6÷2(1+2)=? correctly explained.

I explain the wrong answer, the correct answer obtained the wrong way and the correct answer obtained the correct way. Enjoy!

[lammy]

Ok confused people…let me try to explain why the correct answer for 6 ÷ 2(1+2) =? is 1

Consider this:
x = 6 y = 2(1+2)
x ÷ y = ?
Solve for y first:
y = 2(3)
y = 6

Now insert values in the equation x ÷ y = ?
6 ÷ 6 = ?
Answer is 1.
As many have said (and the author as well), the implied multiplication between the 2 and the brackets has to be done first as it is all part of the only term on the right side of the division sign.


The only way the answer would be 9 is if the original problem was written as:
6 ÷ 2 × (1 + 2) = ? <notice the actual multiplication sign between the 2 and the open bracket

Conclusion:
6 ÷ 2(1+2) = 1
6 ÷ 2 × (1+2) = 9

[lswote]

Both ways of coming to different answers can be reasonably argued but the expression 6÷2(1+2) couldn't be programmed into a computer as such. At least not with most modern programming languages. You would have to explicitly put a multiplication symbol in the expression or it would give a run-error as the expression is incorrect. So really this problem breaks down to what do you mean by the expression and how would you modify it if you had to run it on a computer.

The simplest modification to make it run on most C based programming languages would be 6/2*(1+2) where the slash is used instead of ÷ and asterisk is used for multiply. The expression written that way would be equal to 9. If you wanted to take the distributive property into account the expression would have to be written with explicit parentheses, 6/(2*(1+2)) which would be equal to 1.

[ericvega]

the correct answer is 1 .any number next to a parenthesis is solve together by multiplication.you can not solve this separate one from the other ex: x(5) you have to multiply first x by 5 to get 5x now 5x becomes one entity forever from that point on 5x is always solve together say 3÷5x is equal to 3 / 5x or 3 over 5x.. it will never be 3÷5 * x never

[slayerzhunter]

*I strongly agree that the answer is 1.* no more debate, BODMAS or PEMDAS are rules that teachers use to teach students. When you growing up and doing research, you should be able to identify the priority of each operation.

[yuma]

At last mathematics is just a language where you must declare and define at first the noation and convention of used rulesets before you work with it.

[ALaModePi]

The real problem is that math is an abstraction, but math is only used in the classroom as an abstraction. To clarify, math is a way of modeling a real-world situation using a syntax that can be manipulated to come to a solution. However, the real-world aspects of the problem will tell you exactly whether the equation should be written 6/2*(2+1) or 6/(2*(2+1)). If you understand the situation, you'll know which equation to use.
You're right to point out the correct way to solve this problem as written (and as every science text book I could find says is the correct way to solve the problem), however, I can't help think that the whole reason for the controversy is that we simply don't have the context of the equation.

[brucesmith]

the 2(1+2) is like a function. If I wrote this like a computer function, the 2(3) would be performed first. It is valuable to have such ability to override the order of operation.
Almost Orwellian, to say otherwise. The answer is 1.

2*(1+2) is not same as 2(1+2). in 2(1+2) the ( )s serve as a function. In 2*(1+2), the ( )s serve to group operations.

To solve this use Keneth Iversons APL.

[rampakeshbharat]

You're the only one I've seen that understands why so many fail this problem. 2x means 2 lots of x, 2(a + b) means 2 lots of (a + b), you can't separate the number of a term from the term itself, and why so many fail this problem, as they say cream always rises to to top...

[aeromodeller]

By using the distributive property, you are simply doing the multiplication prior to the division. You have not justified that choice. You have also failed to complete the operations within the parenthesis first, as required. You have missed the whole point of the problem, which is, which do you do first, the division or the multiplication? And why?

[flashgordon]

At 6:38, the term you want to use is: Juxtaposed implicit multiplication

[chilewong]

(9a² ÷ 3) × a = (9a² / 3) × a = 3a³
9a² ÷ (3a) = 9a² / (3a) = 3a³

But 9a² ÷ 3a is not as same as 9a²/3a

÷ means right product of 3a Solve the first or Vinculum 3a (÷ can be a Vinculum Bar!!!!)
It will be 9a² ÷ 3a =9a² ÷ (3a) = 9a² / (3a) = 3a

Solutions:

9a²
= 3a
3a

9a²/3a = 9 × (a²/3) × a = 3a² × a = 3a³
9a²/3 is the Factor of a
9a²/3 is Coefficient and the Fraction Bar

It can be Written as (9a²/3)a = 3a³

9a²
a = 3a³
3

Atheism, If you read this
I hope Many People know 6/2(1+2) is a Fractional Expression to be handled (Functionally) difference from 6 ÷ 2(1+2)
6 ÷ 2(a+b) to be handled from and end up with 6 ÷ (2a + 2b)
Share it to many friends to know that!!!!

