6÷2(1+2)=?

4xyz ÷ 2xz = 2y

Why is it when people use numbers, they use a different rule set than algebra?

6 ÷ 2x = 3/x
Let x = 2+1
6 ÷ 2(2+1) = 3/(2+1)

Anyone with a solid mathematical background will know the importance of factorizing.
In this particular instance, a 2 was factored from 2 terms inside the parentheses.
It is illegal to use this 2 as an operand on its own without restoring it to the other terms first.
This is why the P in your pemdas, is first. The parentheses must be "solved" first, ie,
evaluated fully and properly.
This would be coincidental with the distributive property. 2(2+1) = [2(2) + 2(1)]
What people fail to understand is what properties ARE in maths.
They are equality statements, which means you replace expression A with expression B
in a larger expression or equation and STILL GET THE SAME SOLUTION.
a(b + c) = (ab + ac)
Here, a = b = 2, and c = 1.
I have seen people try to argue that a = 6/2.
If that were the case, the expression would then look like (6/2)(2+1).
This is not how the original equation looks, however.
I have been asked, "Why did you choose to use distributive property when you can
solve what is inside parentheses without it"? What? Really?
That is a "justification" for your incorrect answer?? The justification is quite opposite
in that you are getting a different answer without it, which means THAT solution is wrong.
Properties are there for proofs, and to make solutions "more apparant" if there is confusion.
This is exactly what the distributive property does in this case: It removes the so-called "ambiguity".
There is no ambiguity here, only a right and wrong answer.
6 ÷ 6 = 6 ÷ (4+2) = 6 ÷ 2(2+1)
and..
6 + 3 = (6/2)2 + (6/2)1 = (6/2)(2+1)

reply to post by Itop1


I live in The Netherlands (Europe) and overhere we have the same outcome.....1.

There are cardinal rules to obey in such situations....

These rules are made because otherwise there will be a communication breakdown....

Algebra and such should be considered a language...For example; if you order a bread you do not want to receive a patato.....

reply to post by Itop1


9

A pox to whomever bumped this thread, now I won't sleep tonight.

Please
Excuse
My
Dear
Aunt
Sally

6/2(1+2)=6/2x3=3x3=9

Its basic mathematical Order of Operations that I learned in 7th grade Pre algebra. The confusion is in what order to do the multiplication and division, in all algebraic equations you perform division and multiplication in the order in which the equation is written.

Therefore you would first perform the action of the parenthesis (1+2), the sum of which is 3. So therefore we are left with 6/2x3, so by following the proper Order of Operations and working from left to right we are left with 3x3=9.

In order for the equation to equal 1 it would need to be written as follows, 6/[2(1+2)]=?

BIMDAS

its 9.

division DOES come after multiplication thats true.. BUT indicies come before the both of them!

6÷2(1+2)=?

TWENTY-SEVEN PAGES FOR THIS??? Are you people insane!

The answer is NINE. Now go to bed!

reply to post by ASeeker343


If you multiply before you divide then the answer is clearly 1.

6÷2(1+2)

6÷2(3)

That's one step, you still with me?
Now let's multiply 2 x 3 as the problem now states, "Six divided by two times three".
According to your logic, we should multiply first, correct?

6÷2(3)
2(3) = 6

6÷6 = 1

However, if you look at the problem like this, 6/2(2+1), you could reduce the fraction of 6/2 to 3, and then multpily 3(2+1), which would give you 9. However this is incorrect because multiplication precedes division every time. So the answer is 1.

The real answer is that the problem is written ambiguously and incorrectly (without the appropriate brackets), and that is why you will get two different answers. If it is written in modern notation, no such conflict. Without the real world context for the problem, you can't do a logic check either.

If you follow PEMDAS or BEMDAS to the letter, you will get 9.

If you follow PEMDAS or BEMDAS and also apply multiplication by juxtaposition (as you normally would have during the same time as that divide symbol was generally used), you will get 1.

reply to post by Kody27

However this is incorrect because multiplication precedes division every time.

Not it does not. If there is a contradiction, then It's always left to right, multiplication and division are equal. But this question is too vague, it needs more brackets, if not either answer is correct.

Originally posted by luciddream
reply to post by Kody27

 

However this is incorrect because multiplication precedes division every time.

Not it does not. If there is a contradiction, then It's always left to right, multiplication and division are equal. But this question is too vague, it needs more brackets, if not either answer is correct.

edit on 5/31/2013 by luciddream because: (no reason given)

Yes you are right, I stand corrected. Multiplication does not precede division, nor does division precede multiplication unless it comes first chronologically in the equation because both operations are on the same plane. The answer has to be 9.

RE-POST:

4xyz ÷ 2xz = 2y

Why is it when people use numbers, they use a different rule set than algebra?

