If you love math

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This is a conundrum that comes around every few years as new people are exposed to it.

The discussion is, what is the correct answer to this equation, 8 ÷ 2(2 + 2) = ?

So the old school answer is 1 but “new school” (?) answer can also be 16! This is because of the claim of ambiguity of the expression itself and how computers parse the equation as written.

Here is a link to one discussion. The real fun are the replies below the authors claims. Enjoy!

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I thought the ‘standard’ of equal precedence is ‘left first’. Therefore, 8/2 after (2+2) which becomes 4 * 4 = 16.

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This is where the ambiguity of this whole equation comes in. If it was written 8÷(2(2+2)) then it becomes apparent that the answer is 1. If you adhere to multiplication, division, add then subtract the original equation is still true to equal 1. Unfortunately there are groups that will say because there are no parentheses and therefore not properly grouped you could divide the 8 by 2 and have a result of 16.

If you go to the link and look at the discussion thread, you will see a lot of interesting ways to logically come to one answer or the other.

The two best ones I thought were solving for x and writing it as a ratio.

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My wife, a math PhD who loves math and loves teaching math, turns red with annoyance every time this one comes up.

  1. It’s not math it’s just a convention; the point of math is to be clear not to be obscure.
  2. In general when actual math is involved, if the precedence isn’t obvious, it’s bad math; add parentheses to make it clear. They are cheap.

The answer by established mathematical convention is not ambiguous, but it’s not mathematically important. The fact that (for example) not all calculators follow precedence rules accurately doesn’t rewrite mathematical conventions, it’s just a bug; but it’s also just not very important.

If you love math, add the parentheses. :slight_smile:

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Well said!

Interestingly, if you copy-paste this into a search engine, not only does one get the correct answer, but the rendering of it is updated to have parentheses added so as to make it unambiguous.

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