Math: 6÷2(1+2) = ?

The "dropping symbol between" Law. I cannot argue with you since it is not socially unacceptable to do so with someone who is "special"

Last Edited by caper_26 on 01/23/2013 04:03 AM

(6)/(2)*(1+2)

Add 2 to 1 to get 3.
(6)/(2)*(3)

Reduce the expression (6(3))/(2) by removing a factor of 2 from the numerator and denominator.
3(3)

Multiply 3 by each term inside the parentheses.

=9

You separated the (2+1) from the denominator.

Here is how to rewrite the problem properly when the obelus is used. Notice how they don't change 2x into 2 * x and then use only the 2 for the divisor??

[link to i47.tinypic.com]

ref: [link to go.hrw.com]

The 9ers somewhat understand the order of operations, but it is the algebra that is killing them in the end

You are incorrect.
The answer is still 9, even with the distributive property being, needlessly, applied.

If you have 4x(2y+3) you get 8xy + 12x Right?

That's because when you parse these units you don't just distribute the x by it's self you also distribute the 4 along with it.

4x = 4*x multiplication is of equal value of to division so rules are applied to them equally.

So like how both the x and the 4 are distributed the 2 and the 6 are distributed in the equation 6÷2(1+2).

And there for you end up with 6÷2*1 + 6÷2*2 = 9.

This is a needless way of solving the equation because it has no variables and therefore can be solved simply with pemdas which gives you the same answer yet again.

Thank you. 1.

If you're using a sci calculator, you have to separate the 6 from everything else, or it does not follow the parenthesis order.... otherwise it will think the 6 should be divided by 2 first, because there are no parameters in multiply/divide going from left to right. The operator needs to understand this. Thanks.

NINE!!!!!

9.

With distributive property properly applied.

6÷2*1+6÷2*2= still equals 9.

With basic pemdas application.

step one "P"
(1+2) = 3.

step two. From left to right solve any multiplication or division equations. Again from Left to Right.

so 6÷2*3 = 9 (Still)

Notice how the distributive property is not needed to reach the same absolute answer of 9, but even when applied you still get 9.

So 9. thank you basic arithmetic and algebra. =]

Last Edited by Zinthaniel on 03/05/2013 05:22 PM

If you substitute the plus sign with a multiply, in the parenthesis, what do you get then? Parenthesis are there to determine order.

6

A different answer obviously, but I don't get your point.

With the distributive property used even with pemdas used in conjunction you still get 9.

6÷2(1+2)
1: "P"

1+2=3 you can choose to leave the 3 in the parentheses if you so choose, but this is not necessary because the parentheses are not relevant at this point. But if you do then you have this.

6÷2(3) Now to distribute, if we must, but why?

anyways at this point since only 3 remains in the parentheses we get this

6÷2*3.

guess what it still equals 9.

Last Edited by Zinthaniel on 03/05/2013 05:36 PM

Then what is this:
(6)/2(1*2)
thought so. thanks.

The parentheses around the six alone means nothing. All you did is parenthesize a whole number that is already at it's simplest form.

So the answer is.

1*2 = 2

now we have 6/2*2= 6

Ok, maybe it's cause of my public education, but I'm going to try to explain what I've learned, and I know it's probably somewhere in the last hundred pages or so, but can you please explain the following:


6/2(1a+2a)= ?
when a=1

(6)/2(1a+2a)=?
when a=1


6/2(1a+2a)=?
when a=2

(6)/2(1a+2a)=?
when a=2

Under your theory, these should all be the same, yes?

SO, is there any difference between this:
6/2(1+2)

and this?
6/(2+(1+2))

Ok.

well If I know the variables value then there is no need for the variable to be in there because I can simply replace it with it's value. So your equations look like this.

6/2(1*1+2*1) At this point Pemdas is applied at the answer is discover through simple arithmetic.

Without knowledge of the values of your variable then the distributive property is applied.

so:
6/2(1a+2a) Well one the parentheses can be simplified to 3a squared. Then you can do 6/2*3a squared or 3*3a squared.

Yes there is. Parentheses do in fact denote the order in which the equation is solved. The inner most parentheses comes first. so in this case it is.

1+2 = 3*2 = 6 and then 6/6 = 1

Yup.

Nope and nope again.

Keep trying...

It may sink in one day...

=] Try what? You're buddy is referencing the distributive property? yes I can see that.

He is now asserting that the use of the distributive property demands that the answer be 1. But that is incorrect.

In a common binomial or polynomial equation the distributive property is most commonly used because it's usually the only time is makes since to even bother with it.

so we have an equation that looks like this.

4x(3xy-7)

No as I'm sure we all know when we parse the units we are not going to isolate the x and distribute it by it's self. It's get distributed along with it's buddy 4. So we end up with this.

12x squared*y - 28x =

This same distributive property application is applied to division as well.

So we have:

6÷2(1+2)

if you are going to use the distributive property, which is not necessary, it looks like this.

6÷2*1+6÷2*2=9

The answer is still and will always be 9. =]

You're friend is half right when enforcing this tedious and not required rule on this basic arithmetic equation, only he forgets the 6÷2 are unit together so they have to be distributed together.

See, I was taught, and succeeded in algebra (their method anyway), that anything adjacent to the parenthesis equation is performed first, before the others, regardless of left to right. I don't think it has anything to do with our English form of the left to right interpretation, however I got a business degree that is absolutely worthless, so what do I know.. hehe.

The common problem people are overlooking is brackets, or lack of brackets.

6 divided by [2(1+2)] = 1

6 divided by 2 times (1+2) = 9

So since the problem, lacks or doesn't specify brackets, the answer is 9.

Well technically you could do it that way, but the problem is you are isolating the 2 when, in fact, the 6÷2 is a whole unite that needs to be distributed.

Technically distributive property can be used in basic arithmetic but there is not point since you are dealing with whole numbers at their simplest form and can be solved with out the use of that property.

So yes you are right, but you are applying it wrong.

6÷2 is what is directly adjacent to the parentheses and therefore is what needs to be distributed and therefore making you way of being taught still valid.

I don't think this is correct man. Why are you carrying the 6 into the equation that should be left for only the 2? Damn, I came here to see the article about the unnecessary drones flying over us, and I've now wasted 20 mins debating a plus b equals c. gotta love glp.

7

You don't leave the six out. You are isolating the 2, but that's not possible.

For instance when using the distributive property when it would be most useful would be in polynomial and binomial equations. They have variables.

4x(x+xy)

as we all know 4x= 4*x
but you don't isolate the x and then distribute it by it's self like this:

4(x squared + x squared*y)
you always keep the 4 and the x together.

this also applies to division.
so 4/x(x+xy) = 4/x squared + 4/x squared *y)

that is how it has always been done. Check any distributive property article explaining it function and application.

you can not isolate the 2.
the 2 in this instants it equivalent to and is acting as the x in any binomial or polynomial equation. In which the x is never separated when distributed unless it is explicitly alone.

Don't believe me check his links:


Notice the x is not be distributed alone, it's not being isolated in the way everyone seems to be isolating the 2 in this instance, it's numerical partner is coming along for the ride.
Why would this rule suddenly be dropped in this equation? The 6 has to be distributed along with the 2. So the when done correctly it looks like such:

6÷2*1+6÷2*2=9

I did say to keep trying...