8 ÷ 2(2+2) = ?

[Swirls]

PLEASE EXCUSE MY DEAR AUNT SALLY

Bingo.

[CardsofSTL]

[Arthur Dent]

Parentheses first then work left to right. The answer is 16.

Parenthesis first means getting rid of 2(4) first and that gets you to 1 and that leads me to my original answer: blue and black.

Parentheses first means you evaluate what’s inside the parenthesis first. It says nothing about how to evaluate operations on that result.

The problem here is in syntax ambiguity and the fact that complex expressions should never be written with the ÷ symbol.

A computer will expand this as:
8 ÷ 2(2+2) = 8 / 2 * (2+2)
Parenthesis first:
= 8 / 2 * 4
Left to right:
= 4 * 4 = 16

Humans will tend to see the implicit multiplication against the parentheses as implying it has a higher precedence in order of operations, but there’s no formal rule stating that. So:

8 ÷ 2(2+2) = 8 / (2*(4)) = 8/8 = 1

The correct choice is to write division as a fraction and/or add extra parentheses for clarity rather than relying on legal rulings about order of operations.

[AWvsCBsteeeerike3]

The correct choice is to write division as a fraction and/or add extra parentheses for clarity rather than relying on legal rulings about order of operations.

Obviously, but that wouldn't get the internet all up in a tizzy now, would it? Hence it being asked this way.

I'm pretty sure there was almost an identical problem posted like 10 years ago: 6÷3(1+1) iirc and everyone had the same conversation.

[Michael]

I knew it was 16 or 1, but I voted 16. I'm dumb.

As AD notes, math equations shouldn't be written this way.

[Jocephus]

i would have picked 1

[G. Keenan]

It's 1.

Real humans support implicit multiplication.

[wart57]

My question is... why the [expletive] do we need to know the answer to that [expletive] question? Where in life could that equation actually be used?

[expletive]!

[33anda3rd]

If

8 ÷ 2(2+2)

gets us to

8 ÷ 2(4)

then is that or is that not also:

8 / 2(4)

which is also:

8
-----
2(4)

which is 1

?

[Arthur Dent]

8 / 2(4)

which is also:

8
-----
2(4)

Those two expressions are not the same. In the second, you've assumed an additional set of parenthesis are implicit i.e:
8 / 2(4) = 8 / (2(4))

Try writing the same expression with an explicit multiplication operator instead
8 / 2(4) = 8 / 2 * (4)

and suddenly you don't feel the need to do 2*4 before 8/2. I think without the explicit operator, the multiplication feels like it is closely coupling 2 * 4, so you should do it first, but again, there is no actual rule about that.

In fact, the notation is confusing because it is mixing styles together. If you were writing with pen and paper or a fancy equation editor you'd do either:

Code: Select all

  8        8
----- or ----- (4)
 2(4)      2

In a basic text editor like for programming you'd write:
8/(2*4) or 8/2*4

In both cases, the interpretation is clear, but mixing these styles together leads to confusion, which is the point of this trick.