This might be a pretty stupid question, but the following was asked in a german quiz show:

"How much is two times two plus two divided by two minus two?"

My question now is, is there any literature, if the rule multiplication and division first, then addition and subtraction does also apply in a formula written in words. Even i was unsure if i was meant to calculate $$ (2 \cdot 2)+(2/2)-2 = 3 $$ or $$ (((2\cdot 2)+2)/2)-2 = 1. $$

enter image description here

(please correct formulation errors, english is not my mother tongue)

  • 2
    $\begingroup$ I think that the problem is that the person who wrote this has no respect for unambiguous mathematical statements. $\endgroup$
    – zz20s
    Mar 5, 2016 at 16:59
  • $\begingroup$ At least nobody thinks it is $2\times (2+(2/(2-2)))$ $\endgroup$ Mar 5, 2016 at 17:02
  • 1
    $\begingroup$ Another problem is that linguistics may have a very different point of view than mathematics. Moreover, as it cannot be taken for granted that every natural language represents binary operations as infix lexems (just imagine what would happen if the Polish language actually used the equivalent of polish notation as word order ;) ) , it cannot be taken for granted that the notational rules to dave parentheses in fomulae apply to any language. $\endgroup$ Mar 5, 2016 at 17:07
  • $\begingroup$ Should be 3 ... $\endgroup$
    – Nikunj
    Mar 5, 2016 at 17:10

1 Answer 1


Unless parentheses are inserted, the order of operations is first division, then multiplication, then addition and then subtraction. As the question does not include parentheses, your first answer is correct (it is equal to 3).


You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .