6÷2(1+2)??

The real reason why I posted was because recently there has been a mathematics question that has been on facebook. It is:

6÷2(1+2)

The two possible answers are 9, or 1. Although I originally thought that it was 1, I have come to realise that it is actually 9. The problem in the question arises because of the ambiguity of the division sign (which no one ever uses) and the implied multiplication sign between the 2 and (1+2). It is well known that by BIDMAS, division and multiplication have the same priority and should be done left to right and hence the question should be worked out like this:

6÷2(1+2)

6÷2(3)

3(3)

9

However the problem arises with the lack of multiplication sign causing people to think that the 2(1+2) should be treated as a single entity:

6÷2(1+2)

6÷(2+4)

6÷6

1

Although I originally agreed with this, I realised that just because there is no multiplication sign present and the multiplication is implied, the expression 2(1+2) cannot be treated as a single entity because if it was then

2(1+2)² would be equal to (2(1+2))²

Which is complete nonsense.



THEREFORE,



6÷2(1+2) ≡ 9 QED

Ok maybe the use of QED was unwarranted but I felt like using it.

This was originally written by Matt

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