Math: 6÷2(1+2) = ?

My 4 year old can type 9 and call people morons. Back it up with something. Read THIS for example:

Distribute 2 into the parentheses. Why? because it is a factor of the original terms INSIDE them, and cannot be ripped apart. I will show you why:
6 = 4+2 = 2(2+1) = 2(3) The 2 is a common factor of 4 & 2.
No matter which way you view it, the value 6 MUST maintain its value. Just as you cannot take the 4 from (4+2) and divide it into a number with the "+ 2". I cannot take the 2 from 2(2+1) and divide it into another number without the (2+1).
You ARE allowed to distribute before division, or any other operator, since you are allowed to simplify any equation first. There are MANY references which state "Remove parentheses by distribution" Try Googling that as a search term.
6÷2(2+1) = 6÷(4+2) = 1
Now, some people have argued that you don't NEED to distribute the 2; you just add the 2+1, and end up with 2(3). Then they go on the say that this is the same as 2*(3). WRONG! You STILL have parentheses and STILL need to distribute that 2 inside them, for the reasons discussed about factoring above. Therefore you have this:
6÷2(3) and must distribute like this:
6÷2(3+0) = 6÷[2(3) + 2(0)] = 6÷6 = 1
These people who get 9 try and rip the 2 away from the parentheses by inserting a times symbol like this:
6÷2*(3), and then do the division of 6÷2 first. I explained the illegalities of doing this, since the 2 is a factor of the 2+1.
Lastly, 6÷2 is NOT (6/2), as in (6/2)(2+1). This is totally incorrect, since it lacks that parentheses in the original equation. Check any online or written text. Leading fractions as a coefficient ALWAYS have ( ) around them.
I hope this clears things up.
Regards.

If you think the equation should = 9 then it should look like this:

(6/2)(1+2)=

3*3 =9

but we have:

6/2(1+2)=

6/6 =1

because you do the sum in the bracket first.

So the answer is 1.

Mensa posted this on their FB page about a week ago. I can only assume someone has answered it already but I'll give it a go.

6÷2(1+2) = ?
3(1+2) = ?
3(3) = 9

Order of operations are a grade 9 level understanding of math.

Correct.

If you think it is NOT 1, PROVE OTHERWISE. Prove that property of distribution is WRONG. Prove that fractions as coefficients do not require ( ).

Because that is what it means.

2(1+2) = 2 x (1+2)

Parentheses are FIRST in the order of operations, not DIVISION, so if you want to distribute, you do that first!

Then you have:

6 ÷ 2 x (1+2)

= 6 ÷ 2 x 3

= 3 x 3

= 9

Then you have:

6 ÷ 2 x (1+2)

= 6 ÷ 2 x 3

= 3 x 3

= 9

Casio says 1, en Texas Instruments says 9.

It is nine.

That's just 3 because 1 +2 1 +2 brackets.
So we have:

6 ÷ 2 x 3

Multiplication and division is on a par in terms of priority calculations, because a division does not actually exist: a division by two is a multiplication by 1/2. A multiplication therefore has no priority for a division, as this is the case at a summation. 2 + 3 X 5 = 17.

Given multiplication and division rank equally, they are just left to right.
So first 6/2 gives 3 times 3 is 9 and that
In order to get to 1 you should depart from that rule and that can only by EXTRA parentheses to insert:

6 ÷ (2 x 3)

as one would give.

Casio says 1, en Texas Instruments says 9.

It is nine.

That's just 3 because 1 +2 1 +2 brackets.
So we have:

6 ÷ 2 x 3

Multiplication and division is on a par in terms of priority calculations, because a division does not actually exist: a division by two is a multiplication by 1/2. A multiplication therefore has no priority for a division, as this is the case at a summation. 2 + 3 X 5 = 17.

Given multiplication and division rank equally, they are just left to right.
So first 6/2 gives 3 times 3 is 9 and that
In order to get to 1 you should depart from that rule and that can only by EXTRA parentheses to insert:

6 ÷ (2 x 3)

as one would give.

parentheses first, then solve left to right...

9