[doughendrie]

If we just use the rules of algebra and transposition, what we do to one side of the equation we do to the other side.
6/2(1+2)=1 there’s only one explicit operation, the division, se we divide both sides by 2(1+2) to give
6=1*2(1+2) simplify both sides
6=1*(2+4) simplify both sides
6=1*6 and
6/6=1 proven

[samuelbroncek]

I guess I'm a bit late to the party but here we go.
The mistake you did was assuming it is 6/(2(1+2))
But it's not and then you have to start at the left side as division isn't commutative
So first you should the correct answer goes as follows
6/2(1+2)=
=(6/2)(1+2)=
=3(1+2)=
=(3+6)=
=9
You might also know that division is just disguised multiplication
So
6/2=
=6*(1/2)=
=6*0, 5
In that case you get
6*0, 5*(1+2)=
=9 all the time as multiplication is commutative.
PS. Sorry for repeating some things from the video. I just copy pasted a comment I shared elsewhere and guessed Noone is gonna read this so didn't bother changing it.

[johnsciara]

For some people who would agree with you when using a variable "y" for some reason once you put a number in as the term replacing the variable, they then follow a different set of rules and will argue that the two are not the same thing.

[jared]

This argument is so useless, the question is ambiguous and only exploits the fact that there are two beliefs.
Is 2(1+2) = 1*(2*(1+2)) or is (1+2) a complete whole factor on its own basically (2/1)*((1+2)/1) forget the 6 and the division for a second. It is like if there were something, some random drawing that looks like half horse and half cow. Half of us are calling it a cow and half of us are calling it a horse but it is just an ambiguous drawing. Now if the artist labelled it saying it is a horse or this is a cow then an authority would of settled it.
If the equation were showing us what is on the other side of equal sign then there would be no ambiguity of how the question should be interpreted, but there is not so it is ambiguous and a pointless argument.

[chrisjackson]

The part of the problem 2(1+2) has to be worked out first. That's why P is at the top of PEMDAS and there is a distributive property of math. All the work has to be done to satisfy the parentheses portion. If you want to work it out as (2x1) + (2x2) or as 2(3), both are fine as long as you continue to follow the order of operations. Either way you want to work it, you satisfy the parentheses first. That answer is 6. Then do the remaining part of the problem. 6/6 = 1

[ProtonStalker]

I'm curious for those who say this problems answer 9, please show me where I'm going wrong here:
9 = 9
36 / 4 = 9
36 / (2+2) = 9
36 / 2(1+1) = 9
36 / 2 x (1+1) = 9
18 x (1+1) = 9
18 x 2 = 9
36 = 9 ?

[Madvin]

I totally disagree with your answer... distribution is not an operator, a(b+c) is just a simplification of notation for a multiplication and so is the same than a*(b+c). At 5:36, you write 6 / (3y) = 6 / 3y = 6 / 3 * y : this is wrong ! 6 / (3y) = 6 / (y*3) = 6 / y * 3, so 6 / 3 * y = 6 / y * 3 ?? Nope ! The answer 9 is the correct one !

[FirstnameLastname-nkfl]

Yes you do have to follow the law of distribution, but first you have to read the law of distribution. When you do, you'll see that the law of distribution does not say that a(b+c) = (a(b+c)). That fact is so vital I'll repeat it. The law of distribution has no provision that says that a(b+c) = (a(b+c)). And if it's not there, you can't just assume it's there; that's not how math works. So, like it or not, d/a(b+c) = (d/a)(b)+(d/a)(c) ≠ d/((a)(b)+(a)(c)).

[larryscott]

The reason (imo) that “9” answer is so heavily advocated for is they seem to think Excel rules trump. And Excel needs explicit help with coefficients.

2(1+2) is a monomial. A forgotten piece of mathematics. As is 2(3) as is 3y.

And no doubt 6 / 2(1+2) = 1,
but in Excel one has to enter:
6 / (2(1+2)) which = 1.

Excel is not the ‘new’ math just because it’s software and different softwares have different rules.