6 ÷ 2x = 3/x
Let x = 2+1
6 ÷ 2(2+1) = 3/(2+1)

Anyone with a solid mathematical background will know the importance of factorizing.
In this particular instance, a 2 was factored from 2 terms inside the parentheses.
It is illegal to use this 2 as an operand on its own without restoring it to the other terms first.
This is why the P in your pemdas, is first. The parentheses must be "solved" first, ie,
evaluated fully and properly.
This would be coincidental with the distributive property. 2(2+1) = [2(2) + 2(1)]
What people fail to understand is what properties ARE in maths.
They are equality statements, which means you replace expression A with expression B
in a larger expression or equation and STILL GET THE SAME SOLUTION.
a(b + c) = (ab + ac)
Here, a = b = 2, and c = 1.
I have seen people try to argue that a = 6/2.
If that were the case, the expression would then look like (6/2)(2+1).
This is not how the original equation looks, however.
I have been asked, "Why did you choose to use distributive property when you can
solve what is inside parentheses without it"? What? Really?
That is a "justification" for your incorrect answer?? The justification is quite opposite
in that you are getting a different answer without it, which means THAT solution is wrong.
Properties are there for proofs, and to make solutions "more apparant" if there is confusion.
This is exactly what the distributive property does in this case: It removes the so-called "ambiguity".
There is no ambiguity here, only a right and wrong answer.
6 ÷ 6 = 6 ÷ (4+2) = 6 ÷ 2(2+1)
and..
6 + 3 = (6/2)2 + (6/2)1 = (6/2)(2+1)

Originally posted by _BoneZ_

Originally posted by Itop1
already half of you put 9 and half of you put 1, so which is it, 1 or 9?

The answer is 9. Use my method above:

Please Excuse My Dear Aunt Sally

Please -- Parenthesis
Excuse -- Exponents
My ------- Multiplication
Dear ----- Division
Aunt ----- Addition
Sally ----- Subtraction


6÷2(1+2)=

You do the Parenthesis first, so

6÷2(3)

There are no Exponents or Multiplication just yet, so 6÷2=3:

3(3)

The above is the same as 3x3, which = 9.

Your answer is 9.

In the equations the parenthesis denote a multiplication and not an exponent, therefore you go from left to right after adding what is inside the parenthesis.

6/2*(1+2) = 6/2(1+2)
6/2*(3)
3*(3)
9

Originally posted by mathman26
RE-POST:

4xyz ÷ 2xz = 2y

Why is it when people use numbers, they use a different rule set than algebra?

6 ÷ 2x = 3/x
Let x = 2+1
6 ÷ 2(2+1) = 3/(2+1)

Anyone with a solid mathematical background will know the importance of factorizing.
In this particular instance, a 2 was factored from 2 terms inside the parentheses.
It is illegal to use this 2 as an operand on its own without restoring it to the other terms first.
This is why the P in your pemdas, is first. The parentheses must be "solved" first, ie,
evaluated fully and properly.
This would be coincidental with the distributive property. 2(2+1) = [2(2) + 2(1)]
What people fail to understand is what properties ARE in maths.
They are equality statements, which means you replace expression A with expression B
in a larger expression or equation and STILL GET THE SAME SOLUTION.
a(b + c) = (ab + ac)
Here, a = b = 2, and c = 1.
I have seen people try to argue that a = 6/2.
If that were the case, the expression would then look like (6/2)(2+1).
This is not how the original equation looks, however.
I have been asked, "Why did you choose to use distributive property when you can
solve what is inside parentheses without it"? What? Really?
That is a "justification" for your incorrect answer?? The justification is quite opposite
in that you are getting a different answer without it, which means THAT solution is wrong.
Properties are there for proofs, and to make solutions "more apparant" if there is confusion.
This is exactly what the distributive property does in this case: It removes the so-called "ambiguity".
There is no ambiguity here, only a right and wrong answer.
6 ÷ 6 = 6 ÷ (4+2) = 6 ÷ 2(2+1)
and..
6 + 3 = (6/2)2 + (6/2)1 = (6/2)(2+1)

However you are right using the algebraic philosophy based on the way the question is written. It could also be written like this.

6 /2(x) = 6/2(1+2)
6 / 2*3
6/6
1

Looking at this problem using algebraic method the answer is 1.


In the equations the parenthesis denote a multiplication and not an exponent, therefore you go from left to right after adding what is inside the parenthesis.

6/2*(1+2) = 6/2(1+2)
6/2*(3)
3*(3)
9

Solving by using simple arithmatic the answer is 9.

I submit that both answers are correct. Simply because the way the problem was written it can be perceived either way. Although I would agree the algebraic argument is stronger than using simple arithmetic. I believe a teacher would have to accept both as correct.

Originally posted by sacgamer25
However you are right using the algebraic philosophy based on the way the question is written. It could also be written like this.

