

(10x2)+2=22
(11x2)+2=24
(12x2)+2=26
(13x2)+2=28
(14x2)+2=30
$130

vs.

5x25 = $125

She argued that it was actually supposed to be calculated ((10x2)+2)x5=$110, but didn't actually specify that his age was fixed. Since gift was to be paid in installments each year, an 11 year old waffle can figure out that Andy's age changed from year to year and it would affect the equation. She wouldn't budge on the question though and marked off 5 points because of it. I hated her. She wore a lot of eye makeup and looked like a racoon.

Hahaha. Yup. That's the problem with expressing mathematical relationships using the english language - there are too many ambiguities. This is why the answer to the original question is 20. It was given in a purely mathematical context, and should be answered as such.

I hate English. Well, not necessarily the language, but the fact that other people don't use it properly. If you explain things and leave nothing to assumption, it's great. Problems arise when things are left to semantics. Standards are key.

Bankotsu,

Tell whoever gave you this question that BlueEyes says to GO TO HELL!!

Much better :D:

Mrs Gomez is wrong in her thinking.

i think it was in 8th grade algebra, or pre-calculus, either from the textbook or the teacher, that basically says, if you use a scalar in front of a variable (eg 3a), a parenthesis is ASSUMED to wrap around that multiplication, and the order of operation is performed as if there is parenthesis around that value.

at all the higher math levels, it is treated as such :D:

That is why God invented parenthesis. Are atheists poor at math?

you guys are crazy....clearly the ture awnser is ELEVENTEEN

You guys are smart. We were having a debate in our math discussion class.

--------------------------------------------------------------------------------

a = 10, b = 2, 3a ÷ 3b = ?

5 or 20?


Is there suppose to be a variable after the "="? cuz if there is suppose to be one, then the answer is 0, otherwise, I solved it this way.

3a/3b

3(10)/3(2)

30/6

5


Why did I solve it that way. Cuz thats what I was taught. You say I'm wrong. Then blame public education here in California. Which was\is rated one of the stupider states.

ROCK 'N ROLL DUDES!!! :rock:

answer is 20 based on how it's written out, i don't have the time to show a discrete mathematics proof.. But trust me, it's 20.. :)

and for programming languages the way the intpreter reads the language depends on the type of language, whether it's postfix/prefix/infix or something like that.. been awhile since i took my semantics course.

Also WE may read from left to right, but remember, many many other cultures read from right to left


MrJynx

i think it was in 8th grade algebra, or pre-calculus, either from the textbook or the teacher, that basically says, if you use a scalar in front of a variable (eg 3a), a parenthesis is ASSUMED to wrap around that multiplication, and the order of operation is performed as if there is parenthesis around that value.

at all the higher math levels, it is treated as such :D:
I don't think so. If that is the case all the calculators and programing languages I have are doing it wrong.

The key word is still assumed. We shouldn't assume anything. It's all semantics now.

I don't think so. If that is the case all the calculators and programing languages I have are doing it wrong.
Indeed, and in all the higher level math classes I've taken (I was 6 classes shy of getting a BS in Mathematics when I graduated) there were no assumed parenthesis.

well, ok, i guess if it's written left to right, yeah no assumed parenthesis

how about when you write it:

3a
-----
3b

^this has 'assumed' parenthesis then?

That's a different notation. If you were to convert that notation back to standard notation, you would include the parenthesis.

edit:
perhaps I should explain this a bit more. It's not that the parenthesis are assumed, it's that they aren't needed. When using that notation (i believe it's called basic notation, but don't quote me on that) there is a rule that states you must do all operations to the numerator and demoninator seperately, before doing the division operation.

If the original problem was converted to basic(?) notation, it would like like this:


3 * a * b
----
3


Simplified:


3*a*b
------
3


Cancel the threes:

a*b

your answer is 20.

yes

The answer is 4.

20/5 = 4.

The end.

NOW WHERE IS MY COOKIE!@#

What? ... No COOKIE?!@

DEALBREAKER@$^%&

DELABORKER!!@$#%

20

I say 7

lol at least you people aren't calling each other stupid.

It's 5!!!!!!!!!!!!!!!!!!!!!!!11

It's 5 times 4!!!!!

It's G!?!?!?!?!

pi!!!

mmmm pie


:icon_droo

You are partially right, and partially wrong.

You have conceptual problems, I suggest a math course at your local college.

Wow. You're really obnoxious. You must be so proud.

"Questions" like this one cause so many people to learn to hate math, which is such fun when taught right.

Simple fact: 3a is shorthand for (3 x a)
Simple fact: 3b is shorthand for (3 x b)

You can invent all the trick questions you want, but that doesn't mean that there is any validity to the trick. In this case, there is only foolishness and confusion.

5

Should've made a poll :uhh:

These trukey burgers are quite good

You mean Tukey Burgers? They are statistically significant!

These trukey burgers are quite good




You mean Tukey Burgers? They are statistically significant!


Don't you mean terkee. :rollingla