6 /2(x) = 6/2(1+2)
6 / 2*3
6/6
1

Looking at this problem using algebraic method the answer is 1.


In the equations the parenthesis denote a multiplication and not an exponent, therefore you go from left to right after adding what is inside the parenthesis.

6/2*(1+2) = 6/2(1+2)
6/2*(3)
3*(3)
9

Solving by using simple arithmatic the answer is 9.

I submit that both answers are correct. Simply because the way the problem was written it can be perceived either way. Although I would agree the algebraic argument is stronger than using simple arithmetic. I believe a teacher would have to accept both as correct.

edit on 6-6-2013 by sacgamer25 because: (no reason given)

A slight problem with your notation. 2x, where x = 2+1 is 2(2+1). The rule when substituting is to include parentheses around the substituted value(s). When you do the reverse, you eliminate them, ie, if we have 2(2+1), and we let x = 2+1, then we have 2x, not 2(x). It is a small technicality, I know. Regardless, a(b+c) = (ab + ac).
This is a math property. Math properties are ALWAYS EQUAL. I cannot stress this enough. All proofs are based on this understanding. If c = 0, this property is still the same: a(b+c) = (ab + ac), and if c=0, then a(b) = (ab). One can then say (ab) = (a * b). Therefore, a(b) = (ab) = (a * b) = ab.
This is in line with the theory behind 2 things:
1 - factors. A factor of a set of terms cannot be used as an operand without the terms it was factored from.
2 - Coefficients: Coefficients and literals are commutative, eg, if we have 2xyz, then 2xy are coefficients of z, and 2xz are coefficients of y, etc... This is why 4x⁴y²z³ ÷ 2x²yz = 2x²yz². No matter how you rearrange the 2nd operand's coefficients, that being 2x²yz, you get the same solution. Using "simple" math as you put it, would incorrectly state that there in fact several operators all separated by multiplcation signs. This is a problem with most of the people who firmly believe this answer is 9. They think that 2x = 2 * x. Well, of course it does... IN THIS CASE. We cannot blindly go substituting this in a bunch of expressions. 2x = (2 * x) in ALL cases. This is because if you make substitutions in maths/algebra, you must contain the substituted expression in parentheses. 2x is a simplistic way of writing x + x, which is (x+x).
Because the obelus is not used often in math/algebra/calculus, there are not a lot of references online... however...that doesn't mean there are none. Here are a few which show examples of inline division with multiple coefficients and literals. Not one explains that 6x ÷ 2x = 6x ÷ 2 * x, because it is wrong:

cstl.syr.edu...
www.wisc-online.com... (Slide 4)
www.math-mate.com... (This whole page is good, especially the notes on factorizing and expanding parentheses)

I am also not sure where everyone was taught "parentheses denote multiplication". Parentheses are a grouping symbol. A coefficient of a parenthetical group is a factor of the terms inside the group. It isn't "simply multiplication". Maybe for gradeschool students...

Final note: What is a ÷ a? and what is 1a ÷ 1a ?

Originally posted by Itop1
Once and for all i want to know the real answe to this equation...

is it 1 or 9?

Hope somebody here knows their maths

Is it because of math problems like this why there is no Nobel Prize for mathematics..?

6÷2(1+2)=?

I'm wondering why people are implying that the 2 is an exponent and therefore causing the equation to read as if it were a fraction because they're implying that the 2 then must be calculated before the 6 ??


You are forcing a fraction bar (between the 6 and 2) by implication.

This is an illegal mathematical move...



The order of operation is:

Parenthesis first = 3
At least everyone agrees on that part.

That parenthesis is now in its simplest form (3), therefore the rest of the equation falls under the rule of "order of operation".

Order of operation is solving left to right AFTER all parenthesis and exponents have been resolved down to their simplest form... reading it EXACTLY as it is written and solving the equation from left to right.



So basically, we are now looking at the equation as if each number is in it's own parenthesis: (6) ÷ (2) x (3)

Multiplication and division are on equal ground, there is NO rule stating that multiplication always comes before division or vice versa. Thus, it MUST be calculated by order of operation: left to right.



Implying that juxtaposition and/or distribution plays into this is an illegal math assumption.

Using the symbol "/" to replace the "÷" is what's caused this debate (and the equation) to become ambiguous. The symbol "/" can mean "to divide by" OR it could mean a fraction bar.

But the equation is written as: 6÷2(1+2)
NOT 6/2(1+2)

Using the "/" symbol would be the only way you could come up with an answer of 1...

It is important to note: The "÷" symbol is used. It CANNOT be changed to mean a fraction bar "/" because that would change the order of operations and therefore causing the ambiguity problem

The equation is NOT written that way.



Therefore getting rid of all implication and assumption, and thus the ambiguity...

The correct answer is 9.

reply to post by CranialSponge


that it is, I just dont want to be thinking about that math problem all day again.